Answer:
Step-by-step explanation:
h=V/lw
Answer:
163
Step-by-step explanation:
2(7)^2+9(7)+2=
2(49)+63+2=163
Answer:
A)
![\displaystyle \frac{dy}{dt}=-\frac{33}{8}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bdy%7D%7Bdt%7D%3D-%5Cfrac%7B33%7D%7B8%7D)
B)
![\displaystyle \frac{dx}{dt}=\frac{3}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bdx%7D%7Bdt%7D%3D%5Cfrac%7B3%7D%7B2%7D)
Step-by-step explanation:
<em>x</em> and <em>y</em> are differentiable functions of <em>t, </em>and we are given the equation:
![xy=6](https://tex.z-dn.net/?f=xy%3D6)
First, let's differentiate both sides of the equation with respect to <em>t</em>. So:
![\displaystyle \frac{d}{dt}\left[xy\right]=\frac{d}{dt}[6]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdt%7D%5Cleft%5Bxy%5Cright%5D%3D%5Cfrac%7Bd%7D%7Bdt%7D%5B6%5D)
By the Product Rule and rewriting:
![\displaystyle \frac{d}{dt}[x(t)]y+x\frac{d}{dt}[y(t)]=0](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdt%7D%5Bx%28t%29%5Dy%2Bx%5Cfrac%7Bd%7D%7Bdt%7D%5By%28t%29%5D%3D0)
Therefore:
![\displaystyle y\frac{dx}{dt}+x\frac{dy}{dt}=0](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%5Cfrac%7Bdx%7D%7Bdt%7D%2Bx%5Cfrac%7Bdy%7D%7Bdt%7D%3D0)
A)
We want to find dy/dt when <em>x</em> = 4 and dx/dt = 11.
Using our original equation, find <em>y</em> when <em>x</em> = 4:
![\displaystyle (4)y=6\Rightarrow y=\frac{3}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%284%29y%3D6%5CRightarrow%20y%3D%5Cfrac%7B3%7D%7B2%7D)
Therefore:
![\displaystyle \frac{3}{2}\left(11\right)+(4)\frac{dy}{dt}=0](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B3%7D%7B2%7D%5Cleft%2811%5Cright%29%2B%284%29%5Cfrac%7Bdy%7D%7Bdt%7D%3D0)
Solve for dy/dt:
![\displaystyle \frac{dy}{dt}=-\frac{33}{8}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bdy%7D%7Bdt%7D%3D-%5Cfrac%7B33%7D%7B8%7D)
B)
We want to find dx/dt when <em>x</em> = 1 and dy/dt = -9.
Again, using our original equation, find <em>y</em> when <em>x</em> = 1:
![(1)y=6\Rightarrow y=6](https://tex.z-dn.net/?f=%281%29y%3D6%5CRightarrow%20y%3D6)
Therefore:
![\displaystyle (6)\frac{dx}{dt}+(1)\left(-9)=0](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%286%29%5Cfrac%7Bdx%7D%7Bdt%7D%2B%281%29%5Cleft%28-9%29%3D0)
Solve for dx/dt:
![\displaystyle \frac{dx}{dt}=\frac{3}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bdx%7D%7Bdt%7D%3D%5Cfrac%7B3%7D%7B2%7D)
Answer:
The area of the remaining sheet is 22 square cm.
Answer:
2
Step-by-step explanation:
2 x 2 = 4
4x2 is 8
8x2 = 16
16x2= 32
And then 32 x 2 = 64