The cosine equation of the attached graph is; y = 5 cos [( π/40)(x - (π/2))] + 3
<h3>How to plot a trigonometric graph?</h3>
The given parameters are:
Diameter = 10 m
Thus;
Radius; r = 5 m
Time; t = 80 s
Height above the ground, h = 2 m
The above means that:
Amplitude; A = 5 m
Period, T = 80 s
Minimum = 2 m
The cosine function is represented as:
y = a cos [k(x - d)] + c.
where;
A is amplitude
B is cycles from 0 to 2π
period = 2π/k
d is horizontal shift
c is vertical shift (displacement)
Thus;
2π/k = 80
k = 2π/80 = π/40
Where
c = Amplitude - Minimum
c = 5 - 2
c = 3
Shift to the left by π/2 gives;
d = π/2
Thus, the equation of the cosine graph is;
y = 5 cos [( π/40)(x - (π/2))] + 3
Read more about Trigonometric Graph at; brainly.com/question/28054826
#SPJ1
You should know that a whole circle consists of 360 degrees. Since the problem states that an angle measures 75 degrees you would then realize it is 75 degrees out of 360 degrees, or 75/360. This simplifies to 5/24.
Answer:
12. a = 2
13. ![x = \dfrac{4}{3}](https://tex.z-dn.net/?f=%20x%20%3D%20%5Cdfrac%7B4%7D%7B3%7D%20)
Step-by-step explanation:
12.
6a(a + 3) = 2a(3a + 5) + 16
First, distribute 6a on the left side, and distribute 2a on the right side.
6a² + 18a = 6a² + 10a + 16
Subtract 6a² from both sides.
18a = 10a + 16
Subtract 10a from both sides.
8a = 16
Divide both sides by 8.
a = 2
13.
![\dfrac{1}{3}x + \dfrac{1}{2}x = \dfrac{1}{3}(x + 2)](https://tex.z-dn.net/?f=%20%5Cdfrac%7B1%7D%7B3%7Dx%20%2B%20%5Cdfrac%7B1%7D%7B2%7Dx%20%3D%20%5Cdfrac%7B1%7D%7B3%7D%28x%20%2B%202%29%20)
The LCD of 2 and 3 is 6. We multiply both sides of the equation by 6 to get rid of all denominators.
![6 \times \dfrac{1}{3}x + 6 \times \dfrac{1}{2}x = 6 \times \dfrac{1}{3}(x + 2)](https://tex.z-dn.net/?f=%206%20%5Ctimes%20%5Cdfrac%7B1%7D%7B3%7Dx%20%2B%206%20%5Ctimes%20%5Cdfrac%7B1%7D%7B2%7Dx%20%3D%206%20%5Ctimes%20%5Cdfrac%7B1%7D%7B3%7D%28x%20%2B%202%29%20)
![\dfrac{6}{3}x + \dfrac{6}{2}x = \dfrac{6}{3}(x + 2)](https://tex.z-dn.net/?f=%20%5Cdfrac%7B6%7D%7B3%7Dx%20%2B%20%5Cdfrac%7B6%7D%7B2%7Dx%20%3D%20%5Cdfrac%7B6%7D%7B3%7D%28x%20%2B%202%29%20)
![2x + 3x = 2(x + 2)](https://tex.z-dn.net/?f=%202x%20%2B%203x%20%3D%202%28x%20%2B%202%29%20)
Combine like terms on the left side. Distribute the 2 on the right side.
![5x = 2x + 4](https://tex.z-dn.net/?f=%205x%20%3D%202x%20%2B%204%20)
Subtract 2x from both sides.
![3x = 4](https://tex.z-dn.net/?f=%203x%20%3D%204%20)
Divide both sides by 3.
![x = \dfrac{4}{3}](https://tex.z-dn.net/?f=%20x%20%3D%20%5Cdfrac%7B4%7D%7B3%7D%20)
Answer: B. An angle that has its vertex at the center of a circle
Step-by-step explanation:
It is 2.1 inches longer. Plz plz plz give me brainiest answer I only need 3 more to rank up. If u do I will show my work and show the answer as a fraction.