The voltage of the alternating current coming through an electrical outlet can be modeled by the function V(t) = 167 sin(110πt), where t is measured in seconds and V in volts. Find all times at which the voltage is at its maximum. (Let k be any integer.

for k =0, 1,2,3............

Step-by-step explanation:

From the function

For ,

...................(1)

That is, = 1...............(2)

Comparing equations (1) and (2)

For all positive integer values of k, i.e. k = 0, 1, 2, ........

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.