Option 3: a 90 degree rotation clockwise
You can tell that it is 90 degrees because the original started completely in quadrant 2 and the final image is completely in quadrant 1. If it was only rotated 45 degrees the final image would be part in quadrant 2 and part in quadrant 1. It was rotated clockwise because that is the way a clock goes.
Hope this helps! ;)
A meter is about 3 feet and a magazine is about 1 inch thick. so 36 inches would mean 36 magazines
Answer: 43 degrees
Step-by-step explanation:
Answer:
![f'(x) = \frac{2{x}^{2}}{ \sqrt[3]{( {x}^{3} - 8) } }](https://tex.z-dn.net/?f=%20f%27%28x%29%20%3D%20%20%20%5Cfrac%7B2%7Bx%7D%5E%7B2%7D%7D%7B%20%5Csqrt%5B3%5D%7B%28%20%7Bx%7D%5E%7B3%7D%20%20-%208%29%20%7D%20%7D)
Step-by-step explanation:
![f(x) = ( {x}^{3} - 8)^{ \frac{2}{3} } \\ \\ f'(x) = \frac{2}{3} ( {x}^{3} - 8)^{ \frac{2}{3} - 1 } (3 {x}^{2} - 0) \\ \\ f'(x) = \frac{2}{3} ( {x}^{3} - 8)^{ \frac{2 - 3}{3} } \times 3 {x}^{2} \\ \\ f'(x) = 2{x}^{2}( {x}^{3} - 8)^{ \frac{ - 1}{3} } \\ \\ f'(x) = \frac{2{x}^{2}}{( {x}^{3} - 8)^{ \frac{ 1}{3} } } \\ \\ \huge \red{ \boxed{ f'(x) = \frac{2{x}^{2}}{ \sqrt[3]{( {x}^{3} - 8) } } }}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%28%20%7Bx%7D%5E%7B3%7D%20%20-%208%29%5E%7B%20%5Cfrac%7B2%7D%7B3%7D%20%7D%20%20%5C%5C%20%20%5C%5C%20f%27%28x%29%20%3D%20%20%5Cfrac%7B2%7D%7B3%7D%20%28%20%7Bx%7D%5E%7B3%7D%20%20-%208%29%5E%7B%20%5Cfrac%7B2%7D%7B3%7D%20-%201%20%7D%20%283%20%7Bx%7D%5E%7B2%7D%20%20-%200%29%20%5C%5C%20%20%5C%5C%20f%27%28x%29%20%3D%20%20%5Cfrac%7B2%7D%7B3%7D%20%28%20%7Bx%7D%5E%7B3%7D%20%20-%208%29%5E%7B%20%5Cfrac%7B2%20-%203%7D%7B3%7D%20%20%7D%20%20%5Ctimes%203%20%7Bx%7D%5E%7B2%7D%20%5C%5C%20%20%5C%5C%20f%27%28x%29%20%3D%20%202%7Bx%7D%5E%7B2%7D%28%20%7Bx%7D%5E%7B3%7D%20%20-%208%29%5E%7B%20%5Cfrac%7B%20-%201%7D%7B3%7D%20%20%7D%20%5C%5C%20%20%5C%5C%20f%27%28x%29%20%3D%20%20%20%5Cfrac%7B2%7Bx%7D%5E%7B2%7D%7D%7B%28%20%7Bx%7D%5E%7B3%7D%20%20-%208%29%5E%7B%20%5Cfrac%7B%201%7D%7B3%7D%20%20%7D%20%7D%20%5C%5C%20%20%5C%5C%20%5Chuge%20%5Cred%7B%20%5Cboxed%7B%20f%27%28x%29%20%3D%20%20%20%5Cfrac%7B2%7Bx%7D%5E%7B2%7D%7D%7B%20%5Csqrt%5B3%5D%7B%28%20%7Bx%7D%5E%7B3%7D%20%20-%208%29%20%7D%20%7D%20%7D%7D)
