G(f(2)) means work out whatever f(2) is then plug this into g(x).
So f(2) is 3 because we just find the x-value 2 in the left hand column and read across. This is 3.
So then we find g(3) by finding the x-value 3 in the left hand column and read across. This is 10.
So g(f(2)) = 10
Answer: ![\bold{(A): g=\dfrac{\sqrt{15}}{2},\quad h=\dfrac{\sqrt{5}}{2}}](https://tex.z-dn.net/?f=%5Cbold%7B%28A%29%3A%20g%3D%5Cdfrac%7B%5Csqrt%7B15%7D%7D%7B2%7D%2C%5Cquad%20h%3D%5Cdfrac%7B%5Csqrt%7B5%7D%7D%7B2%7D%7D)
<u>Step-by-step explanation:</u>
This is a special triangle because the side lengths have the following relationship:
30° ⇄ side length "a" <em>represented as "h" in your picture</em>
60° ⇄ side length "a√3" <em>represented as "g" in your picture</em>
90° ⇄ side length "2a" <em>represented as "√5" in your picture</em>
<u>Step 1: solve for "a" </u> <em>hypotenuse (2a) is given as √5</em>
![2a=\sqrt{5}](https://tex.z-dn.net/?f=2a%3D%5Csqrt%7B5%7D)
![a=\dfrac{\sqrt{5}}{2}](https://tex.z-dn.net/?f=a%3D%5Cdfrac%7B%5Csqrt%7B5%7D%7D%7B2%7D)
According to your picture, a = h, so ![h=\dfrac{\sqrt{5}}{2}](https://tex.z-dn.net/?f=h%3D%5Cdfrac%7B%5Csqrt%7B5%7D%7D%7B2%7D)
<u>Step 2: use the a-value from Step 1 to solve for the remaining side</u>
![g=a\sqrt{3}](https://tex.z-dn.net/?f=g%3Da%5Csqrt%7B3%7D)
![=\bigg( \dfrac{\sqrt{5}}{2}\bigg)\sqrt{3}](https://tex.z-dn.net/?f=%3D%5Cbigg%28%20%5Cdfrac%7B%5Csqrt%7B5%7D%7D%7B2%7D%5Cbigg%29%5Csqrt%7B3%7D)
![=\dfrac{\sqrt{15}}{2}](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B%5Csqrt%7B15%7D%7D%7B2%7D)
Step-by-step explanation:
![\sin^{4}x \: - \cos^{4} x = (\sin^{2}x)^{2} - (\cos^{2}x)^{2}](https://tex.z-dn.net/?f=%5Csin%5E%7B4%7Dx%20%20%5C%3A%20%20-%20%20%5Ccos%5E%7B4%7D%20x%20%3D%20%28%5Csin%5E%7B2%7Dx%29%5E%7B2%7D%20%20-%20%28%5Ccos%5E%7B2%7Dx%29%5E%7B2%7D%20)
![= (\sin^{2}x)^{2} - (1 - \sin^{2}x)^{2}](https://tex.z-dn.net/?f=%20%3D%20%28%5Csin%5E%7B2%7Dx%29%5E%7B2%7D%20%20-%20%281%20-%20%5Csin%5E%7B2%7Dx%29%5E%7B2%7D%20)
![= \sin^{4}x - (1 - 2\sin^{2}x + \sin^{4}x)](https://tex.z-dn.net/?f=%20%3D%20%5Csin%5E%7B4%7Dx%20-%20%281%20-%202%5Csin%5E%7B2%7Dx%20%2B%20%5Csin%5E%7B4%7Dx%29)
![= 2\sin^{2}x - 1](https://tex.z-dn.net/?f=%20%3D%202%5Csin%5E%7B2%7Dx%20-%201)
![= - \cos2x](https://tex.z-dn.net/?f=%20%3D%20%20-%20%5Ccos2x)
Note: I used the identity
![{ \sin }^{2} x = \frac{1}{2} (1 - \cos \: 2x)](https://tex.z-dn.net/?f=%20%7B%20%5Csin%20%7D%5E%7B2%7D%20x%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20%281%20-%20%20%5Ccos%20%5C%3A%202x%29)
for the last step.
PS. I love proving trigonometric identities!
Answer:
905.26
Step-by-step explanation:
905.255
We are rounding to the hundredths place, so we need to look at the thousandths place. That digit is also a 5. 5>= 5 so we need to round the 5 in the hundredths place up to a 6
905.255 rounds to 905.26
Answer:
89 if you pay 11$ to go to the museum for Justin 1$
Step-by-step explanation:
100 - 11 = 89.