the equation that models the height above or below equilibrium in inches, h, of a spring over time in seconds, t, is h=-30cos(2pi/5 t). at which times will the spring be at a height of 20 in. above equilibrium?

answer options:

1.3 seconds
1.8 seconds
3.2 seconds
4.3 seconds
5.7 seconds

there are 2 correct !

the answers are 1.8 and 3.2 seconds. So both B and C.

Step-by-step explanation:

Option 1 and 3 - 1.3 seconds and 3.2 seconds

Step-by-step explanation:

Given : The equation that models the height above or below equilibrium in inches, h, of a spring over time in seconds, t, is .

To find : At which times will the spring be at a height of 20 in. above equilibrium?        

Solution :

We have given,              

The equation that models the height above or below equilibrium in inches      

We have to find at h=20 inches the time of spring.

We show it graphically,

Plot the graph of the model  

Then, Substitute h=20

The points of their intersections are the solution of the model.

The intersection points are (1.831,20), (3.169,20) and many more.

From the given options,

The time are 1.3 seconds and 3.2 seconds.

Therefore, Option 1 and 3 are correct.    

Refer the attached figure below.  

the answer is:

the answer is:

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

then, calculating we have:

hence, the answer is:

have a nice day!