Question

Q6 Q2.) A ball on a spring is pulled 8 inches above its rest position and then released. After t​ seconds, the​ ball's distance,​ d, in inches from its rest position is given by the equation below.

Answer 1

d = 8cos[(pi/3)t] = 4, solve general formula for t

cos[(pi/3)t] = 4/8 = 1/2

(pi/3)t = pi/3 + n*2pi where n is an integer

t = 1 + 6n

Answer 2

All the value of t will be given as 1, 5, 7, 11,... and so on.

What is a function?

A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.

A ball on a spring is pulled 8 inches above its rest position and then released.

After t​ seconds, the​ ball's distance,​ d, in inches from its rest position is given by the equation below.

d = 8 cos [(π/3)t]

Then all the value of t for which the ball is 4 inches above its rest position will be

4 = 8 cos [(π/3)t]

0.5 = cos [(π/3)t]

Taking cosine inverse on both sides, then the equation will be

(π/3)t = π/3, 5π/3, 7π/3, 11π/3, …..

t = 1, 5, 7, 11,....

Thus, all the value of t will be given as 1, 5, 7, 11,... and so on.

More about the function link is given below.

https://brainly.com/question/5245372

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