Answer:
Good Morning my favorite is Attack on Titan.
Step-by-step explanation:
The inverse of the function f(x) = 4(x-3)² + 2 is ![f^{-1}(x) = \sqrt{\frac{x-2}{4} } + 3](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%20%3D%20%5Csqrt%7B%5Cfrac%7Bx-2%7D%7B4%7D%20%7D%20%2B%203)
The given function is:
f(x) = 4(x - 3)² + 2
To find the inverse of the function:
Make x as the subject of the formula
![4(x-3)^2 = f(x) - 2\\(x-3)^2 = \frac{f(x)-2}{4} \\x - 3 = \sqrt{\frac{f(x)-2}{4} } \\x = \sqrt{\frac{f(x)-2}{4} } + 3](https://tex.z-dn.net/?f=4%28x-3%29%5E2%20%3D%20f%28x%29%20-%202%5C%5C%28x-3%29%5E2%20%3D%20%5Cfrac%7Bf%28x%29-2%7D%7B4%7D%20%5C%5Cx%20-%203%20%3D%20%5Csqrt%7B%5Cfrac%7Bf%28x%29-2%7D%7B4%7D%20%7D%20%5C%5Cx%20%3D%20%5Csqrt%7B%5Cfrac%7Bf%28x%29-2%7D%7B4%7D%20%7D%20%2B%203)
Replace x by
and replace f(x) by x
![f^{-1}(x) = \sqrt{\frac{x-2}{4} } + 3](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%20%3D%20%5Csqrt%7B%5Cfrac%7Bx-2%7D%7B4%7D%20%7D%20%2B%203)
Therefore, the inverse of the function is:
![f^{-1}(x) = \sqrt{\frac{x-2}{4} } + 3](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%20%3D%20%5Csqrt%7B%5Cfrac%7Bx-2%7D%7B4%7D%20%7D%20%2B%203)
Learn more here: brainly.com/question/17285960
Answer:
t(32) = 94
Step-by-step explanation:
a. I think s is the independent variable
b I think t or t(s) is the dependent variable since the total amount of money depends on how many treats are sold.
t(32) = 30 + 2(32)
t(32) = 30 + 64
t(32) = 94
I'm a little unsure on the dependent and independent variable but I know the function is correct.
Hope this helps :)
ANSWER
![r = 2 \sqrt{29} ( \cos(292 \degree) + \sin(292 \degree))](https://tex.z-dn.net/?f=r%20%3D%202%20%5Csqrt%7B29%7D%20%28%20%5Ccos%28292%20%5Cdegree%29%20%20%2B%20%5Csin%28292%20%5Cdegree%29%29%20)
EXPLANATION
The polar form of a complex number ,
![z = x + yi](https://tex.z-dn.net/?f=z%20%3D%20x%20%2B%20yi)
is given by:
![z = r( \cos( \theta) + i \sin( \theta) )](https://tex.z-dn.net/?f=z%20%3D%20r%28%20%5Ccos%28%20%5Ctheta%29%20%20%2B%20i%20%5Csin%28%20%5Ctheta%29%20%29)
where
![r = \sqrt{ {x}^{2} + {y}^{2} }](https://tex.z-dn.net/?f=r%20%3D%20%20%5Csqrt%7B%20%7Bx%7D%5E%7B2%7D%20%2B%20%20%7By%7D%5E%7B2%7D%20%20%7D%20)
The given complex number is:
![z = 4 - 10i](https://tex.z-dn.net/?f=z%20%3D%204%20-%2010i)
![r = \sqrt{ {4}^{2} + {( - 10)}^{2} }](https://tex.z-dn.net/?f=r%20%3D%20%20%5Csqrt%7B%20%7B4%7D%5E%7B2%7D%20%20%2B%20%20%7B%28%20-%2010%29%7D%5E%7B2%7D%20%7D%20)
![r = \sqrt{16 + 100}](https://tex.z-dn.net/?f=r%20%3D%20%20%5Csqrt%7B16%20%20%2B%20100%7D%20)
![r = \sqrt{116} = 2 \sqrt{29}](https://tex.z-dn.net/?f=r%20%3D%20%20%5Csqrt%7B116%7D%20%20%3D%202%20%5Csqrt%7B29%7D%20)
And
![\theta= \tan^{ - 1}(\frac{ y}{x} )](https://tex.z-dn.net/?f=%5Ctheta%3D%20%20%5Ctan%5E%7B%20-%201%7D%28%5Cfrac%7B%20y%7D%7Bx%7D%20%29)
![\theta= \tan^{ - 1}(\frac{ - 10}{4} )](https://tex.z-dn.net/?f=%5Ctheta%3D%20%20%5Ctan%5E%7B%20-%201%7D%28%5Cfrac%7B%20%20-%2010%7D%7B4%7D%20%29)
![\theta= 292 \degree](https://tex.z-dn.net/?f=%5Ctheta%3D%20%20292%20%5Cdegree)
Hence the polar form is :
![r = 2 \sqrt{29} ( \cos(292 \degree) + \sin(292 \degree))](https://tex.z-dn.net/?f=r%20%3D%202%20%5Csqrt%7B29%7D%20%28%20%5Ccos%28292%20%5Cdegree%29%20%20%2B%20%5Csin%28292%20%5Cdegree%29%29%20)
Distribute the -2 to get
-16x + 8 < 2x + 5
3 < 18x
1/6 < x
so x > 1/6