To rewrite y(t) = 2sin4πt + 5cos4πt in the form asin(ωt+φ), solve for φ. show your work and solution in the response box.

¢=68.2

Step-by-step explanation:

y(t) = 2sin4πt + 5cos4πt

Let , x = Asin¢ = 5

y = Acos¢ = 2

A = sqrt(5²+2²)

A= 5.39

y(t) = Acos¢sin4πt + Asin¢cos4πt

From Trigonometry rule,

y(t)= Asin(wt +¢)

tan¢ = 5/2

¢ = arctan(5/2) = 68.2°

y(t) = 5.39sin(wt + 68.2)

Where w = 4π

The angle ¢= 68.2°

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).

idk lol

step-by-step explanation: