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.  

< coa = 150 ( given)

as ba and bc are tangents

so oc and oa is perpendicular to cb and ab respectively because in circle normal passes through centre

so in quadrilateral oabc

< coa + < oab + < ocb + < abc = 360

150 +90+90 + < abc = 360

330 + < abc = 360

< abc = 360 -330 = 30

so < abc = 30

⭐dhruv⭐