For what values of k does the function y = cos(kt) satisfy the differential equation 81y'' = â16y? (Enter your answers as a comma-separated list.)K =

16/81

Step-by-step explanation:

Given the expression, 81y'' = -16y where y = coskt,

We want to know the value of k that satisfies the expression

y' = -ksinkt

y" = -k²coskt

Substitute y and y" into the expression given;

81y'' = -16y

81(-k²coskt) = -16(kcoskt)

-81k = -16

Divide both sides by -81

-81k/-81 = -16/-81

k = 16/81

Hence the value of k is 16/81

80π/3 or about 83.775

step-by-step explanation:

since a cone is 1/3 of a cylinder, we need to find the base's area. since area = πr^2, we get 16π. then, multiplying this by 5, we get 80π. dividing by 3, since the cone's volume is 1/3 of that of a cylinder's, we get 80π/3.

hope this !

answer is 12345678900987654321234567890987654321

step-by-step explanation: