An object is dropped from a height of 150 feet. Its heights s at time, t is given by the

equation s(t) =-16t^2+150 ,where s is measured in feet and t is measured in seconds.

Find the average rate of change of the height over the interval [1, 2.5).

O 1) -56 ft/sec

O2) 77 ft/sec

03) 56 ft/sec

O4) -35 ft/sec

Answers

Answer 1

Answer:

The average rate of change of the height over the interval [1, 2.5] is - 56 feet per second.

Step-by-step explanation:

Let [tex]s(t) = -16\cdot t^{2} + 150[/tex]. Geometrically speaking, average rate of change over a given interval ([tex]\bar v[/tex]), measured in feet per second, is determined by definition of secant line, which is defined:

[tex]\bar v = \frac{s(t_{2})-s(t_{1}) }{t_{2}-t_{1}}[/tex] (1)

Where:

[tex]s(t_{1})[/tex], [tex]s(t_{2})[/tex] - Initial and final position of the object, measured in feet.

[tex]t_{1}[/tex], [tex]t_{2}[/tex] - Initial and final times, measured in seconds.

If we know that [tex]t_{1} = 1\,s[/tex] and [tex]t_{2} = 2.5\,s[/tex], then the average rate of change over the interval [tex][1,2.5][/tex]:

[tex]s(1) = -16\cdot (1)^{2}+150[/tex]

[tex]s(1) = 134[/tex]

[tex]s(2.5) = -16\cdot (2.5)^{2}+150[/tex]

[tex]s(2.5) = 50[/tex]

[tex]\bar v = \frac{50\,ft-134\,ft}{2.5\,s-1\,s}[/tex]

[tex]\bar v = -56\,\frac{ft}{s}[/tex]

The average rate of change of the height over the interval [1, 2.5] is - 56 feet per second.


Related Questions

What are the terms in x - 53 - 4x - w + 6x + 8

Answers

Answer:

3x, -45, -w

Step-by-step explanation:

We want to simplify this expression to find which terms there are.

x - 53 - 4x - w + 6x + 8

We can group the x's, w's and constants.

(x - 4x + 6x) + (-53 + 8) + (-w)

3x - 45 - w

The terms are, 3x, -45, -w

Answer is 3x-w-45 how did I get the answer.

1. steps: x- 53 - 4x - w + 6x + 8

2. Steps: Group like terms x - 4x + 6x - w -53 + 8

3. Steps: Addsimilar elements: x - 4x + 6x = 3x

= 3x - w - 53 + 8

4. Steps: Add/Subtract the numbers: - 53 + 8 = -45

= 3x - w -45

That is your answer for this problem.

You are offered a job that pays ​$41,000 during the first​ year, with an annual increase of 7​% per year beginning in the second year. That​ is, beginning in year​ 2, your salary will be 1.07 times what it was in the previous year. What can you expect to earn in your fourth year on the​ job? Round your answer to the nearest dollar.

Answers

Answer:

50227

Step-by-step explanation:

very confusing , help me out please ...?

Answers

Step-by-step explanation:

[tex] \sqrt{7} = {7}^{ \frac{1}{2} } = \sqrt{7} [/tex]

lena purchased a prepaid phone card for $20. long distance call cost 18 cents a minute using this card. Lena used her cared only once to make a libg distance call. if the remaining credit on her card is $13.34, how many minutes did her call last?

Answers

Answer:

37 minutes

Step-by-step explanation:

We start by finding the difference between the original amount and what is left

Mathematically, that will be;

20-13.34 = 6.66

To

cents that will be 6.66 * 100 = 666 cents

We now divide by the amount per minute

The amount per minute is 18 cents

Thus, the number of minutes will

be 666/18 = 37

Help me please!!

What is the speed of a wave with a wavelength of 2.0 m and a frequency of 6.0 Hz?

Answers

6m/s

calculate the number of balloon that can be filled up.

Step-by-step explanation:

speed =wavelength ×Frequency

=6×2 =12m/d

Indicate below whether the equation in the box is true or false 1/8 = to 2/4 true or false​

Answers

Answer:

false

Step-by-step explanation:

1/8 = .125

2/4 = .5

therefore 1/8 does not = 2/4

What is the equation of the linear function represented by the table?

y=-X+9
y=-x+ 13
Y = X+ 13
Y = X+9

Answers

Answer:

Step-by-step explanation:

I am sorry but please give detailed question where is the table

Equivalent factored form for 10x^2+15x-9=2x^2+x-14

Answers

Factored form - x= -1/2, -5/4

Simplify: ⅕y - ⅗y + 5 - ⅖y - 8
pls

Answers

Answer:

The answer is -(4/5)y - 3.

Step-by-step explanation:

The steps are :

[tex] \frac{1}{5} y - \frac{3}{5} y + 5 - \frac{2}{5} y - 8[/tex]

[tex] = ( \frac{1 - 3 - 2}{5} y) + (5 - 8)[/tex]

[tex] = - \frac{4}{5} y - 3[/tex]

Step-by-step explanation:

⅕y - ⅗y + 5 - ⅖y - 8

-0.8y-3

-4/5y-3

Someone plz help me

Answers

Answer:

8.5 i think

Step-by-step explanation:

Answer:

the answer would be 8.5 inches

Step-by-step explanation:

its 8and a half not 0.85 so its placed wrong

solve the equation P=b+c+a solve for b

Answers

Answer:

b = P - c - a

Step-by-step explanation:


hello , how to do 6(iii)?

Answers

Answer:

[tex]\displaystyle \frac{dS}{dt}=\frac{3}{50r}[/tex]

Step-by-step explanation:

Water is being pumped into an inflated rubber sphere at a constant rate of 0.03 cubic meters per second.

So, dV/dt = 0.03.

We want to show that dS/dt is directly proportional to 1/r.

In other words, we want to establish the relationship that dS/dt  = k(1/r), where k is some constant.

First, the volume of a sphere V is given by:

[tex]\displaystyle V=\frac{4}{3}\pi r^3[/tex]

Therefore:

[tex]\displaystyle \frac{dV}{dt}=4\pi r^2\frac{dr}{dt}[/tex]

Next, the surface area of a sphere S is given by:

[tex]\displaystyle S=4\pi r^2[/tex]

Therefore:

[tex]\displaystyle \frac{dS}{dt}=8\pi r\frac{dr}{dt}[/tex]

We can divide both sides by 2:

[tex]\displaystyle \frac{1}{2}\frac{dS}{dt}=4\pi r\frac{dr}{dt}[/tex]

We can substitute this into dV/dt. Rewriting:

[tex]\displaystyle \frac{dV}{dt}=r\Big(4\pi r\frac{dr}{dt}\Big)[/tex]

So:

[tex]\displaystyle \frac{dV}{dt}=\frac{1}{2}r\frac{dS}{dt}[/tex]

Since dV/dt = 0.03 or 3/100:

[tex]\displaystyle \frac{3}{100}=\frac{1}{2}r\frac{dS}{dt}[/tex]

Therefore:

[tex]\displaystyle \frac{dS}{dt}=\frac{3}{50r}=\frac{3}{50}\Big(\frac{1}{r}\Big)[/tex]

Where k = 3/50.

And we have shown that dS/dt is directly proportional to 1/r.

The diameter of a plant cell measures about 0.00012 m.
What is this number in scientific notation?
A
0.12 x 10-3
B 1.2 x 10-4
1.2 x 10-5
12.0 x 10-5

Answers

A: 0.12 X 10-3

Remember that you have to go to the right 3x.

I really hope this helped you, and have a blessed day.

A new bank customer with $3,500 wants to open a money market account. The bank is offering a
simple interest rate of 1.1%.
a. How much interest will the customer earn in 10 years?
b. What will the account balance be after 10 years?

Answers

Answer:

A. they will earn 385 dollars in interest in ten years

B. the accounts balance will be $3,885 after 10 years

Step-by-step explanation:

for part A, there are 2 possible answers, depending on what your looking for, if your looking for the percentage interest, then its 11%, but if your looking for how much they will make off of interest in 10 years, then the answer would be $385.  

n
Which equation represents the line that passes through (-6, 7) and (-3, 6)?
O y=-x+9
y=-*x+5
y=-3x - 11y
y=-3x + 25

Answers

Answer:

Y=-3x-11y

Step-by-step explanation:

Not sure but I am pretty sure it is this

Suppose that 8% of all cars produced at Plant A have a certain defect, and 5% of all cars produced at Plant B have this defect. A quality control manager takes separate random samples of 150 cars from each plant. The manager will then look at the difference (A-B) between the proportions of cars with the defect in each sample.

What will be the shape of the sampling distribution of the difference in sample proportions, and why?

Choose 1 answer:

A. Approximately normal, because we expect 12 defective and 138 defect-free cars from Plant A, and 15 and 135 from Plant B, and all of these counts are at least 10.

B. Approximately normal, because we expect 16 defective and 134 defect-free cars from Plant A, and 10 and 140 from Plant B, and all of these counts are at least 10.

C. Not normal, because we expect fewer than 10 defective cars in Plant A.

D. Not normal, because we expect fewer than 10 defective cars in Plant B.

Answers

Answer:

Not normal, because we expect fewer than 10 defective cars in plant B

Step-by-step explanation:

Answer: D

Not normal, because we expect fewer than 10 defective cars in Plant B. [tex].05*150=7.5[/tex]

Step-by-step explanation: Khan Answer

What is r - 8.5 = -2.1 pls help♥️

Answers

Answer:

r=6.4

Step-by-step explanation:

Get r by itself you need to add 8.5 to get 6.4

Hope this helps (:

Answer:

r-8.5=-2.1

r=-2.1+8.5

r=6.4

Step-by-step explanation:

Find the sum of 0.5 and -0.5.

Answers

Amswer

The answer is 0

A ______________ is a relation that assigns exactly one output value to one input value

Answers

Answer:

A __function__ is a relation that assigns exactly one output value to one input value.

Step-by-step explanation:

Answer:

A function is a relation that assigns exactly one output value to one input value.        

PLS HELP!!!!!!!!!!!!!!!!!!!!!!!!
A rectangular pyramid has a volume of 216 in³. A rectangular prism has the same height as the rectangular pyramid and a base that is congruent to the base of the rectangular pyramid.

What is the relationship between the volume of the rectangular pyramid and the rectangular prism?

A.The volume of a rectangular prism is 2 times the volume of a rectangular pyramid. The volume of the rectangular prism is 432 in3.

B.The volume of a rectangular prism is 13 the volume of a rectangular pyramid. The volume of the rectangular prism is 72 in3.

C.The volume of a rectangular prism is 12 the volume of a rectangular pyramid. The volume of the rectangular prism is 108 in3.

D.The volume of a rectangular prism is 3 times the volume of a rectangular pyramid. The volume of the rectangular prism is 648 in3.

Answers

The relationship between a prism and a pyramid is the volume of a rectangular prism is 3 times the volume of a rectangular pyramid. The volume of the rectangular prism is 648 in3.

What is a rectangular prism?

A rectangular prism is a 3-dimensional object. It has six rectangular faces .  It has 8 vertices, 6 faces, and 12 edges. The volume of a rectangular prism = width x height x length

What is a rectangular pyramid?

A rectangular pyramid is a three-dimensional object. It is made up of a rectangular base and a triangular face.  The volume of a rectangular pyramid = 1/3(width x height x length )

To learn more about rectangle pyramid, please check: https://brainly.com/question/9222686

Answer:

It  is C

Step-by-step explanation:I Have the exact answer on my test

help I will give brainless to whoever answers correctly​

Answers

Answer:

The answer to this question is 9cm^2, the second answer

Step-by-step explanation:

To find the area of this parallelogram, you have to first find the area of one of the two triangles shown. The formula to solve a triangle is (base * height)/2, so that would be 4.5cm^2 for each triangle, times two for two triangles would be 9cm^2. If you wanted to do it an easier way, just multiply the length of the bottom of the parallelogram with the height. The measures telling you 3.5 are telling you the length of the diagonal line, so don't pay attention to that.  

Here is the sales tax on the same items in City 3.
What is the tax rate in this city? Show work on the
sketch. (Remember to round to the nearest penny.)
Sales tax percentage
Check
For the sales tax on the laundry soap, Kiran says it
should be $0.84. Lin says it should be $0.87. Do you
agree with either of them? Explain your reasoning.
I agree with Kiran
I agree with Lin
I don't agree with either of them
Explain your thinking.
cause your multiplying the numbers
Edit my response

Answers

Answer:

This needs more detail.

Step-by-step explanation:

Someone please help and PLEASE make sure it’s right! Thank you!!! :)

Answers

Answer:

7

Step-by-step explanation:

i have checked, i have spoken

A taxi travels 2 hours to make a 220 km trip. How fast does it travel?

Answers

He would be driving approximately 110 km an hour

Answer:

= 110 km/h

Step-by-step explanation:

speed = km / 1 hr

distance = 220

time = 2 hrs

speed = 220 / 2 = 110 km/h

(Hope its right!)

in training to run a half marathon, jenny ran 2/5 hours on tuesday, 1 1/6 hours on thursday, and 2 1/15 on Saturday. what is the total amount of hours that jenny ran this week? (simplify your answer and state it as a MIXED NUMBER)

Answers

9514 1404 393

Answer:

  3 19/30 hours

Step-by-step explanation:

The given fractions will have 30 as a common denominator.

  12/30 + 1 5/30 + 2 2/30 = (1 +2) +(12 +5 +2)/30 = 3 19/30 . . . hours

Jenny ran 3 19/30 hours this week.

Answer:

Step-by-step explanation:

Total hours that Jenny ran = 3.63 hours.

Step-by-step explanation:

Jenny ran on Tuesday for = 2/5 hours or 0.4 hours.

Time consumed to run on Thursday = 11/6 hours or 1.83 hours.

Time consumed to run on Saturday = 21/ 15 hours or 1.4 hours.

Here, the total hours can be calculated by just adding all the running hours. So the running hours of Tuesday, Thursday, and Saturday will be added to find the total hours.

Total hours that Jenny ran = 0.4 + 1.83 + 1.4 = 3.63 hours.

jack paid 36.25 for 12 1/2 for his car what is the price per gallon​

Answers

Answer:

66.89

Step-by-step explanation:

Solve 0 = x2 + 6x + 13 by completing the square.

A. x = 5 and x = 1
B. x = 3 + i22−−√ and x = 3 − i22−−√
C. x = −1 and x = 1
D. x = −3 + 2i and x = −3 − 2i

Answers

Answer:

x = -3 - 2i and x = -3 + 2i

Step-by-step explanation:

I was too lazy to complete the square but solved it on WolframAlpha

x /− 8 + 9 = 43 x = ?
Solve for x Round to the nearest 100th if needed.

Answers

Answer:

I love algebra anyways

The ans is in the picture with the  steps how i got it

(hope this helps can i plz have brainlist :D hehe)

Step-by-step explanation:

A total of 150 tickets were sold for the annual concert. Student tickets were $4 and non-students $8. If the total revenue was $840, how many tickets of each type were sold ?

Answers

Answer:

x = 90

y = 60

Step-by-step explanation:

Let x = student

Let y = non-student

x + y = 150

4x + 8y = 840 <—— Use elimination/addition ethos for both equations

8 (x + y = 150)

-1 (4x + 8y = 840) <—— Let’s eliminate y

8x + 8y = 1200

+ -4x - 8y = -840

—————————————

4x = 360

x = 90

x + y = 150 <— substitute for x from above

90 + y = 150

- 90 = - 90 <— subtract from both sides

y = 60

Indicate whether the following question is a statistical question. Explain why or why not.
How much does Susan’s dog weigh?

Answers

It’s a question because there is not value of time.
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