Answer:
Dimensions 30 in x 30 in x 15 in
Surface Area = 2,700 in²
Step-by-step explanation:
Let 'r' be the length of the side of the square base, and 'h' be the height of the bin. The volume is given by:
The total surface area is given by:
Rewriting the surface area function as a function of 'r':
The value of 'r' for which the derivate of the surface area function is zero, is the length for which the area is minimized:
![A=54,000*r^{-1}+r^2\\\frac{dA}{dr}=0= -54,000*r^{-2}+2r\\\frac{54,000}{r^2}=2r\\ r=\sqrt[3]{27,000}\\r=30\ in](https://tex.z-dn.net/?f=A%3D54%2C000%2Ar%5E%7B-1%7D%2Br%5E2%5C%5C%5Cfrac%7BdA%7D%7Bdr%7D%3D0%3D%20-54%2C000%2Ar%5E%7B-2%7D%2B2r%5C%5C%5Cfrac%7B54%2C000%7D%7Br%5E2%7D%3D2r%5C%5C%20r%3D%5Csqrt%5B3%5D%7B27%2C000%7D%5C%5Cr%3D30%5C%20in)
The value of 'h' is:
The dimensions that will ensure the minimum surface area are 30 in x 30 in x 15 in.
The surface area is:
Answer:
B, y is the greater number than every x.
Step-by-step explanation:
Answer: 0.22hz
Step-by-step explanation:
Hi to answer this question we have to analyze the information given:
- <em>Period (T) = 4.5 Seconds
</em>
So, to calculate the frequency of the pendulum we have to apply the formula;
Frequency (f)= 1 / period
Replacing with the value given:
f = 1/ 4.5 sec = 0.22 hz
Feel free to ask for more if needed or if you did not understand something.
Answer:
f(6) ≈ 31
Step-by-step explanation:
If f(x) varies directly with x, we can write f(x) this way:
f(x) = kx
Using the given values, we can find k:
f(25) = k×25 = 130
k = 130/25 = 5.2
Then for x = 6, we have ...
f(x) = 5.2x
f(6) = 5.2×6 = 31.2
Rounded to the nearest whole number, ...
f(6) ≈ 31
