5. (6 pts pts) The displacement of a spring vibrating in damped harmonic motion is given by
y = 4e-3t sin(2πt)
Find the times when the spring is at its equilibrium position (y = 0). '

The  times when the spring is at its equilibrium position (y = 0) are t = 0, 1/2, 1, 3/2, ... and so on.

To find the times when the spring is at its equilibrium position (y = 0), we can set the displacement equation equal to zero and solve for t:

[tex]4e^{(-3t)[/tex] sin(2πt) = 0

Since the product of two factors is zero if and only if at least one of the factors is zero, we have two cases to consider:

4[tex]e^{(-3t)[/tex] = 0

This equation has no solution since [tex]e^{(-3t)[/tex] is always positive and nonzero.

sin(2πt) = 0

The sine function is zero at integer multiples of π.

So, we can set 2πt equal to integer multiples of π:

2πt = 0, π, 2π, 3π, ...

Solving for t in each case, we get:

t = 0, 1/2, 1, 3/2, ...

Therefore, the times when the spring is at its equilibrium position (y = 0) are t = 0, 1/2, 1, 3/2, ... and so on.

Learn more about Integral Multiple here:

https://brainly.com/question/30156681

#SPJ1

PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA POINTS*..
IM GIVING 40 POINTS !! DONT SKIP :((.

Solve for x. Enter the solutions from least to greatest.
(2+8)^2 – 2 = 0
lesser x =
greater x =

Help me answer question 2 ​

Find the circumference of the circle.
4 mi
Find The circumference
(Type an exact answer in terms of pie)

A ticket to Silver Dollar City costs $125. You have a coupon that will save you 33%. How much will you SAVE? In the same scenario, how much will you end up SPENDING for you ticket if you use your coupon?

Using the data from the table, which statements are correct?
A)
The ratio of Y is consistent.
Х
G
B)
The ratio of Y is not consistent.
Х
C)
The table represents a proportional relationship.
D)
The table does not represent a proportional relationship.
E)
The graph of the data shown on the table is a straight line.

HELPP I NEED THIS BY 2:30

The second angle of a triangle is 7 more than twice the first angle. The third angle is 3 less than the first. Find all
three angles if the sum of their angles is equal to 180°. (Let x = the measure of the first angle)

If bananas are $0.50 each, how much would it cost for 7 bananas?

The sum of three numbers is 123. The second number is 8 more than the first. The third number is 3 times the first. What are the numbers ?

First number:

Second number:

Third number:

how do i answer this question?

1. A bank account started with $1000 and earned $10 interest per month
for two years. The bank then paid 2% interest on the account for the
next two years.

A number line going from 1 to 13. 1 dot is above 1. 3 dots are above 2. 1 dot is above 3. 3 dots are above 4. 1 dot is above 5. 0 dots are above the remaining numbers. If a new data point at 12 is added to the graph, which will be true? The mean will increase, and the median will stay the same. The median will increase, and the mean will stay the same. The mean will increase more than the median, but both will increase. The median will increase more than the mean, but both will increase.

find the sum of 3/4 and 5/7.​

The local ranger station tracked and tagged 2,844 adult female black bears in a national park. A random sample of 9 adult female black bears from those tagged had an average body weight of 203 pounds with standard deviation 25 pounds. Which of the following is a point estimate for the population mean weight of all female black bears that are tagged?

a. 9
b. 25/√9
c. 25
d. 203
e. 2,844

Will make 1st answer brainleist

Al simplificar la fraccion 150/600 a su mínima expresión se obtiene 15/6
​

-Let g(x) be a function defined by g(x) = x3.
a) Sketch the graph of g(x).
b) Find the inverse g-1(x) of g(x) then sketch the graph of g-1(x). c) Specify the domain and range of g(x) and g-1(x).
d) Determine the end behavior of g(x) and g-1(x).

Which of the following graphs is the solution set of 2x+7>3?
PLS HELP WILL MARK BRAINLIEST

PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA POINTS*..
IM GIVING 40 POINTS !! DONT SKIP :((.

2x + y = 7
-2x - y = 6
Solve systems of equations by substitution

Select the correct option from the menu.
Raj determined that the equation 3 (x+3) = 8 - 5x +7 is equivalent to 9 = 7. This means that this equation has:
no solutions

One solution

Two solutions

Infinity many solutions

2x + y = 2
x - y = 1

In the evening, a water tank contained 30cm of water. A few days later, it contained 21 cm of water. Ahmed claims that there is a 30% decrease. is Ahmed correct

answer this for me pls

If the markup rate is 50%, then the cost of a shirt that regularly sells for $60 is $40. true or false?​

If y varies directly as x and y =6 when x =2 ... find y when x=9

A coffee table is on sale for 20% off the original price of $115. If there is a 6% sales tax, what is the final price of the coffee table?

Which of the following is equal to this expression? (256⋅64)^1/4

Write the formula for slope, for the point-slope
form of a line, and for the slope-intercept form of a
line.

Carla draws two rectangles.
One of the rectangles has an area of 35 square inches.
The other has a perimeter of 20 inches
Select the two rectangles that could be the rectangles Carla draws
A rectangle with a width of 2 inches and a length of 6 inches
A rectangle with a width of 2 inches and a length of 8 inches
A rectangle with a width of 4 inches and a length of 6 inches
A rectangle with a width of 5 inches and a length of 7 inches
A rectangle with a width of 6 inches and a length of 10 inches