Answer:
Step-by-step explanation:
Note: For this problem we use the calculator on degrees
For this case we need to remember this identity :
For this case if we apply for our desired formula we got this:
![a cos (x-c) = a [cos (c) cos (x) + sin (c) sin (x)]](https://tex.z-dn.net/?f=%20a%20cos%20%28x-c%29%20%3D%20a%20%5Bcos%20%28c%29%20cos%20%28x%29%20%2B%20sin%20%28c%29%20sin%20%28x%29%5D)
And we want this equal to 
so we can set up the following equality:
![6 sin (x) + 8 cos (x)= a cos (c) [cos (x)] + a sin (c) [sin(x)]](https://tex.z-dn.net/?f=%206%20sin%20%28x%29%20%2B%208%20cos%20%28x%29%3D%20a%20cos%20%28c%29%20%5Bcos%20%28x%29%5D%20%2B%20a%20sin%20%28c%29%20%5Bsin%28x%29%5D)
(1)
If we apply direct comparison between the factors on equation (1) we see this:
(2)
(3)
If we solve a from equation (2) we got:
(4)
If we replace equation (4) into equation (3) we got:
If we apply inverse tangent on both sides we got:
So then the value of c= 36.870 degrees. And since w ehave the value of c we can find the value for a and we got:
![[tex] a = \frac{8}{cos (36.870)}=10](https://tex.z-dn.net/?f=%20%5Btex%5D%20a%20%3D%20%5Cfrac%7B8%7D%7Bcos%20%2836.870%29%7D%3D10)
And then our expression in the form 
is:
And we can check that:
![h(x)= 10 cos (36.870) [cos (x)] + 10 sin (36.870) [sin(x)]= 8 cos (x) + 6 sin (x)](https://tex.z-dn.net/?f=%20h%28x%29%3D%2010%20cos%20%2836.870%29%20%5Bcos%20%28x%29%5D%20%2B%2010%20sin%20%2836.870%29%20%5Bsin%28x%29%5D%3D%208%20cos%20%28x%29%20%2B%206%20sin%20%28x%29)
Answer:
plug in 0 for y and solve for x
to find y plug in 0 for x
Step-by-step explanation:
Ok
Perimeter=38cm
Area=88cm
2 numbers that multiply to 88
4 numbers that add up to 38
Length=11
Width= 8
Here are a few rules with exponents that you need to know:
- Dividing exponents of the same base:
For this, divide:
<u>Your final answer is 
</u>
Step-by-step explanation: The place value chart can help us write a number in expanded notation. When we put 2,930,365 into the place value chart, we can recognize that our number is equal to 2 millions + 9 hundred thousands + 3 ten thousands + 0 thousands + 3 hundreds + 6 tens + 5 units.
The place value chart is attached in the image provided.
