{"segment":[{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"<span class='basic_left'>T\u00ecm s\u1ed1 t\u1ef1 nhi\u00ean c\u00f3 hai ch\u1eef s\u1ed1, bi\u1ebft r\u1eb1ng ch\u1eef s\u1ed1 h\u00e0ng ch\u1ee5c l\u1edbn h\u01a1n ch\u1eef s\u1ed1 h\u00e0ng \u0111\u01a1n v\u1ecb l\u00e0 $2$ v\u00e0 s\u1ed1 \u0111\u00f3 l\u1edbn h\u01a1n t\u1ed5ng c\u00e1c b\u00ecnh ph\u01b0\u01a1ng c\u00e1c ch\u1eef s\u1ed1 c\u1ee7a n\u00f3 l\u00e0 $1.$<br\/>S\u1ed1 c\u1ea7n t\u00ecm l\u00e0:","select":["A. $86$ ","B. $97$ ","C. $75$ ","D. $57$"],"hint":"S\u1ed1 t\u1ef1 nhi\u00ean c\u00f3 hai ch\u1eef s\u1ed1 c\u00f3 d\u1ea1ng: $\\overline{ab}=10.a+b$ <br\/> Trong \u0111\u00f3 $a$ l\u00e0 ch\u1eef s\u1ed1 h\u00e0ng ch\u1ee5c v\u00e0 $b$ l\u00e0 ch\u1eef s\u1ed1 h\u00e0ng \u0111\u01a1n v\u1ecb.","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> B\u01b0\u1edbc 1: G\u1ecdi ch\u1eef s\u1ed1 h\u00e0ng \u0111\u01a1n v\u1ecb l\u00e0 $x.$ Bi\u1ec3u di\u1ec5n ch\u1eef s\u1ed1 h\u00e0ng ch\u1ee5c qua $x.$<br\/>B\u01b0\u1edbc 2: T\u1eeb gi\u1ea3 thi\u1ebft, l\u1eadp ph\u01b0\u01a1ng tr\u00ecnh<br\/>B\u01b0\u1edbc 3: Gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh, so s\u00e1nh nghi\u1ec7m v\u1edbi \u0111i\u1ec1u ki\u1ec7n v\u00e0 k\u1ebft lu\u1eadn b\u00e0i to\u00e1n.<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i<\/span> <br\/> G\u1ecdi ch\u1eef s\u1ed1 h\u00e0ng \u0111\u01a1n v\u1ecb l\u00e0 $x.$ \u0110i\u1ec1u ki\u1ec7n: $0 \\le x \\le 9 $ v\u00e0 $ x \\in \\mathbb{N}$ <br\/>V\u00ec ch\u1eef s\u1ed1 h\u00e0ng ch\u1ee5c l\u1edbn h\u01a1n ch\u1eef s\u1ed1 h\u00e0ng \u0111\u01a1n v\u1ecb l\u00e0 $2$ n\u00ean ch\u1eef s\u1ed1 h\u00e0ng ch\u1ee5c l\u00e0 $x+2.$<br\/>Khi \u0111\u00f3 s\u1ed1 c\u1ea7n t\u00ecm l\u00e0: $10(x+2)+x=11x+20$<br\/>V\u00ec s\u1ed1 c\u1ea7n t\u00ecm l\u1edbn h\u01a1n t\u1ed5ng c\u00e1c b\u00ecnh ph\u01b0\u01a1ng c\u00e1c ch\u1eef s\u1ed1 c\u1ee7a n\u00f3 l\u00e0 $1$ n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: <br\/>$\\begin{aligned} & 11x+20={{\\left( x+2 \\right)}^{2}}+{{x}^{2}}+1 \\\\ & \\Leftrightarrow 11x+20={{x}^{2}}+4x+4+{{x}^{2}}+1 \\\\ & \\Leftrightarrow 2{{x}^{2}}-7x-15=0 \\\\ & \\Delta =169\\Rightarrow \\sqrt{\\Delta }=13 \\\\ & \\Rightarrow {{x}_{1}}=\\dfrac{7+13}{4}=5;{{x}_{2}}=\\dfrac{7-13}{4}=-\\dfrac{3}{2} \\\\ \\end{aligned}$<br\/> V\u00ec $0\\le x\\le 9$ v\u00e0 $x\\in \\mathbb{N}$ n\u00ean $x=x_1=5$<br\/>V\u1eady s\u1ed1 ph\u1ea3i t\u00ecm l\u00e0 $11x+20=11.5+20=75$ <br\/> <span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 C<\/span><\/span>","column":4}]}],"id_ques":991},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"<span class='basic_left'>M\u1ed9t h\u00ecnh ch\u1eef nh\u1eadt c\u00f3 chu vi l\u00e0 $100$ $m.$ N\u1ebfu t\u0103ng chi\u1ec1u r\u1ed9ng l\u00ean g\u1ea5p \u0111\u00f4i v\u00e0 gi\u1ea3m chi\u1ec1u d\u00e0i \u0111i $10$ $m$ th\u00ec di\u1ec7n t\u00edch h\u00ecnh ch\u1eef nh\u1eadt t\u0103ng th\u00eam $200$ $m^2.$ Kh\u1eb3ng \u0111\u1ecbnh n\u00e0o sau \u0111\u00e2y <b>kh\u00f4ng \u0111\u00fang<\/b>?","select":["A. K\u00edch th\u01b0\u1edbc ban \u0111\u1ea7u c\u1ee7a h\u00ecnh ch\u1eef nh\u1eadt l\u00e0 $20$ $m$ v\u00e0 $30$ $m$ ","B. K\u00edch th\u01b0\u1edbc ban \u0111\u1ea7u c\u1ee7a h\u00ecnh ch\u1eef nh\u1eadt l\u00e0 $15$ $m$ v\u00e0 $35$ $m$ ","C. K\u00edch th\u01b0\u1edbc ban \u0111\u1ea7u c\u1ee7a h\u00ecnh ch\u1eef nh\u1eadt l\u00e0 $10$ $m$ v\u00e0 $40$ $m$ "],"hint":"G\u1ecdi chi\u1ec1u r\u1ed9ng ban \u0111\u1ea7u c\u1ee7a h\u00ecnh ch\u1eef nh\u1eadt l\u00e0 \u1ea9n.","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn<\/span><br\/>Ph\u00e2n t\u00edch b\u00e0i to\u00e1n:<br\/><table><tr><th>C\u00e1c \u0111\u1ea1i l\u01b0\u1ee3ng<br><\/th><th>Chi\u1ec1u r\u1ed9ng $(m)$<br><\/th><th>Chi\u1ec1u d\u00e0i $(m)$<br><\/th><th>Di\u1ec7n t\u00edch $(m^2)$<br><\/th><\/tr><tr><th>Ban \u0111\u1ea7u<br><\/th><td>$x$<\/td><td>$50-x$<\/td><td>$x(50-x)$<\/td><\/tr><tr><th>Sau khi thay \u0111\u1ed5i<br><\/th><td>$2x$<\/td><td>$40-x$<\/td><td>$2x(40-x)$<\/td><\/tr><\/table><br\/><b>Ghi nh\u1edb:<\/b> Cho h\u00ecnh ch\u1eef nh\u1eadt v\u1edbi k\u00edch th\u01b0\u1edbc $a$ v\u00e0 $b.$ Khi \u0111\u00f3:<br\/>Chu vi h\u00ecnh ch\u1eef nh\u1eadt l\u00e0 $2(a+b)$. <br\/>Di\u1ec7n t\u00edch h\u00ecnh ch\u1eef nh\u1eadt l\u00e0 $ab$<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i<\/span><br\/>G\u1ecdi chi\u1ec1u r\u1ed9ng c\u1ee7a h\u00ecnh ch\u1eef nh\u1eadt ban \u0111\u1ea7u l\u00e0 $x$ $(m ; 0 < x < 25) $<br\/>V\u00ec chu vi c\u1ee7a h\u00ecnh ch\u1eef nh\u1eadt l\u00e0 $100$ $m$ n\u00ean chi\u1ec1u d\u00e0i c\u1ee7a h\u00ecnh ch\u1eef nh\u1eadt l\u00e0 $50-x$ $(m)$<br\/>Di\u1ec7n t\u00edch c\u1ee7a h\u00ecnh ch\u1eef nh\u1eadt ban \u0111\u1ea7u l\u00e0 $x(50-x)$ $(m^2)$<br\/>N\u1ebfu t\u0103ng chi\u1ec1u r\u1ed9ng l\u00ean g\u1ea5p \u0111\u00f4i v\u00e0 gi\u1ea3m chi\u1ec1u d\u00e0i \u0111i $10$ $m$ th\u00ec chi\u1ec1u r\u1ed9ng l\u00e0 $2x$ $(m),$ chi\u1ec1u d\u00e0i l\u00e0 $40-x$ $(m).$ <br\/>Khi \u0111\u00f3 di\u1ec7n t\u00edch c\u1ee7a h\u00ecnh ch\u1eef nh\u1eadt m\u1edbi l\u00e0 $2x(40-x)$ $(m^2)$<br\/>V\u00ec di\u1ec7n t\u00edch c\u1ee7a h\u00ecnh ch\u1eef nh\u1eadt t\u0103ng th\u00eam $200$ $m^2$ n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh:<br\/>$\\begin{aligned} & \\,\\,\\,\\,\\,2x\\left( 40-x \\right)-\\text{ }x\\left( 50-x \\right)=200 \\\\ & \\Rightarrow 80x-2{{x}^{2}}-50x+{{x}^{2}}=200 \\\\ & \\Leftrightarrow -{{x}^{2}}+30x-200=0 \\\\ & \\Leftrightarrow {{x}^{2}}-30x+200=0 \\\\ & \\Delta '=25 \\\\ & \\Rightarrow {{x}_{1}}=15+5=20;{{x}_{2}}=15-5=10 \\\\ \\end{aligned}$ <br\/>C\u1ea3 hai gi\u00e1 tr\u1ecb \u0111\u1ec1u th\u1ecfa m\u00e3n \u0111i\u1ec1u ki\u1ec7n $ 0 < x < 25 $<br\/>V\u1eady chi\u1ec1u r\u1ed9ng l\u00fac \u0111\u1ea7u l\u00e0 $20$ $m$ th\u00ec chi\u1ec1u d\u00e0i l\u00e0 $30$ $m;$ Chi\u1ec1u r\u1ed9ng l\u00fac \u0111\u1ea7u l\u00e0 $10$ $m$ th\u00ec chi\u1ec1u d\u00e0i l\u00e0 $40$ $m$<br\/> <span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 B<\/span><\/span>","column":1}]}],"id_ques":992},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["36"]]],"list":[{"point":5,"width":60,"type_input":"","ques":"<span class='basic_left'>M\u1ed9t tam gi\u00e1c c\u00f3 di\u1ec7n t\u00edch l\u00e0 $180$ $m^2.$ T\u00ednh c\u1ea1nh \u0111\u00e1y c\u1ee7a tam gi\u00e1c bi\u1ebft r\u1eb1ng n\u1ebfu t\u0103ng c\u1ea1nh \u0111\u00e1y $4$ $m$ v\u00e0 gi\u1ea3m chi\u1ec1u cao t\u01b0\u01a1ng \u1ee9ng \u0111i $1$ $m$ th\u00ec di\u1ec7n t\u00edch kh\u00f4ng \u0111\u1ed5i.<br\/><b>\u0110\u00e1p s\u1ed1:<\/b> _input_ $(m)$","hint":"C\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch tam gi\u00e1c: $S=\\dfrac{1}{2}$. c\u1ea1nh \u0111\u00e1y . chi\u1ec1u cao","explain":"<span class='basic_left'><span class='basic_green'>L\u1eadp b\u1ea3ng ph\u00e2n t\u00edch b\u00e0i to\u00e1n<\/span><br\/><table><tr><th>C\u00e1c \u0111\u1ea1i l\u01b0\u1ee3ng<br><\/th><th>C\u1ea1nh \u0111\u00e1y$(m)$<br><\/th><th>Chi\u1ec1u cao $(m)$<br><\/th><th>Di\u1ec7n t\u00edch $(m^2)$<br><\/th><\/tr><tr><th>Ban \u0111\u1ea7u<br><\/th><td>$x$<\/td><td>$\\dfrac{360}{x}$<\/td><td>$180$<\/td><\/tr><tr><th>Sau khi thay \u0111\u1ed5i<br><\/th><td>$x+4$<\/td><td>$\\dfrac{360}{x+4}$ <\/td><td>$180$<\/td><\/tr><\/table><br\/>T\u1eeb gi\u1ea3 thi\u1ebft chi\u1ec1u cao gi\u1ea3m \u0111i $1$ $m$, ta \u0111i thi\u1ebft l\u1eadp ph\u01b0\u01a1ng tr\u00ecnh<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i<\/span><br\/>G\u1ecdi \u0111\u1ed9 d\u00e0i c\u1ea1nh \u0111\u00e1y c\u1ee7a tam gi\u00e1c l\u00e0 $x$ $(m),$ $x>0$<br\/>V\u00ec di\u1ec7n t\u00edch tam gi\u00e1c l\u00e0 $180$ $m^2$ n\u00ean chi\u1ec1u cao tam gi\u00e1c l\u00e0 $\\dfrac{360}{x}$ $(m)$<br\/>T\u0103ng c\u1ea1nh \u0111\u00e1y $4$ $m$ th\u00ec c\u1ea1nh \u0111\u00e1y c\u00f3 \u0111\u1ed9 d\u00e0i l\u00e0 $x+4$ $(m).$ V\u00ec di\u1ec7n t\u00edch kh\u00f4ng \u0111\u1ed5i n\u00ean chi\u1ec1u cao l\u00e0 $\\dfrac{360}{x+4}$ $(m).$<br\/> Theo \u0111\u1ec1 ra, chi\u1ec1u cao gi\u1ea3m \u0111i $1$ $m$ n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh:<br\/>$\\begin{align} & \\dfrac{360}{x}-\\dfrac{360}{x+4}=1 \\\\ & \\Rightarrow 360\\left( x+4 \\right)-360x=x\\left( x+4 \\right) \\\\ & \\Leftrightarrow {{x}^{2}}+4x-1440=0 \\\\ & \\Delta '=1444\\Rightarrow \\sqrt{\\Delta '}=38 \\\\ & \\Rightarrow {{x}_{1}}=36;{{x}_{2}}=-40 \\\\ \\end{align}$<br\/>V\u00ec $x>0$ n\u00ean $x=x_1=36$ $(m)$<br\/>V\u1eady \u0111\u1ed9 d\u00e0i c\u1ea1nh \u0111\u00e1y c\u1ee7a tam gi\u00e1c l\u00e0 $36$ $m$<br\/><span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $36.$<\/span><\/span>"}]}],"id_ques":993},{"time":24,"part":[{"title":"\u0110i\u1ec1n c\u00e1c s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank_random","correct":[[["3"],["4"],["5"]]],"list":[{"point":5,"width":60,"type_input":"","ques":"<span class='basic_left'>Bi\u1ebft \u0111\u1ed9 d\u00e0i c\u00e1c c\u1ea1nh c\u1ee7a m\u1ed9t tam gi\u00e1c vu\u00f4ng l\u00e0 ba s\u1ed1 t\u1ef1 nhi\u00ean li\u00ean ti\u1ebfp.<br\/>\u0110\u1ed9 d\u00e0i ba c\u1ea1nh c\u1ee7a tam gi\u00e1c vu\u00f4ng l\u00e0 _input_;_input_ v\u00e0 _input_","hint":"Trong tam gi\u00e1c vu\u00f4ng, c\u1ea1nh huy\u1ec1n l\u00e0 c\u1ea1nh l\u1edbn nh\u1ea5t. \u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00fd Pitago, ta thi\u1ebft l\u1eadp ph\u01b0\u01a1ng tr\u00ecnh. ","explain":"<span class='basic_left'>Trong tam gi\u00e1c vu\u00f4ng, c\u1ea1nh huy\u1ec1n l\u00e0 c\u1ea1nh l\u1edbn nh\u1ea5t n\u00ean ta g\u1ecdi \u0111\u1ed9 d\u00e0i hai c\u1ea1nh g\u00f3c vu\u00f4ng v\u00e0 c\u1ea1nh huy\u1ec1n l\u1ea7n l\u01b0\u1ee3t l\u00e0 $x;$ $x+1;$ $x+2$ trong \u0111\u00f3 $x\\in \\mathbb{N}$ <br\/>\u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00ed Pytago, ta c\u00f3:<br\/>$\\begin{align} & {{x}^{2}}+{{\\left( x+1 \\right)}^{2}}={{\\left( x+2 \\right)}^{2}} \\\\ & \\Leftrightarrow {{x}^{2}}+{{x}^{2}}+2x+1={{x}^{2}}+4x+4 \\\\ & \\Leftrightarrow {{x}^{2}}-2x-3=0 \\\\ \\end{align}$ <br\/>Do $a-b+c=0$ n\u00ean ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 hai nghi\u1ec7m l\u00e0 ${{x}_{1}}=-1;{{x}_{2}}=3$<br\/> Do $x\\in \\mathbb{N}$ n\u00ean $x=x_2=3$<br\/>V\u1eady \u0111\u1ed9 d\u00e0i c\u00e1c c\u1ea1nh c\u1ee7a tam gi\u00e1c vu\u00f4ng l\u00e0 $3;$ $4;$ $5.$<br\/><span class='basic_pink'>V\u1eady c\u00e1c s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $3;$ $4;$ $5.$<\/span><\/span>"}]}],"id_ques":994},{"time":24,"part":[{"title":"\u0110i\u1ec1n c\u00e1c s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["30"],["6"]]],"list":[{"point":5,"width":60,"type_input":"","ques":"<span class='basic_left'>Hai v\u00f2i n\u01b0\u1edbc c\u00f9ng ch\u1ea3y v\u00e0o b\u1ec3 th\u00ec sau $5$ gi\u1edd \u0111\u1ea7y b\u1ec3. N\u1ebfu ch\u1ea3y m\u1ed9t m\u00ecnh th\u00ec v\u00f2i I c\u1ea7n nhi\u1ec1u h\u01a1n v\u00f2i II l\u00e0 $24$ gi\u1edd. H\u1ecfi m\u1ed7i v\u00f2i ch\u1ea3y m\u1ed9t m\u00ecnh th\u00ec sau bao l\u00e2u \u0111\u1ea7y b\u1ec3.<br\/><b>\u0110\u00e1p s\u1ed1:<\/b><br\/>Th\u1eddi gian v\u00f2i I ch\u1ea3y m\u1ed9t m\u00ecnh \u0111\u1ea7y b\u1ec3 l\u00e0 _input_ gi\u1edd;<br\/>Th\u1eddi gian v\u00f2i II ch\u1ea3y m\u1ed9t m\u00ecnh \u0111\u1ea7y b\u1ec3 l\u00e0 _input_ gi\u1edd.","hint":"G\u1ecdi $x$ l\u00e0 s\u1ed1 gi\u1edd v\u00f2i th\u1ee9 nh\u1ea5t ch\u1ea3y m\u1ed9t m\u00ecnh \u0111\u1ea7y b\u1ec3<br\/>Ch\u00fa \u00fd: S\u1ed1 ph\u1ea7n b\u1ec3 m\u00e0 m\u1ed7i v\u00f2i ch\u1ea3y \u0111\u01b0\u1ee3c trong m\u1ed9t gi\u1edd v\u00e0 s\u1ed1 gi\u1edd c\u1ea7n thi\u1ebft \u0111\u1ec3 v\u00f2i \u0111\u00f3 ch\u1ea3y \u0111\u1ea7y b\u1ec3 l\u00e0 hai \u0111\u1ea1i l\u01b0\u1ee3ng t\u1ec9 l\u1ec7 ngh\u1ecbch.","explain":"<span class='basic_left'>G\u1ecdi $x$ (gi\u1edd) l\u00e0 th\u1eddi gian v\u00f2i I ch\u1ea3y m\u1ed9t m\u00ecnh \u0111\u1ea7y b\u1ec3. <br\/>V\u00ec khi ch\u1ea3y m\u1ed9t m\u00ecnh, v\u00f2i I c\u1ea7n nhi\u1ec1u th\u1eddi gian h\u01a1n v\u00f2i II l\u00e0 $24$ gi\u1edd n\u00ean th\u1eddi gian \u0111\u1ec3 v\u00f2i hai ch\u1ea3y m\u1ed9t m\u00ecnh \u0111\u1ea7y b\u1ec3 l\u00e0 $x-24$ (gi\u1edd), $x>24$<br\/>M\u1ed9t gi\u1edd, v\u00f2i I ch\u1ea3y \u0111\u01b0\u1ee3c $\\dfrac{1}{x}$ (b\u1ec3); v\u00f2i II ch\u1ea3y \u0111\u01b0\u1ee3c $\\dfrac{1}{x-24}$ (b\u1ec3)<br\/>Do hai v\u00f2i n\u01b0\u1edbc c\u00f9ng ch\u1ea3y v\u00e0o b\u1ec3 th\u00ec sau $5$ gi\u1edd \u0111\u1ea7y b\u1ec3 n\u00ean $1$ gi\u1edd, hai v\u00f2i ch\u1ea3y \u0111\u01b0\u1ee3c $\\dfrac{1}{5}$ b\u1ec3.<br\/> Ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh:<br\/>$\\begin{align} & \\,\\,\\,\\,\\,\\dfrac{1}{x}+\\dfrac{1}{x-24}=\\dfrac{1}{5} \\\\ & \\Rightarrow 5\\left( x-24+x \\right)=x\\left( x-24 \\right) \\\\ & \\Leftrightarrow 10x-120={{x}^{2}}-24x \\\\ & \\Leftrightarrow {{x}^{2}}-34x+120=0 \\\\ & \\Delta '=169\\Rightarrow \\sqrt{\\Delta '}=13 \\\\ & \\Rightarrow {{x}_{1}}=30;{{x}_{2}}=4 \\\\ \\end{align}$ <br\/>Do $x>24$ n\u00ean $x=x_1=30$<br\/>V\u1eady v\u00f2i I ch\u1ea3y m\u1ed9t m\u00ecnh trong $30$ gi\u1edd th\u00ec \u0111\u1ea7y b\u1ec3; v\u00f2i II ch\u1ea3y m\u1ed9t m\u00ecnh trong $6$ gi\u1edd th\u00ec \u0111\u1ea7y b\u1ec3<br\/><span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u1ea7n l\u01b0\u1ee3t l\u00e0 $30;$ $6.$<\/span><\/span>"}]}],"id_ques":995},{"time":24,"part":[{"title":"Ch\u1ecdn c\u00e1c \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"checkbox","correct":[["2","4"]],"list":[{"point":5,"img":"","ques":"<span class='basic_left'>Hai \u0111\u1ed9i c\u00f9ng \u0111\u00e0o m\u1ed9t con m\u01b0\u01a1ng. N\u1ebfu m\u1ed7i \u0111\u1ed9i l\u00e0m m\u1ed9t m\u00ecnh c\u1ea3 con m\u01b0\u01a1ng th\u00ec th\u1eddi gian t\u1ed5ng c\u1ed9ng hai \u0111\u1ed9i ph\u1ea3i l\u00e0m l\u00e0 $25$ gi\u1edd. N\u1ebfu hai \u0111\u1ed9i c\u00f9ng l\u00e0m chung th\u00ec c\u00f4ng vi\u1ec7c ho\u00e0n th\u00e0nh trong $6$ gi\u1edd. G\u1ecdi $x$ (gi\u1edd) l\u00e0 th\u1eddi gian \u0111\u1ed9i th\u1ee9 nh\u1ea5t l\u00e0m m\u1ed9t m\u00ecnh xong c\u00f4ng vi\u1ec7c th\u00ec nh\u1eefng kh\u1eb3ng \u0111\u1ecbnh n\u00e0o sau \u0111\u00e2y \u0111\u00fang?<\/span>","hint":"","column":1,"number_true":2,"select":["A. $\\dfrac{1}{x}+\\dfrac{1}{x-25}=\\dfrac{1}{6}$ ","B. $x=15$","C. $x=20$","D. $x=10$"],"explain":"<span class='basic_left'>G\u1ecdi $x$ (gi\u1edd) l\u00e0 th\u1eddi gian \u0111\u1ed9i th\u1ee9 nh\u1ea5t l\u00e0m m\u1ed9t m\u00ecnh xong c\u00f4ng vi\u1ec7c, $x>0.$ <br\/>V\u00ec m\u1ed7i \u0111\u1ed9i l\u00e0m m\u1ed9t m\u00ecnh c\u1ea3 con m\u01b0\u01a1ng th\u00ec th\u1eddi gian t\u1ed5ng c\u1ed9ng hai \u0111\u1ed9i ph\u1ea3i l\u00e0m l\u00e0 $25$ gi\u1edd n\u00ean th\u1eddi gian \u0111\u1ec3 \u0111\u1ed9i II l\u00e0m m\u1ed9t m\u00ecnh xong c\u00f4ng vi\u1ec7c l\u00e0 $25-x$ (gi\u1edd). \u0110i\u1ec1u ki\u1ec7n: $x<25$<br\/>M\u1ed9t gi\u1edd, \u0111\u1ed9i th\u1ee9 nh\u1ea5t \u0111\u00e0o \u0111\u01b0\u1ee3c $\\dfrac{1}{x}$ (con m\u01b0\u01a1ng); \u0111\u1ed9i th\u1ee9 hai \u0111\u00e0o \u0111\u01b0\u1ee3c $\\dfrac{1}{25-x}$ (con m\u01b0\u01a1ng)<br\/>Do hai \u0111\u1ed9i c\u00f9ng l\u00e0m chung th\u00ec c\u00f4ng vi\u1ec7c ho\u00e0n th\u00e0nh trong $6$ gi\u1edd n\u00ean $1$ gi\u1edd, hai \u0111\u1ed9i \u0111\u00e0o \u0111\u01b0\u1ee3c $\\dfrac{1}{6}$ (con m\u01b0\u01a1ng).<br\/> Ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: $\\dfrac{1}{x}+\\dfrac{1}{25-x}=\\dfrac{1}{6}$ <br\/>Suy ra \u0111\u00e1p \u00e1n A sai<br\/>Quy \u0111\u1ed3ng v\u00e0 kh\u1eed m\u1eabu ph\u01b0\u01a1ng tr\u00ecnh, ta \u0111\u01b0\u1ee3c:<br\/>$ 6\\left( 25-x+x \\right)=x\\left( 25-x \\right)$$ \\Leftrightarrow 150=25x-{{x}^{2}}$ $\\Leftrightarrow {{x}^{2}}-25x+150=0 $<br\/> $\\Delta '=25\\Rightarrow \\sqrt{\\Delta '}=5$<br\/>$ \\Rightarrow {{x}_{1}}=15;{{x}_{2}}=10$ <br\/>Do $ 0 < x < 25 $ n\u00ean c\u1ea3 hai gi\u00e1 tr\u1ecb c\u1ee7a $x$ \u0111\u1ec1u th\u1ecfa m\u00e3n<br\/>Suy ra \u0111\u00e1p \u00e1n B v\u00e0 D \u0111\u00fang, \u0111\u00e1p \u00e1n C sai.<br\/>V\u1eady \u0111\u1ed9i th\u1ee9 nh\u1ea5t \u0111\u00e0o m\u1ed9t m\u00ecnh xong con m\u01b0\u01a1ng trong $15$ gi\u1edd th\u00ec \u0111\u1ed9i th\u1ee9 hai \u0111\u00e0o m\u1ed9t m\u00ecnh xong con m\u01b0\u01a1ng trong $10$ gi\u1edd v\u00e0 ng\u01b0\u1ee3c l\u1ea1i, n\u1ebfu \u0111\u1ed9i th\u1ee9 nh\u1ea5t \u0111\u00e0o m\u1ed9t m\u00ecnh xong con m\u01b0\u01a1ng trong $10$ gi\u1edd th\u00ec \u0111\u1ed9i th\u1ee9 hai \u0111\u00e0o m\u1ed9t m\u00ecnh xong con m\u01b0\u01a1ng trong $15$ gi\u1edd.<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n c\u1ea7n ch\u1ecdn l\u00e0 B v\u00e0 D.<\/span><\/span>"}]}],"id_ques":996},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank_random","correct":[[["45"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":"<span class='basic_left'>M\u1ed9t \u00f4 t\u00f4 \u0111i qu\u00e3ng \u0111\u01b0\u1eddng $AB$ d\u00e0i $150$ $km$ v\u1edbi th\u1eddi gian \u0111\u00e3 \u0111\u1ecbnh. Sau khi xe \u0111i \u0111\u01b0\u1ee3c m\u1ed9t n\u1eeda qu\u00e3ng \u0111\u01b0\u1eddng, \u00f4 t\u00f4 d\u1eebng l\u1ea1i $10$ ph\u00fat. Do \u0111\u00f3 \u0111\u1ec3 \u0111\u1ebfn B \u0111\u00fang h\u1eb9n, xe ph\u1ea3i t\u0103ng v\u1eadn t\u1ed1c l\u00ean $5$ $km\/h$ tr\u00ean qu\u00e3ng \u0111\u01b0\u1eddng c\u00f2n l\u1ea1i. T\u00ednh v\u1eadn t\u1ed1c d\u1ef1 \u0111\u1ecbnh c\u1ee7a \u00f4 t\u00f4.<br\/><b>\u0110\u00e1p s\u1ed1:<\/b> _input_ $(km\/h)$<\/span>","hint":"L\u1eadp b\u1ea3ng ph\u00e2n t\u00edch chuy\u1ec3n \u0111\u1ed9ng c\u1ee7a \u00f4 t\u00f4 khi d\u1ef1 \u0111\u1ecbnh v\u00e0 khi chuy\u1ec3n \u0111\u1ed9ng th\u1ef1c t\u1ebf r\u1ed3i l\u1eadp ph\u01b0\u01a1ng tr\u00ecnh bi\u1ec3u th\u1ecb th\u1eddi gian chuy\u1ec3n \u0111\u1ed9ng c\u1ee7a \u00f4 t\u00f4.","explain":"<span class='basic_left'><span class='basic_green'>Ph\u00e2n t\u00edch b\u00e0i to\u00e1n<\/span><br\/><table><tr><th>C\u00e1c \u0111\u1ea1i l\u01b0\u1ee3ng<br><\/th><th>V\u1eadn t\u1ed1c $(km\/h)$<br><\/th><th>Qu\u00e3ng \u0111\u01b0\u1eddng $(km)$<br><\/th><th>Th\u1eddi gian (gi\u1edd)<br><\/th><\/tr><tr><th>D\u1ef1 \u0111\u1ecbnh<br><\/th><td>$x$<\/td><td>$150$<\/td><td>$\\dfrac{150}{x}$ <\/td><\/tr><tr><th>N\u1eeda qu\u00e3ng \u0111\u01b0\u1eddng \u0111\u1ea7u<br><\/th><td>$x$<\/td><td>$75$ <\/td><td>$\\dfrac{75}{x}$ <\/td><\/tr><tr><th>N\u1eeda qu\u00e3ng \u0111\u01b0\u1eddng sau<br><\/th><td>$x+5$<\/td><td>$75$ <\/td><td>$\\dfrac{75}{x+5}$ <\/td><\/tr><\/table><br\/>T\u1eeb gi\u1ea3 thi\u1ebft v\u1ec1 th\u1eddi gian ta l\u1eadp ph\u01b0\u01a1ng tr\u00ecnh<br\/>Ch\u00fa \u00fd: Th\u1eddi gian th\u1ef1c t\u1ebf $=$ T\u1ed5ng th\u1eddi gian \u0111i t\u1eeb $A$ \u0111\u1ebfn $B$ (t\u00ednh c\u1ea3 $10$ ph\u00fat d\u1eebng l\u1ea1i) v\u00e0 b\u1eb1ng th\u1eddi gian d\u1ef1 \u0111\u1ecbnh.<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i<\/span><br\/>\u0110\u1ed5i $10$ ph\u00fat $=\\dfrac{1}{6}$ gi\u1edd<br\/>G\u1ecdi v\u1eadn t\u1ed1c d\u1ef1 \u0111\u1ecbnh c\u1ee7a \u00f4 t\u00f4 l\u00e0 $x$ $(km\/h),$ $x>0$<br\/>Th\u1eddi gian d\u1ef1 \u0111\u1ecbnh c\u1ee7a \u00f4 t\u00f4 l\u00e0 $\\dfrac{150}{x}$ (gi\u1edd)<br\/> Qu\u00e3ng \u0111\u01b0\u1eddng $AB$ l\u00e0 $150$ $km$ n\u00ean n\u1eeda qu\u00e3ng \u0111\u01b0\u1eddng l\u00e0 $75$ $km.$ Th\u1eddi gian \u0111i n\u1eeda qu\u00e3ng \u0111\u01b0\u1eddng \u0111\u1ea7u l\u00e0 $\\dfrac{75}{x}$ (gi\u1edd)<br\/>Tr\u00ean n\u1eeda qu\u00e3ng \u0111\u01b0\u1eddng sau, xe t\u0103ng v\u1eadn t\u1ed1c l\u00ean $5$ $km\/h$ n\u00ean v\u1eadn t\u1ed1c c\u1ee7a xe l\u00e0 $x+5$ $(km\/h).$ Khi \u0111\u00f3 th\u1eddi gian \u0111i tr\u00ean n\u1eeda qu\u00e3ng \u0111\u01b0\u1eddng c\u00f2n l\u1ea1i l\u00e0 $\\dfrac{75}{x+5}$ $(gi\u1edd).$<br\/>Do th\u1eddi gian xe \u0111i t\u1eeb $A$ \u0111\u1ebfn $B$ (t\u00ednh c\u1ea3 $10$ ph\u00fat d\u1eebng l\u1ea1i) b\u1eb1ng th\u1eddi gian d\u1ef1 \u0111\u1ecbnh n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh:<br\/>$\\begin{align} & \\,\\,\\,\\,\\,\\,\\dfrac{75}{x}+\\dfrac{1}{6}+\\dfrac{75}{x+5}=\\dfrac{150}{x} \\\\ & \\Leftrightarrow \\dfrac{75}{x}-\\dfrac{75}{x+5}=\\dfrac{1}{6} \\\\ & \\Rightarrow 75.6\\left( x+5 \\right)-75.6x=x\\left( x+5 \\right) \\\\ & \\Leftrightarrow {{x}^{2}}+5x-2250=0 \\\\ & \\Delta =9025\\Rightarrow \\sqrt{\\Delta }=95 \\\\ & \\Rightarrow {{x}_{1}}=45;{{x}_{2}}=-50 \\\\ \\end{align}$<br\/>V\u00ec $x>0$ n\u00ean $x=x_1=45$<br\/>V\u1eady v\u1eadn t\u1ed1c d\u1ef1 \u0111\u1ecbnh c\u1ee7a \u00f4 t\u00f4 l\u00e0 $45$ $km\/h$<br\/><span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 $45.$<\/span><\/span>"}]}],"id_ques":997},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"<span class='basic_left'>L\u00fac $6$ gi\u1edd $30$ ph\u00fat, m\u1ed9t ng\u01b0\u1eddi \u0111i xe m\u00e1y t\u1eeb $A$ \u0111\u1ebfn $B$ d\u00e0i $75$ $km$ v\u1edbi v\u1eadn t\u1ed1c \u0111\u1ecbnh tr\u01b0\u1edbc. \u0110\u1ebfn $B,$ ng\u01b0\u1eddi \u0111\u00f3 ngh\u1ec9 $20$ ph\u00fat r\u1ed3i quay tr\u1edf v\u1ec1 $A$ v\u1edbi v\u1eadn t\u1ed1c l\u1edbn h\u01a1n $5$ $km\/h. $ Ng\u01b0\u1eddi \u0111\u00f3 v\u1ec1 $A$ l\u00fac $12$ gi\u1edd $20$ ph\u00fat. V\u1eadn t\u1ed1c d\u1ef1 \u0111\u1ecbnh c\u1ee7a ng\u01b0\u1eddi \u0111\u00f3 l\u00e0:","select":["A. $20$ $km\/h$","B. $25$ $km\/h$","C. $30$ $km\/h$","D. $35$ $km\/h$"],"hint":"","explain":"<span class='basic_left'><span class='basic_green'>Ph\u00e2n t\u00edch b\u00e0i to\u00e1n<\/span><br\/><table><tr><th>C\u00e1c \u0111\u1ea1i l\u01b0\u1ee3ng<br><\/th><th>V\u1eadn t\u1ed1c $(km\/h)$<br><\/th><th>Qu\u00e3ng \u0111\u01b0\u1eddng $(km)$<br><\/th><th>Th\u1eddi gian (gi\u1edd)<br><\/th><\/tr><tr><th>\u0110i t\u1eeb $A$ \u0111\u1ebfn $B$<br><\/th><td>$x$<\/td><td>$75$<\/td><td>$\\dfrac{75}{x}$ <\/td><\/tr><tr><th>\u0110\u1ebfn $B$<br><\/th><td>$0$<\/td><td>$0$<\/td><td>$20$ ph\u00fat $=\\dfrac{1}{3}$ gi\u1edd<\/td><\/tr><tr><th>\u0110i t\u1eeb $B$ v\u1ec1 $A$<br><\/th><td>$x+5$<\/td><td>$75$ <\/td><td>$\\dfrac{75}{x+5}$ <\/td><\/tr><\/table><br\/>T\u1eeb gi\u1ea3 thi\u1ebft v\u1ec1 th\u1eddi gian ta l\u1eadp ph\u01b0\u01a1ng tr\u00ecnh<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i<\/span><br\/>G\u1ecdi v\u1eadn t\u1ed1c d\u1ef1 \u0111\u1ecbnh c\u1ee7a ng\u01b0\u1eddi \u0111i xe m\u00e1y l\u00e0 $x$ $(km\/h),$ $ x >0. $<br\/>Th\u1eddi gian \u0111i t\u1eeb $A$ \u0111\u1ebfn $B$ l\u00e0 $\\dfrac{75}{x}$ (gi\u1edd)<br\/>Th\u1eddi gian ngh\u1ec9 khi \u0111\u1ebfn $B$ l\u00e0 $20$ ph\u00fat$ =\\dfrac{1}{3}$ gi\u1edd<br\/>V\u1eadn t\u1ed1c khi \u0111i t\u1eeb $B$ v\u1ec1 $A$ l\u00e0 $x+5$ $(km\/h)$ n\u00ean th\u1eddi gian \u0111i t\u1eeb $B$ v\u1ec1 $A$ l\u00e0 $\\dfrac{75}{x+5}$ (gi\u1edd)<br\/>T\u1ed5ng th\u1eddi gian t\u1eeb l\u00fac \u0111i \u0111\u1ebfn l\u00fac v\u1ec1 l\u00e0:<br\/> $12$ gi\u1edd $20$ ph\u00fat \u2013 $6$ gi\u1edd $30$ ph\u00fat $=\\dfrac{37}{3}\\,\\text{(gi\u1edd)}\\,-\\dfrac{13}{2}\\,\\text{(gi\u1edd)}\\,=\\dfrac{35}{6}$ (gi\u1edd)<br\/>Ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh:<br\/>$\\begin{align} & \\,\\,\\,\\,\\,\\,\\dfrac{75}{x}+\\dfrac{1}{3}+\\dfrac{75}{x+5}=\\dfrac{35}{6} \\\\ & \\Leftrightarrow \\,\\,\\dfrac{75}{x}+\\dfrac{75}{x+5}=\\dfrac{11}{2} \\\\ & \\Rightarrow 75.2\\left( x+5 \\right)+75.2.x=11x\\left( x+5 \\right) \\\\ & \\Leftrightarrow 11{{x}^{2}}-245x-750=0 \\\\ & \\Delta =93025\\Rightarrow \\sqrt{\\Delta }=305 \\\\ & \\Rightarrow {{x}_{1}}=\\dfrac{245+305}{22}=25;{{x}_{2}}=\\dfrac{245-305}{22}=-\\dfrac{30}{11} \\\\ \\end{align}$<br\/> V\u00ec $x>0$ n\u00ean $x=x_1=25$<br\/>V\u1eady v\u1eadn t\u1ed1c d\u1ef1 \u0111\u1ecbnh c\u1ee7a ng\u01b0\u1eddi \u0111i xe m\u00e1y l\u00e0 $25$ $(km\/h)$<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 B<\/span><\/span>","column":4}]}],"id_ques":998},{"time":24,"part":[{"title":"Ch\u1ecdn c\u00e1c \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"Ch\u1ecdn \u0111\u01b0\u1ee3c nhi\u1ec1u \u0111\u00e1p \u00e1n","temp":"checkbox","correct":[["1","4"]],"list":[{"point":5,"img":"","ques":"<span class='basic_left'>M\u1ed9t ca n\u00f4 xu\u00f4i d\u00f2ng $45$ $km$ r\u1ed3i ng\u01b0\u1ee3c d\u00f2ng $18$ $km.$ Bi\u1ebft th\u1eddi gian \u0111i xu\u00f4i d\u00f2ng l\u00e2u h\u01a1n th\u1eddi gian \u0111i ng\u01b0\u1ee3c d\u00f2ng l\u00e0 $1$ gi\u1edd v\u00e0 v\u1eadn t\u1ed1c \u0111i xu\u00f4i d\u00f2ng l\u1edbn h\u01a1n v\u1eadn t\u1ed1c \u0111i ng\u01b0\u1ee3c d\u00f2ng l\u00e0 $6$ $km\/h.$ V\u1eadn t\u1ed1c ca n\u00f4 l\u00fac \u0111i ng\u01b0\u1ee3c d\u00f2ng l\u00e0:<\/span>","hint":"","column":2,"number_true":2,"select":["A. $9$ $km\/h$ ","B. $10$ $km\/h$","C. $11$ $km\/h$","D. $12$ $km\/h$"],"explain":"<span class='basic_left'><span class='basic_green'>Ph\u00e2n t\u00edch b\u00e0i to\u00e1n:<\/span><br\/>L\u1eadp b\u1ea3ng:<br\/><table><tr><th>C\u00e1c \u0111\u1ea1i l\u01b0\u1ee3ng<br><\/th><th>V\u1eadn t\u1ed1c $(km\/h)$<br><\/th><th>Qu\u00e3ng \u0111\u01b0\u1eddng $(km)$<br><\/th><th>Th\u1eddi gian (gi\u1edd)<br><\/th><\/tr><tr><th>Xu\u00f4i d\u00f2ng<br><\/th><td>$x+6$<\/td><td>$45$<\/td><td>$\\dfrac{45}{x+6}$ <\/td><\/tr><tr><th>Ng\u01b0\u1ee3c d\u00f2ng<br><\/th><td>$x$<\/td><td>$18$<\/td><td>$\\dfrac{18}{x}$ <\/td><\/tr><tr><\/table><br\/>D\u1ef1a v\u00e0o gi\u1ea3 thi\u1ebft: Th\u1eddi gian \u0111i xu\u00f4i d\u00f2ng l\u00e2u h\u01a1n th\u1eddi gian \u0111i ng\u01b0\u1ee3c d\u00f2ng l\u00e0 $1$ gi\u1edd \u0111\u1ec3 l\u1eadp ph\u01b0\u01a1ng tr\u00ecnh.<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>G\u1ecdi v\u1eadn t\u1ed1c ca n\u00f4 l\u00fac \u0111i ng\u01b0\u1ee3c d\u00f2ng l\u00e0 $x$ $(km\/h),$ $x>0$<br\/>V\u00ec v\u1eadn t\u1ed1c \u0111i xu\u00f4i d\u00f2ng l\u1edbn h\u01a1n v\u1eadn t\u1ed1c \u0111i ng\u01b0\u1ee3c d\u00f2ng l\u00e0 $6$ $km\/h$ n\u00ean v\u1eadn t\u1ed1c l\u00fac \u0111i xu\u00f4i d\u00f2ng c\u1ee7a ca n\u00f4 l\u00e0 $x+6$ $(km\/h)$<br\/>Th\u1eddi gian ng\u01b0\u1ee3c d\u00f2ng c\u1ee7a ca n\u00f4 l\u00e0 $\\dfrac{18}{x}$ (gi\u1edd) v\u00e0 th\u1eddi gian xu\u00f4i d\u00f2ng c\u1ee7a ca n\u00f4 l\u00e0 $\\dfrac{45}{x+6}$ (gi\u1edd)<br\/>V\u00ec th\u1eddi gian \u0111i xu\u00f4i d\u00f2ng l\u00e2u h\u01a1n th\u1eddi gian \u0111i ng\u01b0\u1ee3c d\u00f2ng l\u00e0 $1$ gi\u1edd n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh:<br\/>$\\begin{align} & \\,\\,\\,\\,\\,\\,\\dfrac{45}{x+6}-\\dfrac{18}{x}=1 \\\\ & \\Rightarrow 45x-18\\left( x+6 \\right)=x\\left( x+6 \\right) \\\\ & \\Leftrightarrow 27x-108={{x}^{2}}+6x \\\\ & \\Leftrightarrow {{x}^{2}}-21x+108=0 \\\\ & \\Delta =9 \\\\ & \\Rightarrow {{x}_{1}}=\\dfrac{21+3}{2}=12;{{x}_{2}}=\\dfrac{21-3}{2}=9 \\\\ \\end{align}$<br\/>C\u1ea3 hai gi\u00e1 tr\u1ecb \u0111\u1ec1u th\u1ecfa m\u00e3n.<br\/>V\u1eady v\u1eadn t\u1ed1c ca n\u00f4 l\u00fac \u0111i ng\u01b0\u1ee3c d\u00f2ng l\u00e0 $9$ $km\/h$ ho\u1eb7c $12$ $km\/h$<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n c\u1ea7n ch\u1ecdn l\u00e0 A v\u00e0 D.<\/span><\/span>"}]}],"id_ques":999},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["3"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":"<span class='basic_left'>M\u1ed9t b\u00e8 g\u1ed7 th\u1ea3 tr\u00f4i tr\u00ean s\u00f4ng t\u1eeb \u0111\u1eadp Ya-ly. Sau khi th\u1ea3 b\u00e8 g\u1ed7 $5$ gi\u1edd $20$ ph\u00fat, m\u1ed9t xu\u1ed3ng m\u00e1y c\u0169ng xu\u1ea5t ph\u00e1t t\u1eeb \u0111\u1eadp Ya-ly \u0111u\u1ed5i theo v\u00e0 \u0111i \u0111\u01b0\u1ee3c $20$ $km$ th\u00ec g\u1eb7p b\u00e8. T\u00ednh v\u1eadn t\u1ed1c c\u1ee7a b\u00e8 bi\u1ebft xu\u1ed3ng m\u00e1y ch\u1ea1y nhanh h\u01a1n b\u00e8 $12$ $km\/h.$<br\/><b>\u0110\u00e1p s\u1ed1:<\/b> _input_ $(km\/h)$ <\/span>","hint":"","explain":"<span class='basic_left'><span class='basic_green'>Ph\u00e2n t\u00edch b\u00e0i to\u00e1n:<\/span><br\/>L\u1eadp b\u1ea3ng:<br\/><table><tr><th>C\u00e1c \u0111\u1ea1i l\u01b0\u1ee3ng<br><\/th><th>V\u1eadn t\u1ed1c $(km\/h)$<br><\/th><th>Qu\u00e3ng \u0111\u01b0\u1eddng $(km)$<br><\/th><th>Th\u1eddi gian (gi\u1edd)<br><\/th><\/tr><tr><th>B\u00e8 g\u1ed7<br><\/th><td>$x$<\/td><td>$20$<\/td><td>$\\dfrac{20}{x}$ <\/td><\/tr><tr><th>Xu\u1ed3ng m\u00e1y<br><\/th><td>$x+12$<\/td><td>$20$<\/td><td>$\\dfrac{20}{x+12}$ <\/td><\/tr><tr><\/table><br\/>V\u00ec xu\u1ed3ng m\u00e1y xu\u1ea5t ph\u00e1t sau khi th\u1ea3 b\u00e8 g\u1ed7 $5$ gi\u1edd $20$ ph\u00fat n\u00ean th\u1eddi gian c\u1ee7a b\u00e8 g\u1ed7 nhi\u1ec1u h\u01a1n th\u1eddi gian c\u1ee7a xu\u1ed3ng m\u00e1y l\u00e0 $5$ gi\u1edd $20$ ph\u00fat. T\u1eeb \u0111\u00f3 ta l\u1eadp ph\u01b0\u01a1ng tr\u00ecnh.<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>\u0110\u1ed5i $5$ gi\u1edd $20$ ph\u00fat $=\\dfrac{16}{3}$ gi\u1edd<br\/>G\u1ecdi v\u1eadn t\u1ed1c c\u1ee7a b\u00e8 g\u1ed7 l\u00e0 $x$ $(km\/h),$ $x>0.$<br\/>V\u00ec v\u1eadn t\u1ed1c c\u1ee7a xu\u1ed3ng m\u00e1y h\u01a1n $12$$km\/h$ n\u00ean v\u1eadn t\u1ed1c c\u1ee7a xu\u1ed3ng m\u00e1y l\u00e0 $x+12$ $(km\/h)$<br\/>Do xu\u1ed3ng m\u00e1y \u0111i \u0111\u01b0\u1ee3c $20$$km$ th\u00ec g\u1eb7p b\u00e8 g\u1ed7 n\u00ean<br\/>+ Th\u1eddi gian b\u00e8 tr\u00f4i \u0111\u1ebfn l\u00fac g\u1eb7p xu\u1ed3ng l\u00e0 $\\dfrac{20}{x}$ (gi\u1edd)<br\/>+ Th\u1eddi gian xu\u1ed3ng \u0111i \u0111\u1ebfn khi \u0111u\u1ed5i k\u1ecbp b\u00e8 g\u1ed7 l\u00e0 $\\dfrac{20}{x+12}$ ( gi\u1edd)<br\/>V\u00ec xu\u1ed3ng m\u00e1y xu\u1ea5t ph\u00e1t sau khi th\u1ea3 b\u00e8 g\u1ed7 $5$ gi\u1edd $20$ ph\u00fat n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh:<br\/>$\\begin{align} & \\,\\,\\,\\,\\,\\,\\dfrac{20}{x}-\\dfrac{20}{x+12}=\\dfrac{16}{3} \\\\ & \\Rightarrow 20.3\\left( x+12 \\right)-20.3.x=16\\left( x+12 \\right)x \\\\ & \\Leftrightarrow 16{{x}^{2}}+192x-720=0 \\\\ & \\Leftrightarrow {{x}^{2}}+12x-45=0 \\\\ & \\Delta '=81 \\\\ & \\Rightarrow {{x}_{1}}=-6+9=3;{{x}_{2}}=-6-9=-15 \\\\ \\end{align}$<br\/>V\u00ec $x>0$ n\u00ean $x=x_1=3$<br\/>V\u1eady v\u1eadn t\u1ed1c c\u1ee7a b\u00e8 g\u1ed7 l\u00e0 $3$ $(km\/h)$<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n c\u1ea7n \u0111i\u1ec1n l\u00e0 $3.$ <\/span><\/span>"}]}],"id_ques":1000},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["3"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":"<span class='basic_left'>M\u1ed9t ng\u01b0\u1eddi \u0111i t\u1eeb t\u1ec9nh A \u0111\u1ebfn t\u1ec9nh B c\u00e1ch nhau $78$ $km.$ Sau \u0111\u00f3 $1$ gi\u1edd, ng\u01b0\u1eddi th\u1ee9 hai \u0111i t\u1eeb t\u1ec9nh B \u0111\u1ebfn t\u1ec9nh A, hai ng\u01b0\u1eddi g\u1eb7p nhau t\u1ea1i \u0111\u1ecba \u0111i\u1ec3m C c\u00e1ch B l\u00e0 $36$ $km.$ T\u00ednh th\u1eddi gian ng\u01b0\u1eddi \u0111i t\u1eeb A t\u00ednh t\u1eeb l\u00fac kh\u1edfi h\u00e0nh \u0111\u1ebfn l\u00fac g\u1eb7p nhau, bi\u1ebft v\u1eadn t\u1ed1c ng\u01b0\u1eddi th\u1ee9 hai l\u1edbn h\u01a1n v\u1eadn t\u1ed1c ng\u01b0\u1eddi th\u1ee9 nh\u1ea5t l\u00e0 $4$ $km\/h.$<br\/><b>\u0110\u00e1p s\u1ed1:<\/b>_input_(gi\u1edd) <\/span>","hint":"","explain":"<span class='basic_left'><span class='basic_green'>Ph\u00e2n t\u00edch b\u00e0i to\u00e1n:<\/span><br\/>L\u1eadp b\u1ea3ng:<br\/><table><tr><th>C\u00e1c \u0111\u1ea1i l\u01b0\u1ee3ng<br><\/th><th>V\u1eadn t\u1ed1c $(km\/h)$<br><\/th><th>Qu\u00e3ng \u0111\u01b0\u1eddng $(km)$<br><\/th><th>Th\u1eddi gian (gi\u1edd)<br><\/th><\/tr><tr><th>Ng\u01b0\u1eddi \u0111i t\u1eeb A<br><\/th><td>$x$<\/td><td>$AC=78-36=42$<\/td><td>$\\dfrac{42}{x}$ <\/td><\/tr><tr><th>Ng\u01b0\u1eddi \u0111i t\u1eeb B<br><\/th><td>$x+4$<\/td><td>$BC=36$<\/td><td>$\\dfrac{36}{x+4}$ <\/td><\/tr><tr><\/table><br\/>D\u1ef1a v\u00e0o gi\u1ea3 thi\u1ebft, ng\u01b0\u1eddi \u0111i t\u1eeb B xu\u1ea5t ph\u00e1t sau $1$ gi\u1edd, ta l\u1eadp ph\u01b0\u01a1ng tr\u00ecnh.<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>G\u1ecdi v\u1eadn t\u1ed1c c\u1ee7a ng\u01b0\u1eddi \u0111i t\u1eeb A l\u00e0 $x$ $(km\/h),$ $x>0.$<br\/>V\u00ec v\u1eadn t\u1ed1c ng\u01b0\u1eddi \u0111i t\u1eeb B l\u1edbn h\u01a1n v\u1eadn t\u1ed1c ng\u01b0\u1eddi \u0111i t\u1eeb A l\u00e0 $4$ $km\/h$ n\u00ean v\u1eadn t\u1ed1c c\u1ee7a ng\u01b0\u1eddi \u0111i t\u1eeb B l\u00e0 $x+4$ $(km\/h).$<br\/>\u0110\u1ed9 d\u00e0i \u0111o\u1ea1n \u0111\u01b0\u1eddng AC l\u00e0 $78-36=42$ $(km),$ \u0111\u1ed9 d\u00e0i \u0111o\u1ea1n \u0111\u01b0\u1eddng BC l\u00e0 $36$ $km$<br\/>Th\u1eddi gian c\u1ee7a ng\u01b0\u1eddi \u0111i t\u1eeb A, t\u00ednh t\u1eeb l\u00fac kh\u1edfi h\u00e0nh \u0111\u1ebfn l\u00fac g\u1eb7p nhau l\u00e0 $\\dfrac{42}{x}$ (gi\u1edd).<br\/>Th\u1eddi gian ng\u01b0\u1eddi \u0111i t\u1eeb B, t\u00ednh t\u1eeb l\u00fac kh\u1edfi h\u00e0nh \u0111\u1ebfn l\u00fac g\u1eb7p nhau l\u00e0 $\\dfrac{36}{x+4}$ (gi\u1edd)<br\/>V\u00ec hai ng\u01b0\u1eddi g\u1eb7p nhau t\u1ea1i C v\u00e0 ng\u01b0\u1eddi th\u1ee9 hai \u0111i sau ng\u01b0\u1eddi th\u1ee9 nh\u1ea5t $1$ gi\u1edd n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh:<br\/>$\\begin{align} & \\,\\,\\,\\dfrac{42}{x}-\\dfrac{36}{x+4}=1 \\\\ & \\Rightarrow 42\\left( x+4 \\right)-36x=x\\left( x+4 \\right) \\\\ & \\Leftrightarrow 6x+168={{x}^{2}}+4x \\\\ & \\Leftrightarrow {{x}^{2}}-2x-168=0 \\\\ & \\Delta '=169\\Rightarrow \\sqrt{\\Delta '}=13 \\\\ & \\Rightarrow {{x}_{1}}=1+13=14;{{x}_{2}}=1-13=-12 \\\\ \\end{align}$<br\/> V\u00ec $x>0$ n\u00ean $x=x_1=14$<br\/>V\u1eady th\u1eddi gian c\u1ee7a ng\u01b0\u1eddi \u0111i t\u1eeb A, t\u00ednh t\u1eeb l\u00fac kh\u1edfi h\u00e0nh \u0111\u1ebfn l\u00fac g\u1eb7p nhau l\u00e0 $\\dfrac{42}{x}=\\dfrac{42}{14}=3$ (gi\u1edd)<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n c\u1ea7n \u0111i\u1ec1n l\u00e0 $3.$ <\/span><\/span>"}]}],"id_ques":1001},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"<span class='basic_left'>L\u00fac $7$ gi\u1edd $30$ ph\u00fat, m\u1ed9t \u00f4 t\u00f4 kh\u1edfi h\u00e0nh t\u1eeb A. \u0110\u1ebfn B, \u00f4 t\u00f4 ngh\u1ec9 $30$ ph\u00fat r\u1ed3i \u0111i ti\u1ebfp \u0111\u1ebfn C l\u00fac $10$ gi\u1edd $15$ ph\u00fat. Bi\u1ebft qu\u00e3ng \u0111\u01b0\u1eddng AB d\u00e0i $30$ km, qu\u00e3ng \u0111\u01b0\u1eddng BC d\u00e0i $50$ $km;$ v\u1eadn t\u1ed1c c\u1ee7a \u00f4 t\u00f4 tr\u00ean qu\u00e3ng \u0111\u01b0\u1eddng BC l\u1edbn h\u01a1n v\u1eadn t\u1ed1c c\u1ee7a n\u00f3 tr\u00ean qu\u00e3ng \u0111\u01b0\u1eddng AB l\u00e0 $10$ $km\/h.$ V\u1eadn t\u1ed1c c\u1ee7a \u00f4 t\u00f4 tr\u00ean qu\u00e3ng \u0111\u01b0\u1eddng AB l\u00e0:<\/span>","select":["A. $40$ $(km)$","B. $30$ $(km)$ ","C. $20$ $(km)$ ","D. $50$ $(km)$ "],"hint":"","explain":"<span class='basic_left'><span class='basic_green'>Ph\u00e2n t\u00edch b\u00e0i to\u00e1n:<\/span><br\/>L\u1eadp b\u1ea3ng:<br\/><table><tr><th>C\u00e1c \u0111\u1ea1i l\u01b0\u1ee3ng<br><\/th><th>V\u1eadn t\u1ed1c $(km\/h)$<br><\/th><th>Qu\u00e3ng \u0111\u01b0\u1eddng $(km)$<br><\/th><th>Th\u1eddi gian (gi\u1edd)<br><\/th><\/tr><tr><th>AB<br><\/th><td>$x$<\/td><td>$30$<\/td><td>$\\dfrac{30}{x}$ <\/td><\/tr><tr><th>BC<br><\/th><td>$x+10$<\/td><td>$50$<\/td><td>$\\dfrac{50}{x+10}$ <\/td><\/tr><tr><\/table><br\/>D\u1ef1a v\u00e0o gi\u1ea3 thi\u1ebft v\u1ec1 th\u1eddi gian, ta l\u1eadp ph\u01b0\u01a1ng tr\u00ecnh.<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>G\u1ecdi v\u1eadn t\u1ed1c c\u1ee7a \u00f4 t\u00f4 tr\u00ean qu\u00e3ng \u0111\u01b0\u1eddng AB l\u00e0 $x$ $(km\/h),$ $ x> 0.$<br\/>V\u00ec v\u1eadn t\u1ed1c c\u1ee7a \u00f4 t\u00f4 tr\u00ean qu\u00e3ng \u0111\u01b0\u1eddng BC l\u1edbn h\u01a1n v\u1eadn t\u1ed1c c\u1ee7a n\u00f3 tr\u00ean qu\u00e3ng \u0111\u01b0\u1eddng AB l\u00e0 $10 $ $km\/h$ n\u00ean v\u1eadn t\u1ed1c c\u1ee7a \u00f4 t\u00f4 tr\u00ean qu\u00e3ng \u0111\u01b0\u1eddng BC l\u00e0 $x+10$ $(km\/h)$<br\/>Th\u1eddi gian \u0111i t\u1eeb A \u0111\u1ebfn B l\u00e0 $\\dfrac{30}{x}$ (gi\u1edd)<br\/>Th\u1eddi gian ngh\u1ec9 khi \u0111\u1ebfn B l\u00e0 $30$ ph\u00fat$ =\\dfrac{1}{2}$ gi\u1edd<br\/>V\u1eadn t\u1ed1c khi \u0111i t\u1eeb B \u0111\u1ebfn C l\u00e0 $x+10$ (km\/h) n\u00ean th\u1eddi gian \u0111i t\u1eeb B \u0111\u1ebfn C l\u00e0 $\\dfrac{50}{x+10}$ (gi\u1edd)<br\/>T\u1ed5ng th\u1eddi gian t\u1eeb A \u0111\u1ebfn C l\u00e0:<br\/> $10$ gi\u1edd $15$ ph\u00fat $\u2013 7$ gi\u1edd $30$ ph\u00fat $=\\dfrac{41}{4}\\,(\\text{gi\u1edd})\\,-\\dfrac{15}{2}\\,(\\text{gi\u1edd})\\,=\\dfrac{11}{4}$ (gi\u1edd)<br\/>Ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh:<br\/>$\\begin{align} & \\,\\,\\,\\,\\,\\,\\dfrac{30}{x}+\\dfrac{1}{2}+\\dfrac{50}{x+10}=\\dfrac{11}{4} \\\\ & \\Leftrightarrow \\,\\,\\,\\dfrac{30}{x}+\\dfrac{50}{x+10}=\\dfrac{9}{4} \\\\ & \\Rightarrow 30.4\\left( x+10 \\right)+50.4.x=9x\\left( x+10 \\right) \\\\ & \\Leftrightarrow 9{{x}^{2}}-230x-1200=0 \\\\ & \\Delta '=24025\\Rightarrow \\sqrt{\\Delta' }=155 \\\\ & \\Rightarrow {{x}_{1}}=\\dfrac{115+155}{9}=30;{{x}_{2}}=\\dfrac{115-155}{9}=-\\dfrac{40}{9} \\\\ \\end{align}$ <br\/>V\u00ec $x>0$ n\u00ean $x=x_1=30$<br\/>V\u1eady v\u1eadn t\u1ed1c c\u1ee7a \u00f4 t\u00f4 tr\u00ean qu\u00e3ng \u0111\u01b0\u1eddng AB l\u00e0 $30$ $(km\/h)$<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 C <\/span><\/span>","column":4}]}],"id_ques":1002},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["40"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":"<span class='basic_left'>Hai v\u00f2i n\u01b0\u1edbc ch\u1ea3y v\u00e0o hai b\u1ec3 c\u00f3 dung t\u00edch nh\u01b0 nhau l\u00e0 $2400$ l\u00edt. M\u1ed7i ph\u00fat v\u00f2i th\u1ee9 hai ch\u1ea3y nhi\u1ec1u h\u01a1n v\u00f2i th\u1ee9 nh\u1ea5t l\u00e0 $8$ l\u00edt n\u01b0\u1edbc n\u00ean th\u1eddi gian v\u00f2i th\u1ee9 hai ch\u1ea3y \u0111\u1ea7y b\u1ec3 \u00edt h\u01a1n v\u00f2i th\u1ee9 nh\u1ea5t l\u00e0 $10$ ph\u00fat. T\u00ednh xem m\u1ed7i ph\u00fat v\u00f2i I ch\u1ea3y \u0111\u01b0\u1ee3c bao nhi\u00eau?<br\/><b>\u0110\u00e1p s\u1ed1:<\/b>_input_(l\u00edt)<\/span>","hint":"","explain":"<span class='basic_left'>G\u1ecdi s\u1ed1 n\u01b0\u1edbc v\u00f2i I ch\u1ea3y trong m\u1ed9t ph\u00fat l\u00e0 $x$ (l\u00edt), $x>0$<br\/>V\u00ec m\u1ed7i ph\u00fat v\u00f2i th\u1ee9 hai ch\u1ea3y nhi\u1ec1u h\u01a1n v\u00f2i th\u1ee9 nh\u1ea5t l\u00e0 $8$ l\u00edt n\u00ean s\u1ed1 n\u01b0\u1edbc v\u00f2i II ch\u1ea3y trong m\u1ed9t ph\u00fat l\u00e0 $x+8$ (l\u00edt)<br\/>Do hai v\u00f2i n\u01b0\u1edbc ch\u1ea3y v\u00e0o hai b\u1ec3 c\u00f3 dung t\u00edch nh\u01b0 nhau l\u00e0 $2400$ l\u00edt n\u00ean th\u1eddi gian v\u00f2i th\u1ee9 nh\u1ea5t ch\u1ea3y \u0111\u1ea7y b\u1ec3 l\u00e0 $\\dfrac{2400}{x}$ (ph\u00fat) v\u00e0 th\u1eddi gian v\u00f2i th\u1ee9 hai ch\u1ea3y \u0111\u1ea7y b\u1ec3 l\u00e0 $\\dfrac{2400}{x+8}$ (ph\u00fat)<br\/>V\u00ec th\u1eddi gian v\u00f2i th\u1ee9 hai ch\u1ea3y \u0111\u1ea7y b\u1ec3 \u00edt h\u01a1n v\u00f2i th\u1ee9 nh\u1ea5t l\u00e0 $10$ ph\u00fat n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh:<br\/>$\\begin{align} & \\,\\,\\,\\,\\,\\dfrac{2400}{x}-\\dfrac{2400}{x+8}=10 \\\\ & \\Rightarrow 2400\\left( x+8 \\right)-2400x=10x\\left( x+8 \\right) \\\\ & \\Leftrightarrow 10{{x}^{2}}+80x-19200=0 \\\\ & \\Leftrightarrow {{x}^{2}}+8x-1920=0 \\\\ & \\Delta '=1936\\Rightarrow \\sqrt{\\Delta '}=44 \\\\ & \\Rightarrow {{x}_{1}}=-4+44=40;{{x}_{2}}=-4-44=-48 \\\\ \\end{align}$ <br\/>V\u00ec $x>0$ n\u00ean $x=x_1=40$<br\/>V\u1eady m\u1ed7i ph\u00fat v\u00f2i I ch\u1ea3y \u0111\u01b0\u1ee3c $40$ l\u00edt n\u01b0\u1edbc.<br\/><span class='basic_pink'>V\u1eady c\u00e1c s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0 $40.$ <\/span><\/span>"}]}],"id_ques":1003},{"time":24,"part":[{"title":"Ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"checkbox","correct":[["3"]],"list":[{"point":5,"img":"","ques":"<span class='basic_left'>M\u1ed9t ph\u00f2ng h\u1ecdc c\u00f3 $500$ ch\u1ed7 ng\u1ed3i. Do ph\u1ea3i x\u1ebfp $616$ ch\u1ed7 ng\u1ed3i n\u00ean ng\u01b0\u1eddi ta k\u00ea th\u00eam $3$ d\u00e3y gh\u1ebf v\u00e0 m\u1ed7i d\u00e3y gh\u1ebf th\u00eam hai ch\u1ed7. T\u00ecm s\u1ed1 d\u00e3y gh\u1ebf l\u00fac \u0111\u1ea7u c\u1ee7a ph\u00f2ng h\u1ecdp.<\/span>","hint":"","column":2,"number_true":2,"select":["A. $60$ d\u00e3y ","B. $50$ d\u00e3y","C. $25$ d\u00e3y","D. $30$ d\u00e3y"],"explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/>B\u01b0\u1edbc 1: G\u1ecdi \u1ea9n l\u00e0 d\u00e3y gh\u1ebf ban \u0111\u1ea7u v\u00e0 \u0111\u1eb7t \u0111i\u1ec1u ki\u1ec7n cho \u1ea9n. <br\/>B\u01b0\u1edbc 2: Bi\u1ec3u di\u1ec5n s\u1ed1 ch\u1ed7 ng\u1ed3i m\u1ed7i d\u00e3y l\u00fac \u0111\u1ea7u v\u00e0 sau khi k\u00ea th\u00eam $3$ d\u00e3y gh\u1ebf qua \u1ea9n<br\/>B\u01b0\u1edbc 3: T\u1eeb gi\u1ea3 thi\u1ebft m\u1ed7i d\u00e3y gh\u1ebf l\u00fac sau c\u00f3 th\u00eam hai ch\u1ed7 ng\u1ed3i, ta l\u1eadp ph\u01b0\u01a1ng tr\u00ecnh<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>G\u1ecdi s\u1ed1 d\u00e3y gh\u1ebf l\u00fac \u0111\u1ea7u l\u00e0 $x$ (d\u00e3y), $x\\in \\mathbb{N}$ v\u00e0 $x \\in\\, \\text{\u01af}\\left(500\\right)$<br\/>Suy ra m\u1ed7i d\u00e3y c\u00f3 $\\dfrac{500}{x}$ ch\u1ed7 ng\u1ed3i.<br\/>\u0110\u1ec3 x\u1ebfp $616$ ch\u1ed7 ng\u1ed3i th\u00ec ng\u01b0\u1eddi ta c\u1ea7n k\u00ea th\u00eam 3 d\u00e3y gh\u1ebf n\u00ean m\u1ed7i d\u00e3y c\u00f3 $\\dfrac{616}{x+3}$ ch\u1ed7 ng\u1ed3i<br\/>V\u00ec m\u1ed7i d\u00e3y gh\u1ebf th\u00eam $2$ ch\u1ed7 sau khi x\u1ebfp n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh:<br\/>$\\begin{align} & \\,\\,\\,\\,\\,\\,\\dfrac{616}{x+3}-\\dfrac{500}{x}=2 \\\\ & \\Rightarrow 616x-500\\left( x+3 \\right)=2x\\left( x+3 \\right) \\\\ & \\Leftrightarrow 116x-1500=2{{x}^{2}}+6x \\\\ & \\Leftrightarrow 2{{x}^{2}}-110x+1500=0 \\\\ & \\Leftrightarrow {{x}^{2}}-55x+750=0 \\\\ & \\Delta ={{55}^{2}}-4.750=25 \\\\ & \\Rightarrow {{x}_{1}}=\\dfrac{55+5}{2}=30;{{x}_{2}}=\\dfrac{55-5}{2}=25 \\\\ \\end{align}$ <br\/>V\u00ec $x\\in \\mathbb{N}$ v\u00e0 $x \\in\\, \\text{\u01af}\\left(500\\right)$ n\u00ean $x=x_2=25$<br\/>V\u1eady s\u1ed1 d\u00e3y gh\u1ebf ban \u0111\u1ea7u l\u00e0 $25$ d\u00e3y<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n c\u1ea7n ch\u1ecdn l\u00e0 C.<\/span><\/span>"}]}],"id_ques":1004},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["7"],["10"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":"<span class='basic_left'>Trong ph\u00f2ng h\u1ecdp c\u00f3 $70$ ng\u01b0\u1eddi d\u1ef1 h\u1ecdp \u0111\u01b0\u1ee3c s\u1eafp x\u1ebfp ng\u1ed3i \u0111\u1ec1u tr\u00ean c\u00e1c d\u00e3y gh\u1ebf. N\u1ebfu ta b\u1edbt \u0111i hai d\u00e3y gh\u1ebf th\u00ec m\u1ed7i d\u00e3y gh\u1ebf c\u00f2n l\u1ea1i ph\u1ea3i x\u1ebfp th\u00eam $4$ ng\u01b0\u1eddi m\u1edbi \u0111\u1ee7 ch\u1ed7. H\u1ecfi l\u00fac \u0111\u1ea7u c\u00f3 m\u1ea5y d\u00e3y gh\u1ebf v\u00e0 m\u1ed7i d\u00e3y gh\u1ebf x\u1ebfp \u0111\u01b0\u1ee3c bao nhi\u00eau ng\u01b0\u1eddi?<br\/><b> \u0110\u00e1p s\u1ed1: <\/b>S\u1ed1 d\u00e3y gh\u1ebf l\u00fac \u0111\u1ea7u l\u00e0_input_ (d\u00e3y) v\u00e0 m\u1ed7i d\u00e3y gh\u1ebf x\u1ebfp \u0111\u01b0\u1ee3c_input_ (ng\u01b0\u1eddi)<\/span>","hint":"","explain":"<span class='basic_left'>G\u1ecdi $x$ l\u00e0 s\u1ed1 d\u00e3y gh\u1ebf l\u00fac \u0111\u1ea7u ($x \\in \\mathbb{N}$ v\u00e0 $x>2$)<br\/>Khi \u0111\u00f3 m\u1ed7i d\u00e3y c\u00f3 $\\dfrac{70}{x}$ ng\u01b0\u1eddi d\u1ef1 h\u1ecdp.<br\/>N\u1ebfu ta b\u1edbt \u0111i $2$ d\u00e3y gh\u1ebf th\u00ec m\u1ed7i d\u00e3y c\u00f3 $\\dfrac{70}{x-2}$ ng\u01b0\u1eddi d\u1ef1 h\u1ecdp.<br\/>V\u00ec m\u1ed7i d\u00e3y gh\u1ebf c\u00f2n l\u1ea1i ph\u1ea3i x\u1ebfp th\u00eam $4$ ng\u01b0\u1eddi n\u1eefa m\u1edbi \u0111\u1ee7 ch\u1ed7 n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh:<br\/> $\\begin{align} & \\,\\,\\,\\,\\,\\dfrac{70}{x-2}-\\dfrac{70}{x}=4 \\\\ & \\Rightarrow 70x-70\\left( x-2 \\right)=4x\\left( x-2 \\right) \\\\ & \\Leftrightarrow 4{{x}^{2}}-8x-140=0 \\\\ & \\Leftrightarrow {{x}^{2}}-2x-35=0 \\\\ & \\Delta '=36 \\\\ & \\Rightarrow {{x}_{1}}=1+6=7;{{x}_{2}}=1-6=-5 \\\\ \\end{align}$<br\/>V\u00ec $x>2$ n\u00ean $x=x_1=7$<br\/>V\u1eady l\u00fac \u0111\u1ea7u c\u00f3 $7$ d\u00e3y gh\u1ebf v\u00e0 m\u1ed7i d\u00e3y gh\u1ebf x\u1ebfp \u0111\u01b0\u1ee3c $\\dfrac{70}{x}=\\dfrac{70}{7}=10$ ng\u01b0\u1eddi<br\/><span class='basic_pink'>V\u1eady c\u00e1c s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u1ea7n l\u01b0\u1ee3t l\u00e0 $7$ v\u00e0 $10.$ <\/span><\/span>"}]}],"id_ques":1005},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":"<span class='basic_left'>M\u1ed9t \u0111o\u00e0n xe \u00f4 t\u00f4 ch\u1edf $30$ t\u1ea5n h\u00e0ng t\u1eeb \u0111\u1ecba \u0111i\u1ec3m A \u0111\u1ebfn \u0111\u1ecba \u0111i\u1ec3m B. Khi s\u1eafp b\u1eaft \u0111\u1ea7u kh\u1edfi h\u00e0nh th\u00ec c\u00f3 th\u00eam $2$ \u00f4 t\u00f4 n\u1eefa, n\u00ean m\u1ed7i xe ch\u1edf \u00edt h\u01a1n $\\dfrac{1}{2}$ t\u1ea5n so v\u1edbi d\u1ef1 \u0111\u1ecbnh. H\u1ecfi l\u00fac \u0111\u1ea7u \u0111o\u00e0n xe c\u00f3 bao nhi\u00eau \u00f4 t\u00f4?","select":["A. $10$ \u00f4 t\u00f4 ","B. $12$ \u00f4 t\u00f4","C. $8$ \u00f4 t\u00f4 ","D. $14$ \u00f4 t\u00f4 "],"hint":"","explain":"<span class='basic_left'>G\u1ecdi s\u1ed1 xe \u00f4 t\u00f4 l\u00fac \u0111\u1ea7u c\u1ee7a \u0111o\u00e0n xe l\u00e0 $x$ (xe), l\u00fac sau l\u00e0 $x+2$ (xe), $x\\in \\mathbb{N}$<br\/>\u0110o\u00e0n xe ch\u1edf $30$ t\u1ea5n h\u00e0ng n\u00ean l\u00fac \u0111\u1ea7u m\u1ed7i xe ph\u1ea3i ch\u1edf $\\dfrac{30}{x}$ (t\u1ea5n); l\u00fac sau m\u1ed7i xe ph\u1ea3i ch\u1edf $\\dfrac{30}{x+2}$ (t\u1ea5n). <br\/>V\u00ec m\u1ed7i xe l\u00fac sau ch\u1edf \u00edt h\u01a1n $0,5$ t\u1ea5n so v\u1edbi d\u1ef1 \u0111\u1ecbnh n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh:<br\/>$\\begin{align} & \\,\\,\\,\\,\\,\\,\\dfrac{30}{x}-\\dfrac{30}{x+2}=\\dfrac{1}{2} \\\\ & \\Rightarrow 30.2\\left( x+2 \\right)-30.2x=x\\left( x+2 \\right) \\\\ & \\Leftrightarrow {{x}^{2}}+2x-120=0 \\\\ & \\Delta '=121\\Rightarrow \\sqrt{\\Delta '}=11 \\\\ & \\Rightarrow {{x}_{1}}=-1+11=10;{{x}_{2}}=-1-11=-12 \\\\ \\end{align}$ <br\/>V\u00ec $x>0$ n\u00ean $x=x_1=10$<br\/>V\u1eady l\u00fac \u0111\u1ea7u \u0111o\u00e0n xe c\u00f3 $10$ \u00f4 t\u00f4<br\/> <span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 A<\/span><\/span>","column":4}]}],"id_ques":1006},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"<span class='basic_left'>M\u1ed9t \u0111\u1ed9i s\u1ea3n xu\u1ea5t \u0111\u01b0\u1ee3c giao tr\u1ed3ng $150$ c\u00e2y trong m\u1ed9t th\u1eddi gian nh\u1ea5t \u0111\u1ecbnh. Khi b\u1eaft \u0111\u1ea7u l\u00e0m vi\u1ec7c do \u0111\u01b0\u1ee3c b\u1ed5 sung th\u00eam ng\u01b0\u1eddi n\u00ean m\u1ed7i gi\u1edd \u0111\u1ed9i tr\u1ed3ng \u0111\u01b0\u1ee3c nhi\u1ec1u h\u01a1n d\u1ef1 \u0111\u1ecbnh $11$ c\u00e2y, v\u00ec v\u1eady kh\u00f4ng nh\u1eefng ho\u00e0n th\u00e0nh tr\u01b0\u1edbc d\u1ef1 \u0111\u1ecbnh $1$ gi\u1edd m\u00e0 c\u00f2n tr\u1ed3ng v\u01b0\u1ee3t m\u1ee9c \u0111\u01b0\u1ee3c giao $14$ c\u00e2y. H\u1ecfi s\u1ed1 c\u00e2y \u0111\u1ed9i \u0111\u00f3 tr\u1ed3ng \u0111\u01b0\u1ee3c trong $1$ gi\u1edd theo d\u1ef1 \u0111\u1ecbnh ?","select":["A. 60 c\u00e2y","B. 55 c\u00e2y","C. 30 c\u00e2y ","D. 25 c\u00e2y"],"hint":"","explain":"<span class='basic_left'><span class='basic_green'>Ph\u00e2n t\u00edch b\u00e0i to\u00e1n:<\/span><br\/>L\u1eadp b\u1ea3ng:<br\/><table><tr><th>C\u00e1c \u0111\u1ea1i l\u01b0\u1ee3ng<br><\/th><th>S\u1ed1 c\u00e2y<br><\/th><th>S\u1ed1 c\u00e2y tr\u1ed3ng trong $1$ gi\u1edd<br><\/th><th>Th\u1eddi gian (gi\u1edd)<br><\/th><\/tr><tr><th>D\u1ef1 \u0111\u1ecbnh<br><\/th><td>$150$<\/td><td>$x$<\/td><td>$\\dfrac{150}{x}$ <\/td><\/tr><tr><th>Th\u1ef1c t\u1ebf<br><\/th><td>$150+14=164$<\/td><td>$x+11$<\/td><td>$\\dfrac{164}{x+11}$ <\/td><\/tr><tr><\/table><br\/>D\u1ef1a v\u00e0o gi\u1ea3 thi\u1ebft v\u1ec1 th\u1eddi gian: \u0110\u1ed9i ho\u00e0n th\u00e0nh tr\u01b0\u1edbc d\u1ef1 \u0111\u1ecbnh $1$ gi\u1edd, ta l\u1eadp ph\u01b0\u01a1ng tr\u00ecnh.<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>G\u1ecdi s\u1ed1 c\u00e2y \u0111\u1ed9i \u0111\u00f3 tr\u1ed3ng trong $1$ gi\u1edd theo d\u1ef1 \u0111\u1ecbnh l\u00e0 $x$ (c\u00e2y), $x\\in {{\\mathbb{N}}^{*}}$ <br\/>Th\u1eddi gian d\u1ef1 \u0111\u1ecbnh tr\u1ed3ng xong $150$ c\u00e2y l\u00e0 $\\dfrac{150}{x}$ (gi\u1edd).<br\/>S\u1ed1 c\u00e2y th\u1ef1c t\u1ebf \u0111\u1ed9i \u0111\u00f3 tr\u1ed3ng trong $1$ gi\u1edd l\u00e0 $x+11$ (c\u00e2y)<br\/>Th\u1eddi gian th\u1ef1c t\u1ebf \u0111\u1ed9i l\u00e0m vi\u1ec7c l\u00e0 $\\dfrac{150+14}{x+11}=\\dfrac{164}{x+11}$ (gi\u1edd)<br\/>Do th\u1eddi gian ho\u00e0n th\u00e0nh s\u1edbm h\u01a1n d\u1ef1 \u0111\u1ecbnh $1$ gi\u1edd n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh:<br\/>$\\begin{align} & \\dfrac{150}{x}-\\dfrac{164}{x+11}=1 \\\\ & \\Rightarrow 150\\left( x+11 \\right)-164x=x\\left( x+11 \\right) \\\\ & \\Leftrightarrow {{x}^{2}}+25x-1650=0 \\\\ & \\Delta =7225\\Rightarrow \\sqrt{\\Delta }=85 \\\\ & \\Rightarrow {{x}_{1}}=\\dfrac{-25+85}{2}=30;{{x}_{2}}=\\dfrac{-25-85}{2}=-55 \\\\ \\end{align}$ <br\/>V\u00ec $x\\in {{\\mathbb{N}}^{*}}$ n\u00ean $x=x_1=30.$<br\/>V\u1eady theo d\u1ef1 \u0111\u1ecbnh \u0111\u1ed9i \u0111\u00f3 tr\u1ed3ng trong $1$ gi\u1edd \u0111\u01b0\u1ee3c $30$ c\u00e2y.<br\/> <span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 C<\/span><\/span>","column":2}]}],"id_ques":1007},{"time":24,"part":[{"time":3,"title":"M\u1ed9t ph\u00e2n x\u01b0\u1edfng s\u1ea3n xu\u1ea5t theo k\u1ebf ho\u1ea1ch ph\u1ea3i l\u00e0m $3000$ bao b\u00ec. Trong $8$ ng\u00e0y \u0111\u1ea7u, h\u1ecd th\u1ef1c hi\u1ec7n \u0111\u00fang k\u1ebf ho\u1ea1ch \u0111\u1ec1 ra. Nh\u1eefng ng\u00e0y c\u00f2n l\u1ea1i, h\u1ecd \u0111\u00e3 v\u01b0\u1ee3t m\u1ee9c m\u1ed7i ng\u00e0y $10$ bao b\u00ec, n\u00ean \u0111\u00e3 ho\u00e0n th\u00e0nh k\u1ebf ho\u1ea1ch tr\u01b0\u1edbc $2$ ng\u00e0y. H\u1ecfi theo k\u1ebf ho\u1ea1ch, m\u1ed7i ng\u00e0y ph\u00e2n x\u01b0\u1edfng ph\u1ea3i s\u1ea3n xu\u1ea5t bao nhi\u00eau bao b\u00ec?","title_trans":"H\u00e3y s\u1eafp x\u1ebfp c\u00e1c c\u00e2u sau \u0111\u1ec3 \u0111\u01b0\u1ee3c l\u1eddi gi\u1ea3i \u0111\u00fang","temp":"sequence","correct":[[[2],[6],[4],[1],[5],[3]]],"list":[{"point":5,"image":"","left":["Th\u1eddi gian ph\u00e2n x\u01b0\u1edfng ph\u1ea3i ho\u00e0n th\u00e0nh k\u1ebf ho\u1ea1ch l\u00e0 $\\dfrac{3000}{x}$ (ng\u00e0y)","V\u1eady theo k\u1ebf ho\u1ea1ch, m\u1ed7i ng\u00e0y ph\u00e2n x\u01b0\u1edfng ph\u1ea3i s\u1ea3n xu\u1ea5t $100$ bao b\u00ec ","V\u00ec ph\u00e2n x\u01b0\u1edfng \u0111\u00e3 ho\u00e0n th\u00e0nh k\u1ebf ho\u1ea1ch tr\u01b0\u1edbc $2$ ng\u00e0y n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh:$\\dfrac{3000}{x}=\\dfrac{3000-8x}{x+10}+2+8$","G\u1ecdi s\u1ed1 bao b\u00ec m\u00e0 ph\u00e2n x\u01b0\u1edfng d\u1ef1 \u0111\u1ecbnh l\u00e0m m\u1ed7i ng\u00e0y l\u00e0 $x$ (bao b\u00ec), $x\\in {{\\mathbb{N}}^{*}}$","Gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh, ta \u0111\u01b0\u1ee3c: ${{x}_{1}}=100;{{x}_{2}}=-150.$ V\u00ec $x\\in \\mathbb{N^*}$ n\u00ean $x=100$","Trong $8$ ng\u00e0y \u0111\u1ea7u ph\u00e2n x\u01b0\u1edfng s\u1ea3n xu\u1ea5t \u0111\u01b0\u1ee3c $8x$ (bao b\u00ec). Trong nh\u1eefng ng\u00e0y c\u00f2n l\u1ea1i, m\u1ed7i ng\u00e0y ph\u00e2n x\u01b0\u1edfng l\u00e0m \u0111\u01b0\u1ee3c $x+10$ (bao b\u00ec). S\u1ed1 ng\u00e0y c\u1ea7n thi\u1ebft \u0111\u1ec3 ph\u00e2n x\u01b0\u1edfng l\u00e0m h\u1ebft s\u1ed1 bao b\u00ec c\u00f2n l\u1ea1i l\u00e0 $\\dfrac{3000-8x}{x+10}$(ng\u00e0y)"],"top":110,"hint":"","explain":"<span class='basic_left'><span class='basic_green'>Ph\u00e2n t\u00edch b\u00e0i to\u00e1n:<\/span><br\/> <table><tr><th>C\u00e1c \u0111\u1ea1i l\u01b0\u1ee3ng<br><\/th><th>Bao b\u00ec s\u1ea3n xu\u1ea5t trong $1$ ng\u00e0y<br><\/th><th>S\u1ed1 bao b\u00ec<br><\/th><th>Th\u1eddi gian (ng\u00e0y)<br><\/th><\/tr><tr><th>K\u1ebf ho\u1ea1ch<br><\/th><td>$x$<\/td><td>$3000$<\/td><td>$\\dfrac{3000}{x}$<\/td><\/tr><tr><th>$8$ ng\u00e0y \u0111\u1ea7u<br><\/th><td>$x$<\/td><td>$8x$<\/td><td>$8$<\/td><\/tr><tr><th>Nh\u1eefng ng\u00e0y c\u00f2n l\u1ea1i<br><\/th><td>$x+10$<\/td><td>$3000-8x$<\/td><td>$\\dfrac{3000-8x}{x+10}$<\/td><\/tr><\/table><br\/>D\u1ef1a v\u00e0o gi\u1ea3 thi\u1ebft v\u1ec1 th\u1eddi gian: \u0110\u1ed9i ho\u00e0n th\u00e0nh tr\u01b0\u1edbc k\u1ebf ho\u1ea1ch $2$ gi\u1edd, ta l\u1eadp ph\u01b0\u01a1ng tr\u00ecnh.<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i<\/span><br\/>G\u1ecdi s\u1ed1 bao b\u00ec m\u00e0 ph\u00e2n x\u01b0\u1edfng d\u1ef1 \u0111\u1ecbnh l\u00e0m m\u1ed7i ng\u00e0y l\u00e0 $x$ (bao b\u00ec), $x\\in {{\\mathbb{N}}^{*}}$<br\/>Th\u1eddi gian ph\u00e2n x\u01b0\u1edfng ph\u1ea3i ho\u00e0n th\u00e0nh k\u1ebf ho\u1ea1ch l\u00e0 $\\dfrac{3000}{x}$ (ng\u00e0y).<br\/>Trong $8$ ng\u00e0y \u0111\u1ea7u ph\u00e2n x\u01b0\u1edfng s\u1ea3n xu\u1ea5t \u0111\u01b0\u1ee3c $8x$ (bao b\u00ec)<br\/>Trong nh\u1eefng ng\u00e0y c\u00f2n l\u1ea1i, m\u1ed7i ng\u00e0y ph\u00e2n x\u01b0\u1edfng l\u00e0m \u0111\u01b0\u1ee3c $x+10$ (bao b\u00ec)<br\/>S\u1ed1 ng\u00e0y c\u1ea7n thi\u1ebft \u0111\u1ec3 ph\u00e2n x\u01b0\u1edfng l\u00e0m h\u1ebft s\u1ed1 bao b\u00ec c\u00f2n l\u1ea1i l\u00e0 $\\dfrac{3000-8x}{x+10}$(ng\u00e0y)<br\/>V\u00ec ph\u00e2n x\u01b0\u1edfng \u0111\u00e3 ho\u00e0n th\u00e0nh k\u1ebf ho\u1ea1ch tr\u01b0\u1edbc $2$ ng\u00e0y n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh:<br\/>$\\begin{align} & \\,\\,\\,\\,\\dfrac{3000}{x}=\\dfrac{3000-8x}{x+10}+2+8 \\\\ & \\Rightarrow 3000\\left( x+10 \\right)=\\left( 3000-8x \\right)x+10x\\left( x+10 \\right) \\\\ & \\Leftrightarrow 3000x+30000=3000x-8{{x}^{2}}+10{{x}^{2}}+100x \\\\ & \\Leftrightarrow 2{{x}^{2}}+100x-30000=0 \\\\ & \\Leftrightarrow {{x}^{2}}+50x-15000=0 \\\\ & \\Delta' =15625\\Rightarrow \\sqrt{\\Delta' }=125 \\\\ & \\Rightarrow {{x}_{1}}=-25+125=100;{{x}_{2}}=-25-125=-150 \\\\ \\end{align}$ <br\/>V\u00ec $x\\in \\mathbb{N^*}$ n\u00ean $x=x_1=100$<br\/>V\u1eady theo k\u1ebf ho\u1ea1ch, m\u1ed7i ng\u00e0y ph\u00e2n x\u01b0\u1edfng ph\u1ea3i s\u1ea3n xu\u1ea5t $100$ bao b\u00ec.<\/span>"}]}],"id_ques":1008},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n d\u01b0\u1edbi d\u1ea1ng s\u1ed1 th\u1eadp ph\u00e2n","temp":"fill_the_blank","correct":[[["0,8"],["0,6"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":"<span class='basic_left'>Ng\u01b0\u1eddi ta tr\u1ed9n $8$$g$ ch\u1ea5t l\u1ecfng A v\u1edbi $6$$g$ ch\u1ea5t l\u1ecfng B c\u00f3 kh\u1ed1i l\u01b0\u1ee3ng ri\u00eang nh\u1ecf h\u01a1n kh\u1ed1i l\u01b0\u1ee3ng ri\u00eang c\u1ee7a ch\u1ea5t l\u1ecfng A l\u00e0 $0,2 $$g\/cm^3$ v\u00e0 thu \u0111\u01b0\u1ee3c h\u1ed7n h\u1ee3p C c\u00f3 kh\u1ed1i l\u01b0\u1ee3ng ri\u00eang l\u00e0 $0,7$$g\/cm^3.$ T\u00ecm kh\u1ed1i l\u01b0\u1ee3ng ri\u00eang c\u1ee7a m\u1ed7i ch\u1ea5t l\u1ecfng.<br\/><b>\u0110\u00e1p s\u1ed1:<\/b><br\/>Kh\u1ed1i l\u01b0\u1ee3ng ri\u00eang c\u1ee7a ch\u1ea5t l\u1ecfng A l\u00e0 _input_$(g\/cm^3)$<br\/>Kh\u1ed1i l\u01b0\u1ee3ng ri\u00eang c\u1ee7a ch\u1ea5t l\u1ecfng B l\u00e0 _input_$(g\/cm^3)$<\/span>","hint":"\u00c1p d\u1ee5ng c\u00f4ng th\u1ee9c $D=\\dfrac{m}{V}$ trong \u0111\u00f3 $D,$ $m,$ $V$ th\u1ee9 t\u1ef1 l\u00e0 kh\u1ed1i l\u01b0\u1ee3ng ri\u00eang, kh\u1ed1i l\u01b0\u1ee3ng v\u00e0 th\u1ec3 t\u00edch c\u1ee7a ch\u1ea5t. T\u1eeb c\u00f4ng th\u1ee9c, ta x\u00e1c \u0111\u1ecbnh th\u1ec3 t\u00edch c\u1ee7a t\u1eebng ch\u1ea5t l\u1ecfng. ","explain":"<span class='basic_left'><span class='basic_green'>Ph\u00e2n t\u00edch b\u00e0i to\u00e1n:<\/span><br\/> <table><tr><th>C\u00e1c \u0111\u1ea1i l\u01b0\u1ee3ng<br><\/th><th>Kh\u1ed1i l\u01b0\u1ee3ng ri\u00eang $(g\/cm^3)$<br><\/th><th>Kh\u1ed1i l\u01b0\u1ee3ng $(g)$<br><\/th><th>Th\u1ec3 t\u00edch $(cm^3)$<br><\/th><\/tr><tr><th>Ch\u1ea5t l\u1ecfng A<br><\/th><td>$x$<\/td><td>$8$<\/td><td>$\\dfrac{8}{x}$<\/td><\/tr><tr><th>Ch\u1ea5t l\u1ecfng B<br><\/th><td>$x-0,2$<\/td><td>$6$<\/td><td>$\\dfrac{6}{x-0,2}$<\/td><\/tr><tr><th>Ch\u1ea5t l\u1ecfng C<br><\/th><td>$0,7$<\/td><td>$8+6=14$<\/td><td>$\\dfrac{14}{0,7}=20$<\/td><\/tr><\/table><br\/>T\u1eeb c\u00e1c s\u1ed1 li\u1ec7u v\u1ec1 th\u1ec3 t\u00edch trong b\u1ea3ng tr\u00ean, ta l\u1eadp ph\u01b0\u01a1ng tr\u00ecnh bi\u1ec3u th\u1ecb th\u1ec3 t\u00edch c\u1ee7a c\u00e1c ch\u1ea5t l\u1ecfng.<br\/><span class='basic_green'>B\u00e0i gi\u1ea3i<\/span><br\/>G\u1ecdi kh\u1ed1i l\u01b0\u1ee3ng ri\u00eang c\u1ee7a ch\u1ea5t l\u1ecfng A l\u00e0 $x$ $(g\/cm^3)$<br\/>V\u00ec ch\u1ea5t l\u1ecfng B c\u00f3 kh\u1ed1i l\u01b0\u1ee3ng ri\u00eang nh\u1ecf h\u01a1n kh\u1ed1i l\u01b0\u1ee3ng ri\u00eang c\u1ee7a ch\u1ea5t l\u1ecfng A l\u00e0 $0,2 $ $g\/cm^3$ n\u00ean kh\u1ed1i l\u01b0\u1ee3ng ri\u00eang c\u1ee7a ch\u1ea5t l\u1ecfng B l\u00e0 $x-0,2$ $(g\/cm^3),$ $x>0,2$<br\/>Th\u1ec3 t\u00edch ch\u1ea5t l\u1ecfng A l\u00e0 $\\dfrac{8}{x}$ $(cm^3),$ th\u1ec3 t\u00edch ch\u1ea5t l\u1ecfng B l\u00e0 $\\dfrac{6}{x-0,2}$ $(cm^3)$<br\/>Khi \u0111\u00f3 th\u1ec3 t\u00edch c\u1ee7a h\u1ed7n h\u1ee3p C l\u00e0 $\\dfrac{8}{x}+\\dfrac{6}{x-0,2}$ $(cm^3)$<br\/>V\u00ec h\u1ed7n h\u1ee3p C c\u00f3 kh\u1ed1i l\u01b0\u1ee3ng ri\u00eang l\u00e0 $0,7$ $g\/cm^3$ v\u00e0 c\u00f3 kh\u1ed1i l\u01b0\u1ee3ng l\u00e0 $8+6=14$ $(g)$ n\u00ean c\u00f3 th\u1ec3 t\u00edch l\u00e0 $\\dfrac{14}{0,7}=20$ $(cm^3)$<br\/>Ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh:<br\/>$\\begin{align} & \\,\\,\\,\\,\\,\\dfrac{8}{x}+\\dfrac{6}{x-0,2}=20 \\\\ & \\Rightarrow 8\\left( x-0,2 \\right)+6x=20x\\left( x-0,2 \\right) \\\\ & \\Leftrightarrow 20{{x}^{2}}-18x+1,6=0 \\\\ & \\Delta '=49\\Rightarrow \\sqrt{\\Delta '}=7 \\\\ & \\Rightarrow {{x}_{1}}=\\dfrac{9+7}{20}=0,8;{{x}_{2}}=\\dfrac{9-7}{20}=0,1 \\\\ \\end{align}$<br\/>V\u00ec $x>0,2$ n\u00ean $x=x_1=0,8$<br\/>V\u1eady kh\u1ed1i l\u01b0\u1ee3ng ri\u1ec3ng c\u1ee7a ch\u1ea5t A l\u00e0 $0,8$ $(g\/cm^3);$ kh\u1ed1i l\u01b0\u1ee3ng ri\u00eang c\u1ee7a ch\u1ea5t B l\u00e0 $0,6$ $(g\/cm^3).$<br\/><span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u1ea7n l\u01b0\u1ee3t l\u00e0 $0,8$ v\u00e0 $0,6.$ <\/span><\/span>"}]}],"id_ques":1009},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n d\u01b0\u1edbi d\u1ea1ng s\u1ed1 nguy\u00ean ho\u1eb7c s\u1ed1 th\u1eadp ph\u00e2n","temp":"fill_the_blank","correct":[[["2,5"],["4"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","ques":"<span class='basic_left'>Chu vi b\u00e1nh sau c\u1ee7a m\u1ed9t m\u00e1y c\u1ea7y l\u1edbn h\u01a1n chu vi b\u00e1nh tr\u01b0\u1edbc l\u00e0 $1,5$ $m.$ Khi \u0111i tr\u00ean \u0111o\u1ea1n \u0111\u01b0\u1eddng d\u00e0i $100$ $m$ th\u00ec b\u00e1nh tr\u01b0\u1edbc quay nhi\u1ec1u h\u01a1n b\u00e1nh sau $15$ v\u00f2ng. T\u00ednh chu vi c\u1ee7a m\u1ed7i b\u00e1nh xe?<br\/><b>\u0110\u00e1p s\u1ed1:<\/b><br\/>Chu vi c\u1ee7a b\u00e1nh tr\u01b0\u1edbc l\u00e0 _input_$(m)$<br\/>Chu vi c\u1ee7a b\u00e1nh sau l\u00e0 _input_$(m)$<\/span>","hint":"\u00c1p d\u1ee5ng c\u00f4ng th\u1ee9c $n=\\dfrac{s}{C}$ trong \u0111\u00f3 $n$ l\u00e0 s\u1ed1 v\u00f2ng quay c\u1ee7a b\u00e1nh c\u00f3 chu vi $C$ khi di chuy\u1ec3n tr\u00ean \u0111o\u1ea1n \u0111\u01b0\u1eddng c\u00f3 \u0111\u1ed9 d\u00e0i $s.$<br\/> T\u1eeb gi\u1ea3 thi\u1ebft ''b\u00e1nh tr\u01b0\u1edbc quay nhi\u1ec1u h\u01a1n b\u00e1nh sau $15$ v\u00f2ng'' ta thi\u1ebft l\u1eadp ph\u01b0\u01a1ng tr\u00ecnh.","explain":"<span class='basic_left'>G\u1ecdi chu vi b\u00e1nh tr\u01b0\u1edbc l\u00e0 $x$ $(m),$ $x>0$<br\/>Do chu vi b\u00e1nh sau l\u1edbn h\u01a1n chu vi b\u00e1nh tr\u01b0\u1edbc l\u00e0 $1,5$ $m$ n\u00ean chu vi b\u00e1nh sau l\u00e0 $ x+1,5$ $(m)$<br\/>S\u1ed1 v\u00f2ng quay b\u00e1nh tr\u01b0\u1edbc l\u00e0 $\\dfrac{100}{x}$ (v\u00f2ng)<br\/>S\u1ed1 v\u00f2ng quay b\u00e1nh sau l\u00e0 $\\dfrac{100}{x+1,5}$ (v\u00f2ng)<br\/>Do b\u00e1nh tr\u01b0\u1edbc quay nhi\u1ec1u h\u01a1n b\u00e1nh sau $15$ v\u00f2ng n\u00ean ta c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh:<br\/>$\\begin{align} & \\,\\,\\,\\,\\,\\dfrac{100}{x}-\\dfrac{100}{x+1,5}=15 \\\\ & \\Rightarrow 100\\left( x+1,5 \\right)-100x=15x\\left( x+1,5 \\right) \\\\ & \\Leftrightarrow 100x+150-100x=15{{x}^{2}}+22,5x \\\\ & \\Leftrightarrow 15{{x}^{2}}+22,5x-150=0 \\\\ & \\Leftrightarrow {{x}^{2}}+1,5x-10=0 \\\\ & \\Delta =42,25\\Rightarrow \\sqrt{\\Delta }=6,5 \\\\ & \\Rightarrow {{x}_{1}}=\\dfrac{-1,5+6,5}{2}=2,5;{{x}_{2}}=\\dfrac{-1,5-6,5}{2}=-4 \\\\ \\end{align}$ <br\/>Do $x>0$ n\u00ean $x={{x}_{1}}=2,5$ <br\/>V\u1eady chu vi c\u1ee7a b\u00e1nh tr\u01b0\u1edbc l\u00e0 $2,5$ $m$ v\u00e0 chu vi c\u1ee7a b\u00e1nh sau l\u00e0 $x+1,5=2,5+1,5=4$ $(m)$<br\/><span class='basic_pink'>V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u1ea7n l\u01b0\u1ee3t l\u00e0 $2,5$ v\u00e0 $4.$ <\/span><\/span>"}]}],"id_ques":1010}],"lesson":{"save":0,"level":2}}