Let x =lenght, y = width, and z =height
<span>The volume of the box is equal to V = xyz </span>
<span>Subject to the surface area </span>
<span>S = 2xy + 2xz + 2yz = 64 </span>
<span>= 2(xy + xz + yz) </span>
<span>= 2[xy + x(64/xy) + y(64/xy)] </span>
<span>S(x,y)= 2(xy + 64/y + 64/x) </span>
<span>Then </span>
<span>Mx(x, y) = y = 64/x^2 </span>
<span>My(x, y) = x = 64/y^2 </span>
<span>y^2 = 64/x </span>
<span>(64/x^2)^2 = 64 </span>
<span>4096/x^4 = 64/x </span>
<span>x^3 = 4096/64 </span>
<span>x^3 = 64 </span>
<span>x = 4 </span>
<span>y = 64/x^2 </span>
<span>y = 4 </span>
<span>z= 64/yx </span>
<span>z= 64/16 </span>
<span>z = 4 </span>
<span>Therefor the dimensions are cube 4.</span>
Given:
To find:
The rate of change in volume at 
Solution:
We know that, volume of a cone is
Differentiate with respect to t.
![\dfrac{dV}{dt}=\dfrac{1}{3}\pi\times \left[(r^2\dfrac{dh}{dt}) + h(2r\dfrac{dr}{dt})\right]](https://tex.z-dn.net/?f=%5Cdfrac%7BdV%7D%7Bdt%7D%3D%5Cdfrac%7B1%7D%7B3%7D%5Cpi%5Ctimes%20%5Cleft%5B%28r%5E2%5Cdfrac%7Bdh%7D%7Bdt%7D%29%20%2B%20h%282r%5Cdfrac%7Bdr%7D%7Bdt%7D%29%5Cright%5D)
Substitute the given values.
![\dfrac{dV}{dt}=\dfrac{1}{3}\times \dfrac{22}{7}\times \left[(120)^2(-2.1) +175(2)(120)(1.4)\right]](https://tex.z-dn.net/?f=%5Cdfrac%7BdV%7D%7Bdt%7D%3D%5Cdfrac%7B1%7D%7B3%7D%5Ctimes%20%5Cdfrac%7B22%7D%7B7%7D%5Ctimes%20%5Cleft%5B%28120%29%5E2%28-2.1%29%20%2B175%282%29%28120%29%281.4%29%5Cright%5D)
![\dfrac{dV}{dt}=\dfrac{22}{21}\times \left[-30240+58800\right]](https://tex.z-dn.net/?f=%5Cdfrac%7BdV%7D%7Bdt%7D%3D%5Cdfrac%7B22%7D%7B21%7D%5Ctimes%20%5Cleft%5B-30240%2B58800%5Cright%5D)
Therefore, the volume of decreased by 29920 cubic inches per second.
Answer:
I've been trying to figure this out with out a chart and i keep confusing myself
Step-by-step explanation:
nothing
Answer:
c·c·c·c is the same as saying 4c
Answer: 2x + 15 = 243
x = $114
Step-by-step explanation:
Gas Tank: $15
Matthew: x
Devin: x
Gas Tank + Matthew + Devin = Total
15 + x + x = 243
2x = 228
x = 114
