Broo it’s blank for me....
Answer:
False
Step-by-step explanation:
Measured in cm^2
Answer:
base side = 20cm
height = 40 cm
minimum cost = $7200
Step-by-step explanation:
Let x (cm) be the base side and h (cm) be the height of the box. Since the volume of the box must be 16000 cubic cm, we have:
![x^2h = 16000](https://tex.z-dn.net/?f=x%5E2h%20%3D%2016000)
![h = 16000/x^2](https://tex.z-dn.net/?f=h%20%3D%2016000%2Fx%5E2)
The areas of the top and bottom is
![A_B = 2x^2](https://tex.z-dn.net/?f=A_B%20%3D%202x%5E2)
And so their cost is:
![C_B = A_T*3 = 6x^2](https://tex.z-dn.net/?f=C_B%20%3D%20A_T%2A3%20%3D%206x%5E2)
The areas of the sides is
![A_S = 4xh](https://tex.z-dn.net/?f=A_S%20%3D%204xh)
And so their cost is:
![C_S = A_S*1.5 = 6xh](https://tex.z-dn.net/?f=C_S%20%3D%20A_S%2A1.5%20%3D%206xh)
We can substitute
into the equation above to get
![C_S = 96000/x](https://tex.z-dn.net/?f=C_S%20%3D%2096000%2Fx)
So the total cost of the bases and the sides:
![C = C_S + C_B = 6x^2 + 96000/x](https://tex.z-dn.net/?f=C%20%3D%20C_S%20%2B%20C_B%20%3D%206x%5E2%20%2B%2096000%2Fx)
This is the function we would want to minimize. We can start by taking the 1st derivative, and set it to 0
![C^{'} = 12x - 96000/x^2 = 0](https://tex.z-dn.net/?f=C%5E%7B%27%7D%20%3D%2012x%20-%2096000%2Fx%5E2%20%3D%200)
![12x = 96000/x^2](https://tex.z-dn.net/?f=12x%20%3D%2096000%2Fx%5E2)
![x^3 = 96000/12 = 8000](https://tex.z-dn.net/?f=x%5E3%20%3D%2096000%2F12%20%3D%208000)
![x = 20cm](https://tex.z-dn.net/?f=x%20%3D%2020cm)
So the height would be
![h = 16000/x^2 = 16000/20^2 = 40 cm](https://tex.z-dn.net/?f=h%20%3D%2016000%2Fx%5E2%20%3D%2016000%2F20%5E2%20%3D%2040%20cm)
So the minimum total cost would be
![C = 6x^2 + 96000/x = 6*20^2 + 96000/20 = 7200](https://tex.z-dn.net/?f=C%20%3D%206x%5E2%20%2B%2096000%2Fx%20%3D%206%2A20%5E2%20%2B%2096000%2F20%20%3D%207200)
Answer:
As x gets bigger, y is now getting smaller.
Step-by-step explanation:
A fancy way to say this is that the function y = 2-x is what we get when we reflect y = 2x across the y-axis.
Answer:
x=27
Step-by-step explanation:
180-2x-40+180-3x+180-x-50+180-4x = 360
360-2x-40-3x+360-x-50-4x= 360
360-10x-90= 0
10x= 270
x= 27