Answer:
(-1 , 1)
Step-by-step explanation:
Absicca of midpoint = 4-2 / 2 = -1
Ordinate of midpoint = -4+6 / 2 = 1
Answer:
r = 8 ft
Step-by-step explanation:
Calculate r using the given formula
r =
, with Area = 64π
r =
← cancel π on numerator/ denominator
r =
= 8
Part a)
a) The given function is
![f(x) = 3 \sin(2x)](https://tex.z-dn.net/?f=f%28x%29%20%3D%203%20%5Csin%282x%29%20)
We let
![y = 3 \sin(2x)](https://tex.z-dn.net/?f=y%20%3D%20%203%20%5Csin%282x%29%20)
Interchange x and y.
![x= 3 \sin(2y)](https://tex.z-dn.net/?f=x%3D%20%203%20%5Csin%282y%29%20)
Solve for y;
![\frac{x}{3} = \sin(2y)](https://tex.z-dn.net/?f=%20%5Cfrac%7Bx%7D%7B3%7D%20%20%3D%20%20%5Csin%282y%29%20)
![y = \frac{1}{2} { \sin}^{ - 1}( \frac{x}{3} )](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20%20%7B%20%5Csin%7D%5E%7B%20-%201%7D%28%20%5Cfrac%7Bx%7D%7B3%7D%20%29)
![{f}^{ - 1}(x) = \frac{1}{2} { \sin}^{ - 1}( \frac{x}{3} )](https://tex.z-dn.net/?f=%20%7Bf%7D%5E%7B%20-%201%7D%28x%29%20%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20%20%7B%20%5Csin%7D%5E%7B%20-%201%7D%28%20%5Cfrac%7Bx%7D%7B3%7D%20%29)
Part b) The range of f(x) refers to y-values for which f(x) exists.
The range of f(x) is
![- 3 \leqslant y \leqslant 3](https://tex.z-dn.net/?f=%20-%20%203%20%5Cleqslant%20y%20%5Cleqslant%203)
This is because the function is within y=-3 and y=3.
c) The range of
![{f}^{ - 1} (x)](https://tex.z-dn.net/?f=%20%7Bf%7D%5E%7B%20-%201%7D%20%28x%29)
is
![- \frac{ \pi}{4} \leqslant y \leqslant \frac{\pi}{4}](https://tex.z-dn.net/?f=%20-%20%20%5Cfrac%7B%20%5Cpi%7D%7B4%7D%20%20%5Cleqslant%20y%20%5Cleqslant%20%20%5Cfrac%7B%5Cpi%7D%7B4%7D%20)
The domain is -3≤x≤3
This is because the domain and range of a function and its inverse swaps.
Part d) The graph is shown in the attachment.