Answer:

Step-by-step explanation:
Let,
= y
sin(y) = 


---------(1)


cos(y) = 
= 
= 
Therefore, from equation (1),

Or ![\frac{d}{dx}[\text{sin}^{-1}(\frac{x}{6})]=\frac{1}{6\sqrt{1-\frac{x^2}{36}}}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%5B%5Ctext%7Bsin%7D%5E%7B-1%7D%28%5Cfrac%7Bx%7D%7B6%7D%29%5D%3D%5Cfrac%7B1%7D%7B6%5Csqrt%7B1-%5Cfrac%7Bx%5E2%7D%7B36%7D%7D%7D)
At x = 4,
![\frac{d}{dx}[\text{sin}^{-1}(\frac{4}{6})]=\frac{1}{6\sqrt{1-\frac{4^2}{36}}}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%5B%5Ctext%7Bsin%7D%5E%7B-1%7D%28%5Cfrac%7B4%7D%7B6%7D%29%5D%3D%5Cfrac%7B1%7D%7B6%5Csqrt%7B1-%5Cfrac%7B4%5E2%7D%7B36%7D%7D%7D)
![\frac{d}{dx}[\text{sin}^{-1}(\frac{2}{3})]=\frac{1}{6\sqrt{1-\frac{16}{36}}}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%5B%5Ctext%7Bsin%7D%5E%7B-1%7D%28%5Cfrac%7B2%7D%7B3%7D%29%5D%3D%5Cfrac%7B1%7D%7B6%5Csqrt%7B1-%5Cfrac%7B16%7D%7B36%7D%7D%7D)




Answer:
n = 1500
Step-by-step explanation:
The sample size is the number of students that were asked
n = 1500
Answer:
The answer to your question is 10.5 in
Step-by-step explanation:
Data
First triangle
height = x
base = 7 in
Second triangle
height = 12 in
base = 8 in
Process
1.- Use proportions to solve this problem, relates the sides of a triangle with the same sides of the other triangle.

2.- Multiply both sides by 7

3.- Simplify
x = 
4.- Result
x = 10.5 in
Answer:
x^2 - 6x + 9
Step-by-step explanation:
(x - 3)^2
(x - 3)(x - 3)
x^2 - 3x - 3x + 9
x^2 - 6x + 9
Basic properties that will be used:

![x^{1/n}=\sqrt[n]x](https://tex.z-dn.net/?f=x%5E%7B1%2Fn%7D%3D%5Csqrt%5Bn%5Dx)

All of these expression can be written to match on or more of the patterns above.
![19.\quad\log_5\sqrt[4]{25}=\log_5(5^2)^{1/4}=\dfrac14\log_55^2=\dfrac12\log_55=\dfrac12](https://tex.z-dn.net/?f=19.%5Cquad%5Clog_5%5Csqrt%5B4%5D%7B25%7D%3D%5Clog_5%285%5E2%29%5E%7B1%2F4%7D%3D%5Cdfrac14%5Clog_55%5E2%3D%5Cdfrac12%5Clog_55%3D%5Cdfrac12)



![27.\quad\log_3\sqrt[6]{243}=\log_3(3^5)^{1/6}=\dfrac16\log_33^5=\dfrac56\log_33=\dfrac56](https://tex.z-dn.net/?f=27.%5Cquad%5Clog_3%5Csqrt%5B6%5D%7B243%7D%3D%5Clog_3%283%5E5%29%5E%7B1%2F6%7D%3D%5Cdfrac16%5Clog_33%5E5%3D%5Cdfrac56%5Clog_33%3D%5Cdfrac56)