Y - y₁ = m(x - x₁)
y - 5 = -8(x - 2)
y - 5 = -8(x) + 8(2)
y - 5 = -8x + 16
<u> + 5 + 5</u>
y = -8x + 21
Well if you take 468 and divide it by 18 you get 26 that 26mpg take 754 divide it by 26 and you get 29 and that's how many gallons he used
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)
2)
32/28=w/7
you cross multiply one denominator by the other numerator so
32(7)=(28)(w)
simplify
224=28w
divide 28 from both sides to get w alone
8=w
4)
36/21=24/s
cross multiply just like in the last problem
(36)(s)=(21)(24)
simplify
36s=504
divide 36 to get s alone and essentially solve for s
S=14
