Answer:
a. length = 0.7211 ft
b. width = 0.7211 ft
c. height = 140.3846 ft
Step-by-step explanation:
This is an optimiztion with restriction problem.
We have to minimize the cost, with the restriction of the volume being equal to 72 ft3.
As the cost for the sides is constant, we know that length and width are equal.
Then, we can express the volume as:
being x: length and z: height
We can express the height in function of the length as:
Then, the cost of the box can be expressed as:
To optimize C, we derive and equal to zero
![\dfrac{dC}{dx}=\dfrac{d}{dx}[0.8x^2+0.6x^{-1}]=1.6x-0.6x^{-2}=0\\\\\\1.6x=0.6x^{-2}\\\\x^{1+2}=0.6/1.6=0.375\\\\x=\sqrt[3]{0.375} =0.7211](https://tex.z-dn.net/?f=%5Cdfrac%7BdC%7D%7Bdx%7D%3D%5Cdfrac%7Bd%7D%7Bdx%7D%5B0.8x%5E2%2B0.6x%5E%7B-1%7D%5D%3D1.6x-0.6x%5E%7B-2%7D%3D0%5C%5C%5C%5C%5C%5C1.6x%3D0.6x%5E%7B-2%7D%5C%5C%5C%5Cx%5E%7B1%2B2%7D%3D0.6%2F1.6%3D0.375%5C%5C%5C%5Cx%3D%5Csqrt%5B3%5D%7B0.375%7D%20%3D0.7211)
The height z is then
Y X
(1,3)
The y goes down once and x goes across 3 times
Answer:
Step-by-step explanation:
we know that
The exponential function is of the form
where
a is the initial value
b is the base
In this problem we have
a=200 birds
b=100%+4%=104%=104/100=1.04
substitute
Let change of variables
where
b is the amount of birds in the flock
d is the number of days since the 200 birds started
(3^3 - 9 )^2
First do what is inside the parenthesis:
3^3 = 27
Now you have:
(27-9)^2
Subtract:
27-9 = 18
Now you have:
(18)^2
Raise 18 to the second power:
18^2 = 324
Are you saying 32 is the total perimeter?
