The height, h, in feet of a ball suspended from a spring as a function of time, t, in seconds can be modeled by the equation h = a sine (b (t minus h)) k. what is the height of the ball at its equilibrium?

Answers

Answer 1

Based on the height of the ball suspended from a spring, the height of the ball at equilibrium is K feet.

What is the ball's height at equilibrium?

The model for the height of the ball when it is suspended from a spring is shown as:

= aSin(b ( t - h)) + k

Given this, we can infer the value of h by looking at the general form of the Sin function which is:

y = Asin(Bx) + c

In the above:

A = amplitude

B = (2 x pi) / Period

C = midline

Comparing the function and the general Sin function, we notice that:

C = K

If C = K then it means that K is the height of the ball at its equilibrium because C as the midline represents the equilibrium height.

In conclusion, the height of the ball at equilibrium is K feet.

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Related Questions

John has $80. Every week, he spends $7.
Create an equation that represents how much money, m, he has after t weeks.
How much money, in dollars, will he have after the fourth week?
Enter the equation and the answer on separate lines.

Answers

John would have 52 dollars left by the fourth week.
7(dollars spent each week) x 4 ( number of weeks)=28 (spent in 4 weeks)

80 - 28 =52

The school production of​ 'Our Town' was a big success. For opening​ night, 391 tickets were sold. Students paid ​$4.00 ​each, while​ non-students paid ​$6.00 each. If a total of $1786 was​ collected, how many students and how many​ non-students attended?

Answers

Answer:

280 students

111 non students

Step-by-step explanation:

number of students (S)

number of non students (N)

S+N=391     S=391-N

4S+6N=1786

substitute S

4(391-N)+6N=1786

1564-4N+6N=1786

subtract 1564 from each side

2N=222

N=111

S=391-111=280

Graph the following features:
• Slope = 2
Y-intercept = -5

Answers

y = mx + b

y = 2x - 5

you can go to desmos calculator online and simply put in the equation. but what you're going to do is find -5 on the y axis. then you will go up 2 and then 1 to the right.

it should look like this:

hope this helps !!

The equation is y=2x-5

yoo hii, could yall please help me!!

Answers

1. 9x-10 (I think)
2. B. x=6
12x - 6 - 3x + 4
Rewrite, if it helps, grouping like terms
12x - 3x -6 + 4
9x -2

For the second problem, the answer is B

-2x + 15 + 7x = 45
5x = 30
x = 6

Please help me on this I need help and nobody is really helping

Answers

I believe the answer is (0,0)

Answer:

(0,0)

Step-by-step explanation:

That is the middle.

(-10,-8), (8, 10) what the slope for this plz

Answers

Answer:

1

Step-by-step explanation:

y2 - y1/x2 - x1

10 + 8/8 + 10 = 18/18 = 1

Slope = 1OR2/2OR1/1They're all the same.

que son monomios? y 4 ejemplos

Answers

una expression algebraic

5x9

xy²

8x6y

3x

find the value of z

Answers

Answer:

[tex] z = 12 \sqrt{5} [/tex]

Step-by-step explanation:

By geometric mean property:

[tex]y = \sqrt{24 \times 6} \\ \\ y = \sqrt{144} \\ \\ y = 12 [/tex]

By Pythagoras Theorem:

[tex] z = \sqrt{ {12}^{2} + {24}^{2} } \\ \\ z = \sqrt{144 + 576} \\ \\ z = \sqrt{720} \\ \\ z = 12 \sqrt{5} [/tex]

PLEASE HELP ASAP!!!
(Question in picture! Please include steps :))

Answers

Answer:

90 degree - 60 degree = 30 degree always remember yn will be 90 degree

Answer:

MN = π

Step-by-step explanation:

The arc MN is calculated as

MN = circumference of circle × fraction of circle

      = 2πr × [tex]\frac{60}{360}[/tex] ( r is the radius )

      = 2π × 3 × [tex]\frac{1}{6}[/tex]

     = 6π × [tex]\frac{1}{6}[/tex]

     = π

Platter has six veggie wraps 12 turkey wraps and cost 64.50 another platter has eight veggie wraps turkey wraps and cost 56 what is the cost of a veggie wrap

Answers

Answer:

$3.25

Step-by-step explanation:

The computation of the cost of a veggie wrap is shown below:

Let us assume the veggie strap be x

And the turkey wrap be y

Now the equations are

6x + 12y = $64.50

x + 2y = $10.75

8x + 8y = $56

x + y = 7

Now

x + 2y = $10.75

x + y = $7

y = $3.75

So x = $7 - 3.75

= $3.25

120 pounds decreased by 5%

Answers

Answer:

114 pounds

Step-by-step explanation:

114 should be the answer

I would need you to tell me the answers to each question (3 questions)

Answers

Step-by-step explanation:

For no. 4

x = 180° - 98° - 50°

x = 32°

For no. 5

x = 180°- 67°-56°

x = 57°

For no. 6

x = 180° - 22° - 47°

x = 111°

Hope it will help :)❤

which sentence demonstrates the multiplicative identity?

1. 1/2•1=1/2
2. 1/2•2=1
3. 1/2+0=1/2•

Answers

It’s 1/2•2 equals 1 because it showed correctly in the calculator. 0.5x2=1

Answer:

It’s 1/2•2 equals 1 because it showed correctly in the calculator. 0.5x2=1

Step-by-step explanation:

please please answer will give brainliest

Answers

Answer:

c

Step-by-step explanation:

.5xBxH=.5x16x5=8x5=40

Answer:

c

Step-by-step explanation:

sources: dude trust me

A certain region of America with over 500,000 households has a mean household income of $70,000 with a standard deviation of $20,000. Economists plan to take random samples of 625 households and calculate the sample mean income for each sample. Calculate the mean of the sampling distribution of x-bar.

Answers

Answer: Mean: 70,000

Standard Deviation: 500

Step-by-step explanation:

The  mean is 70, 000 and standard deviation is 800.

What is Standard Deviation?

The term "standard deviation" (or " σ ") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

Given:

A certain region of America with over 500,000 households.

Mean, [tex]\mu[/tex] = 70,000

and, Standard Deviation, [tex]\sigma[/tex] = 20,000

n = 625

So, the new mean = old mean

                               = 70, 000

and, the standard deviation = [tex]\sigma /[/tex]√n

                                              = 20,000 / √625

                                              = 20,000 / 25

                                              = 800.

Hence, the mean is 70, 000 and standard deviation is 800.

Learn more about Standard Deviation here:

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PLEASE HELP!!!! 25 POINTS!!!

don't need to answer all but someone please help with a few questions!!!

(GRAPH INCLUDED)


Which variable did you plot on the x-axis and which variable did you plot on the y-axis? Explain why you assigned the variables in that way.


Write the equation of the line of best fit using the slope-intercept formula y = mx + b. Show all your work, including the points used to determine the slope and how the equation was determined.


What does the slope of the line represent within the context of your graph? What does the y-intercept represent?


Test the residuals of two other points to determine how well the line of best fit models the data.


Use the line of best fit to help you to describe the data correlation.


Using the line of best fit that you found in Part Three, Question 2, approximate how tall is a person whose arms span is 66 inches?


According to your line of best fit, what is the arm span of a 74-inch-tall person?

Answers

Answer:

x variable

Step-by-step explanation:

HOPE IT WILL HELP YOU

Graphf (x) = 3x + 4 and a h(x) = -f(x).

Answers

Answer:

I think the answer is 56 .

The simple interest earned for certain amount for 3 years at 5% is AED. 450. The amount invested is ________.

I need the steps also

Answers

Answer:

AED 3000

Step-by-step explanation:

Let the invested amount is x

Interest rate is r = 5% simple = 0.05 timesTime is t =  3 yearsInterest amount I = AED. 450

Using the interest formula and solving for x:

P*r*t = Ix*0.05*3 = 4500.15x = 450x = 450/0.15x = 3000

The amount invested is AED 3000

Clasificación de los ángulos de acuerdo a sus aberturas

Answers

Answer:

recto, agudo, obtuso, liano, completo, convexo, cóncavo

Step-by-step explanation:

16. Solve the system of equations by graphing.
y = x + 8
y = - x- 6


Answers

Answer:

Step-by-step explanation:

x + 8 = -x - 6

2x + 8 = -6

2x = -14

x = -7

y = -7 + 8

y = 1

(-7, 1)

20 pts help...................

Answers

Answer:

[tex]3 \frac{3}{4}[/tex]

Step-by-step explanation:

We have a right rectangular prism and the question is asking for the volume.

Look for the formula of volume :

V = LWH

L being length

W being width

H being height

The formula is basically saying to multiply all sides together, so let's do as so.

[tex]2*1\frac{1}{4} * 1\frac{1}{2}[/tex]

= [tex]3 \frac{3}{4}[/tex]

Answer:

c

Step-by-step explanation:

What is the product of these two binomials?
(x^2 - 5)(2x - 1)

Answers

Step-by-step explanation:

Please refer to the attachment

what this answer
954328- 864597

Answers

Answer:

Answer is 89,731

Step-by-step explanation:

I hope it's helpful!

Answer:

89731

Step-by-step explanation:

954328 - 864597

= 89731

Hope this helps :)

Let me know if there is any mistake!!

The side lengths of a square are each 4p. By adding 3 to the length and subtracting 3 from the width, a rectangle is made. What is the area of the rectangle?

Answers

Answer:

16p^2 - 24p - 9

Step-by-step explanation:

I literally just took the test lol

A tree casts a shadow that is 9 feet long. The distance from the top of the tree to the end of the shadow is 15 feet. What is the height of the tree?​

Answers

Answer:

15 feet tall hi hi hi hi hi hi

Answer:

10

Step-by-step explanation:

a scientist is studying wildlife. she estimates the population of bats in her state to be 270,000. she predicts the population to grow at an average annual rate of 2.9 percent

using the scientists prediction, create an equation that models the population of bats, y, after t years.

Answers

Answer:

Step-by-step explanation:

y = 270,000 ×1.029^t

8-3(6-6x) please help

Answers

Answer:

-10 + 18x

Step-by-step explanation:

8-3 (6-6x)

distribute -3 with the numbers inside the parenthesis and you end up with

8 -18 + 18x

and you simplify by subtracting 18 from 8 so you get

-10 + 18x

The simplified form of the expression  8 - 3(6 - 6x) is -10+18x.

To simplify the expression 8 - 3(6 - 6x), we can apply the distributive property to remove the parentheses.

Distribute the -3 to both terms inside the parentheses:

8 - 3 × 6 + 3 × 6x

Simplify the multiplication:

8 - 18 + 18x

Combine like terms:

-10 + 18x

Therefore, the simplified expression is -10 + 18x.

To learn more on Expressions click:

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Taylor and Katy repeatedly toss a fair coin. Katy wins if heads are thrown, Taylor wins if tails are thrown, and the game ends when someone has won three times. Katy is currently behind 1 to 2. The chance Katy wins is:

Answers

Answer:

25%

Step-by-step explanation:

In order to find the chance/probability that Katy wins we need to first find the probability of her winning a single coin toss and then multiply it twice. This is because Katy has 1 win already and needs two more win the entire game. Since a coin toss only has 2 options and only 1 of those outcomes will cause Katy to win, then this means that the probability of Katy winning is 1/2 or 50%. Now we can multiply this probability twice to get the probability of Katy winning the entire game

1/2 * 1/2 = 1/4 or 25%

What is the sum of the rational expressions below? 2x + 7 / x + 5 + x - 3 / x + 5

Answers

Answer:

[tex]\frac{3x+4}{x+5}[/tex]

Step-by-step explanation:

Given

[tex]\frac{2x+7}{x+5}[/tex] + [tex]\frac{x-3}{x+5}[/tex]

Since both fractions have a common denominator then add the numerators, placed over the common denominator.

= [tex]\frac{2x+7+x-3}{x+5}[/tex]

= [tex]\frac{3x+4}{x+5}[/tex]

Answer:

The answer is

[tex] \frac{3x + 4}{x + 5} [/tex]

Step-by-step explanation:

We can do this by using the denominators.

[tex]then \\ \frac{2x + 7}{x + 5} + \frac{x - 3}{x + 5} \\ = \frac{2x + 7 + x - 3}{x + 5} \\ = \frac{3x + 4}{x + 5} [/tex]

find the length and the breadth of a rectangular plot whose area is 660 sq.m and its perimeter is 104​

Answers

Answer:

find the mean median mean devialion

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