An object oscillates as it moves along the x-axis. Its displacement varies with time according to the equation x = 4 cos(πt + π/4) where t is in seconds What is the frequency of this motion?

This is equivalent to the fraction 1/2

Explanation:

The template for cosine is

y = A*cos(B(x-C)) + D

The B determines the period T

T = 2pi/B

In this case, B = pi,

T = 2pi/B

T = 2pi/pi

T = 2

The period is 2 seconds, which is the length of each cycle.

The frequency is 1 over the period

frequency = 1/(period)

F = 1/T

F = 1/2

F = 0.5

The frequency is 0.5 hertz to indicate that it completes 0.5 a cycle in 1 second. In other words, the speed of the object (so to speak) is 0.5 cycles per second.

a

step-by-step explanation:

when a number is between two straight lines it means the absolute value.

to find absolute value you need to know how many numbers is that number away from 0.

when finding absolute value the number will always come out positive

so absolute value of -3 is 3

absolute value of 3/2 is 3/2

absolute value of -2 is 2

absolute value of 3.5 is 3.5

absolute value of -1 is 1

now put these numbers in order:

a)   |-1|, |3/2|, |-2|, |-3|, |3.5|

a mantle plume is an upwelling of abnormally hot rock within the earth's mantle. as the heads of mantle plumes can partly melt when they reach shallow depths, they are thought to be the cause of volcanic centers known as hotspots and probably also to have caused flood basalts.

step-by-step explanation: