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Bài 3:
theo đề bài ta có:
\(\left\{{}\begin{matrix}2a-3b=0\\5b-7c=0\\3a-7b+5c=30\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}a=42\\b=28\\c=20\end{matrix}\right.\)
Bài 4:
Đặt \(\dfrac{x}{4}=\dfrac{y}{5}=\dfrac{z}{6}=k\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=4k\\y=5k\\z=6k\end{matrix}\right.\)
Ta có: \(x^2-2y^2+z^2=18\)
\(\Leftrightarrow16k^2-50k^2+36k^2=18\)
\(\Leftrightarrow k^2=9\)
Trường hợp 1: k=3
\(\Leftrightarrow\left\{{}\begin{matrix}x=4k=4\cdot3=12\\y=5k=5\cdot3=15\\z=6k=6\cdot3=18\end{matrix}\right.\)
Trường hợp 2: k=-3
\(\Leftrightarrow\left\{{}\begin{matrix}x=4k=-3\cdot4=-12\\y=5k=-3\cdot5=-15\\z=6k=-3\cdot6=-18\end{matrix}\right.\)
Bài 1:
a. $=\frac{3}{4}+\frac{1}{4}\times \frac{12}{5}$
$=\frac{3}{4}+\frac{3}{5}=3\times (\frac{1}{4}+\frac{1}{5})=3\times \frac{9}{20}=\frac{27}{20}$
b.
$=\frac{5}{6}+4+\frac{3}{5}+\frac{7}{6}-\frac{3}{5}$
$=(\frac{5}{6}+\frac{7}{6})+(\frac{3}{5}-\frac{3}{5})+4$
$=\frac{12}{6}+0+4=2+4=6$
c.
$=\frac{26}{100}+\frac{9}{100}+\frac{41}{100}+\frac{24}{100}$
$=\frac{26+9+41+24}{100}=\frac{100}{100}=1$
d.
$=4,7\times 4+5,3\times 4=(4,7+5,3)\times 4=10\times 4=40$
Bài 2:
a.
$m+5,4:1,8=5,6$
$m+3=5,6$
$m=5,6-3$
$m=2,6$
b.
$(\frac{3}{5}-m)+\frac{3}{10}=\frac{5}{6}$
$\frac{3}{5}+\frac{3}{10}-m=\frac{5}{6}$
$\frac{9}{10}-m=\frac{5}{6}$
$m=\frac{9}{10}-\frac{5}{6}=\frac{1}{15}$
c.
$3636:(12\times m-91)=36$
$12\times m-91=3636:36=101$
$12\times m=101+91=192$
$m=192:12=16$
d.
$0,3\times m+m\times 0,4=7,14$
$m\times (0,3+0,4)=7,14$
$m\times 0,7=7,14$
$m=7,14:0,7=10,2$
\(\left(2x+1\right)^2-\left(x-1\right)^2\)
\(=\left(2x+1-x+1\right)\left(2x+1+x-1\right)\)
\(=3x\left(x+2\right)\)
Your bro giải xong.
\(P=A.B=\dfrac{\sqrt{x}-1}{\sqrt{x}-3}.\dfrac{\sqrt{x}+6}{\sqrt{x}-1}=\dfrac{\sqrt{x}+6}{\sqrt{x}-3}\)
\(=1+\dfrac{9}{\sqrt{x}-3}\le1+\dfrac{9}{0-3}=1-3=-2\)
\(maxP=-2\Leftrightarrow x=0\)
\(1,x=16\Leftrightarrow A=\dfrac{4-1}{4-3}=\dfrac{3}{1}=3\\ 2,B=\dfrac{x+2\sqrt{x}-3+5\sqrt{x}+5+4}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}=\dfrac{x+7\sqrt{x}+6}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\\ B=\dfrac{\left(\sqrt{x}+1\right)\left(\sqrt{x}+6\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}=\dfrac{\sqrt{x}+6}{\sqrt{x}-1}\\ 3,P=AB=\dfrac{\sqrt{x}-1}{\sqrt{x}-3}\cdot\dfrac{\sqrt{x}+6}{\sqrt{x}-1}=\dfrac{\sqrt{x}+6}{\sqrt{x}-3}\\ P=1+\dfrac{9}{\sqrt{x}-3}\\ Vì.\sqrt{x}-3\ge-3\Leftrightarrow\dfrac{9}{\sqrt{x}-3}\le-3\\ \Leftrightarrow P=1+\dfrac{9}{\sqrt{x}-3}\le1-3=-2\\ P_{max}=-2\Leftrightarrow x=0\)
Câu 13.
Công suất cần cẩu A:
\(P_A=\dfrac{A_1}{t_1}=\dfrac{10m_1\cdot h_1}{t_1}=\dfrac{10\cdot1100\cdot6}{1\cdot60}=1100W\)
Công suất cần cẩu B:
\(P_B=\dfrac{A_2}{t_2}=\dfrac{10m_2\cdot h_2}{t_2}=\dfrac{10\cdot800\cdot5}{30}=1333,33W\)
\(\Rightarrow P_B>P_A\)
chưa học đến:v