Một bể cá dạng hình hộp chữ nhật làm bằng kính ( không nắp ) có chiều dài 90cm chiều dài 60cm chiều cao 45cm Mực nước ban đầu trong bể là 35cm

a) Tính diện tích kính dùng để làm bể cá đó

b) Người ta cho vào bể cá một hòn đá Lúc này mực nước đo được là 40cm

Tính thể tích của hòn đá 
Giúp mình nhé

a) x = 2 7                         b) x = 2.

c) x = 2                          d) x = 1.

\(3-\left(\dfrac{1}{6}-x\right).\dfrac{2}{5}=\dfrac{1}{2}\\ \Rightarrow\left(\dfrac{1}{6}-x\right).\dfrac{2}{5}=3-\dfrac{1}{2}\\ \Rightarrow\left(\dfrac{1}{6}-x\right).\dfrac{2}{5}=\dfrac{5}{2}\\ \Rightarrow\dfrac{1}{6}-x=\dfrac{5}{2}:\dfrac{2}{5}\\ \Rightarrow\dfrac{1}{6}-x=\dfrac{25}{4}\\ \Rightarrow x=\dfrac{1}{6}-\dfrac{25}{4}\\ \Rightarrow x=-\dfrac{73}{12}\)

\(a,\Leftrightarrow\left[{}\begin{matrix}x+5=0\\2x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-5\\x=-\dfrac{1}{2}\end{matrix}\right.\\ b,\Leftrightarrow\left(x+2\right)\left(x-3\right)=0\Leftrightarrow\left[{}\begin{matrix}x=-2\\x=3\end{matrix}\right.\\ c,\Leftrightarrow2x^2-10x-3x-2x^2=26\\ \Leftrightarrow-13x=26\Leftrightarrow x=-2\\ d,\Leftrightarrow x^2-18x+16=0\\ \Leftrightarrow\left(x^2-18x+81\right)-65=0\\ \Leftrightarrow\left(x-9\right)^2-65=0\\ \Leftrightarrow\left(x-9+\sqrt{65}\right)\left(x-9-\sqrt{65}\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=9-\sqrt{65}\\9+\sqrt{65}\end{matrix}\right.\)

\(e,\Leftrightarrow x^2-10x-25=0\\ \Leftrightarrow\left(x-5\right)^2-50=0\\ \Leftrightarrow\left(x-5-5\sqrt{2}\right)\left(x-5+5\sqrt{2}\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=5+5\sqrt{2}\\x=5-5\sqrt{2}\end{matrix}\right.\\ f,\Leftrightarrow5x\left(x-1\right)-\left(x-1\right)=0\\ \Leftrightarrow\left(x-1\right)\left(5x-1\right)=0\Leftrightarrow\left[{}\begin{matrix}x=1\\x=\dfrac{1}{5}\end{matrix}\right.\\ g,\Leftrightarrow2\left(x+5\right)-x\left(x+5\right)=0\\ \Leftrightarrow\left(2-x\right)\left(x+5\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=2\\x=-5\end{matrix}\right.\\ h,\Leftrightarrow x^2+2x+3x+6=0\\ \Leftrightarrow\left(x+3\right)\left(x+2\right)=0\Leftrightarrow\left[{}\begin{matrix}x=-3\\x=-2\end{matrix}\right.\\ i,\Leftrightarrow4x^2-12x+9-4x^2+4=49\\ \Leftrightarrow-12x=36\Leftrightarrow x=-3\)

\(j,\Leftrightarrow x^2\left(x+1\right)+\left(x+1\right)=0\Leftrightarrow\left(x^2+1\right)\left(x+1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x^2=-1\left(vô.lí\right)\\x=-1\end{matrix}\right.\Leftrightarrow x=-1\\ k,\Leftrightarrow x^2\left(x-1\right)=4\left(x-1\right)^2\\ \Leftrightarrow x^2\left(x-1\right)-4\left(x-1\right)^2=0\\ \Leftrightarrow\left(x-1\right)\left(x^2-4x+4\right)=0\\ \Leftrightarrow\left(x-1\right)\left(x-2\right)^2=0\\ \Leftrightarrow\left[{}\begin{matrix}x=1\\x=2\end{matrix}\right.\)

a: P(x)=6x^3-4x^2+4x-2

Q(x)=-5x^3-10x^2+6x+11

M(x)=x^3-14x^2+10x+9

b: \(C\left(x\right)=7x^4-4x^3-6x+9+3x^4-7x^3-5x^2-9x+12\)

=10x^4-11x^3-5x^2-15x+21

<=> \(\frac{1.2.3....31}{4.6.8....64}=2^n\Rightarrow\frac{1.2.3....30.31}{2\left(2.3.4.5...31\right).32}=2^n\Leftrightarrow\frac{1}{2.32}=2^n\Leftrightarrow\frac{1}{2^6}=2^n\)

=> 2^6.2^n = 1 

=> 2^ (n + 6 ) = 2^0

=> n+ 6  = 0 

=> n = - 6 

\(\frac{1}{4}.\frac{2}{6}.\frac{3}{8}....\frac{31}{64}=\frac{1.2.3....31}{4.6.8....64}=\frac{1.2.3....31}{2.3.2.4....2.32}=\frac{1.2.3....31}{2^{30}.\left(3.4....32\right)}=\frac{2}{2^{30}.32}=\frac{1}{2^{34}}=2^{-34}=2^n=>n=-34\)

2^n × 2³¹ = \(\dfrac{ }{ }\)2/4×4/6×6/8×...×62/64

2^n×2³¹=1/32=2^-5

2^n=2^-5 ÷ 2³¹=2^-36

=>n=-36

2 x 1 x 2 x 3 x 3 x 4 x 4 x 5 x 5 x 6 x 9 x 8 x​​ 1 =

= 2 x 2 x 3 x 3 x 4 x 4 x 5 x 5 x 6 x 9 x 8 x​​ 1

= 4 x 3 x 3 x 4 x 4 x 5 x 5 x 6 x 9 x 8 x​​ 1

= 12 x 3 x 4 x 4 x 5 x 5 x 6 x 9 x 8 x​​ 1 

= 36 x 4 x 4 x 5 x 5 x 6 x 9 x 8 x​​ 1 

= 144 x 4 x 5 x 5 x 6 x 9 x 8 x​​ 1 

= 576 x 5 x 5 x 6 x 9 x 8 x​​ 1 

= 2 880 x 5 x 6 x 9 x 8 x​​ 1 

= 14 400 x 6 x 9 x 8 x​​ 1 

= 86 400 x 9 x 8 x​​ 1 

= 777 600 x 8 x​​ 1 

= 6 220 800 x​​ 1 

= 6 220 800 

:)

2 x 1 x 2 x3 x3 x4 x4 x5 x5 x6 x9 x8 x 1

= 6 220 800

a) (x-2)³+6(x+1)²-x³+12=0

\(\Rightarrow\)x³-6x²+12x-8+6(x²+2x+1)-x³+12=0

\(\Rightarrow\)x³-6x²+12x-8+6x²+12x+6-x³+12=0

\(\Rightarrow\)24x+10=0

\(\Rightarrow\)24x=-10

\(\Rightarrow\)x=\(\dfrac{-10}{24}=\dfrac{-5}{12}\)

b)(x-5)(x+5)-(x+3)²+3(x-2)²=(x+1)²-(x-4)(x+4)+3x²

\(\Rightarrow\)x²-25-(x²+6x+9)+3(x²-4x+4)=x²+2x+1-(x²-16)+3x²

\(\Rightarrow\)x²​-25-x²-6x-9+3x²-12x+12=x²+2x+1-x²+16+3x²

\(\Rightarrow\)3x²-18x-22=3x²+2x+17

\(\Rightarrow\)3x²-18x-22-3x²-2x-17=0

\(\Rightarrow\)-20x-39=0

\(\Rightarrow\)-20x=39

\(\Rightarrow\)x=\(-\dfrac{39}{20}\)

c) (2x+3)² +(x-1)(x+1)=5(x+2)²-(x-5)(x+1)+(x+4)

⇒4x²+12x+9+x²-1=5(x²+4x+4)-(x²+x-5x-5)+x+4

⇒5x²+12x+8=5x²+20x+20-x²-x+5x+5+x+4

⇒5x²+12x+8-5x²-20x-20+x²+x-5x-5-x-4=0

⇒x²-13x-21=0