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
Perimeter= 2L + 2W
312 cm= 2L + 2(64)
312= 2L + 128
subtract 128 from both sides
184= 2L
divide both sides by 2
92 cm= L
ANSWER: The length is 92cm.
Hope this helps! :)
$21.80 because you will do 20% over 100% = x over $26. Than you will do 26 times 20 divided by 100, and you get 5.2, than you will do 26-5.2 and you get $21.80
Ufff u need to have a little more information for us to help u buddy
For this case we have a function of the form:
y = A * (b) ^ t
Where,
A: initial amount
b: growth rate
t: time
Substituting values we have:
y = 100000 * (1.10) ^ 4
y = 146410
Answer:
the value of his house at the start of 2018 is:
y = 146410
