Answer:
d.) Arionna is incorrect. There are 27 cubic feet in a cubic yard because a cubic yard is a prism with dimensions 3 ft times 3 ft times 3 ft. A prism with those dimensions will take 27 cubes to fill it, if each cube is a unit cube of 1 ft³.
Step-by-step explanation:
There are (3 ft)(3 ft) = 9 ft² in one square yard. To find the volume of a cubic yard, you need to multiply that by 3 ft again: (9 ft²)(3 ft) = 27 ft³.
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<em>Additional comment</em>
For many problems involving units, I like to keep the units with the numbers. That helps ensure the math is done correctly. In this problem, simply multiplying ft by ft gives ft^2, not ft^3, so you know right away that you haven't computed volume correctly.
Answer:
a) 
b) 
Step-by-step explanation:
Given integrals are:
---(1)
---- (2)
Standard form
<h3>Part A</h3>
compare (1) with standard form
![[f'(x)]^{2} = 64x^{8}\\f'(x)=\pm 8x^{4}\\f(x)= \pm8\frac{x^{5}}{5}+C](https://tex.z-dn.net/?f=%5Bf%27%28x%29%5D%5E%7B2%7D%20%3D%2064x%5E%7B8%7D%5C%5Cf%27%28x%29%3D%5Cpm%208x%5E%7B4%7D%5C%5Cf%28x%29%3D%20%5Cpm8%5Cfrac%7Bx%5E%7B5%7D%7D%7B5%7D%2BC)
<h3>Part B</h3>
Compare (2) with standard form
![[f'(x)]^{2}=64cos^{2}(2x)\\f'(x)= \pm 8cos(2x)\\f(x)=\pm 8\frac{sin(2x)}{2}+C\\f(x)= \pm 4sin(2x)+C](https://tex.z-dn.net/?f=%5Bf%27%28x%29%5D%5E%7B2%7D%3D64cos%5E%7B2%7D%282x%29%5C%5Cf%27%28x%29%3D%20%5Cpm%208cos%282x%29%5C%5Cf%28x%29%3D%5Cpm%208%5Cfrac%7Bsin%282x%29%7D%7B2%7D%2BC%5C%5Cf%28x%29%3D%20%5Cpm%204sin%282x%29%2BC)
Thats for questions 3 - 8 that you didn't answer. I'm not quite sure how to answer the last two though.
Answer:
<em>1, 2</em>
Step-by-step explanation:
For each value of x, f(x) is 2 less.
f(x) = x - 2
f(x) = 1x - 2
