The distance traveled, D in feet, is a function of time, t, in seconds, with
D=f(t)= t 3 +1
​Find f(10), f'(10), and the relative rate of change f'/f at t=10. Interpret your answers in terms of distance travele

Answers

Answer 1

Answer:

1001 m/s

300 [tex]m/s^2[/tex]

0.299.

Step-by-step explanation:

Given that:

[tex]D=f(t)=t^3+1[/tex]

[tex]f(10)[/tex] means putting the value of [tex]t=10[/tex] in [tex]f(t)[/tex].

[tex]f(10) = 10^3+1=1001[/tex] [tex]m/s[/tex]

To find [tex]f'(10)[/tex], we need to find [tex]f'(t)[/tex] first.

Differentiating the equation of Distance [tex]D[/tex] w.r.to [tex]t[/tex]:

[tex]f'(t) = \dfrac{d}{dt}(t^3+1)= 3t^{3-1}+1 = 3t^2[/tex]

[tex]f'(10) = 3(10)^2=300[/tex] [tex]m/s^2[/tex]

Relative rate of change:

[tex]\dfrac{f'}{f}\ at\ t = 10 \Rightarrow \dfrac{300}{1001} \approx 0.299[/tex]


Related Questions

Help i am stuck please be fast

Answers

Answer:

Step-by-step explanation:

They are alike because both involve steps for multiplication and addition but part b uses factoring in its estimation to solve the problem while part c dosesn't.

A penny is thrown from the top of a 26.6-meter building and hits the ground 3.59 seconds after it was thrown. The penny reached its maximum height above the ground 0.77 seconds after it was thrown.

1. Define a quadratic function, h, that expresses the height of the penny above the ground (measured in meters) as a function of the number of seconds elapsed since the penny was thrown, t.

2.What is the maximum height of the penny above the ground?

Answers

Answer:

it is at 200 mph

Step-by-step explanation:

bc i did the test

The quadratic function which models the motion of the penny is h(t) = -4.9t² + 10.18t + 26.6 and the maximum height reached is 31.53 meters

The relationship can be expressed in the form :

h(t) = - 0.5gt² + vt + h (downward motion)

g = 9.8 m/s²

h = 26.6 m

v = ?

We can obtain v thus ;

h(t) = -0.5gt² + vt + 26.6

h(t) = - 4.9t² + vt + 26.6

Time when penny hits the ground ; t = 3.59

h(3.59) = 0

0 = -4.9(3.59)² + v(3.59) + 26.6

− 63.15169 + 3.59v + 26.6 = 0

3.59v = 36.55169

v = 36.55169 /3.59

v = 10.181 m/s

Equation becomes :

h(t) = -4.9t² + 10.18t + 26.6

2.) The maximum height of the penny above the ground ;

t = 0.77 seconds

h(0.77) = -4.9(0.77^2)+ 10.18(0.77) + 26.6

Maximum height reached = 31.53 meters

Therefore, the maximum height reached is 31.53 meters

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646 divided by 9 long division with a reimandeir

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Answer:

71 R. 7

Step-by-step explanation:

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Answers

Answer:

x represents +50 for every hour. the inequality is y = 4x + 500 or y = x + 500.

they can ride it for 4 hours

Step-by-step explanation:

y(total cost) = x(50 per hour) + 500(y-intercept)

4. In the equation y = 8x , what is your constant?
A)y
B)8
C)x
D)0

Answers

Answer: it should be 8

1. What are vertical angles?
2. what us the relationship of vertical angles?
3. Name two pair of vertical angles.

Answers

Answer:

1:each of the pair of opposite angles made by two intersecting lines are known as vertical angles

2. the angles opposite Each Other when two lines cross they are all always equal for example" a " and "b" all vertical angles " vertical " refer to the vertex where they cross

PLA HELP QUESTION IN PHOTO

Answers

Answer:

Step-by-step explanation:

its the first one

Answer:

C

Step-by-step explanation:

Coconut oil freezes at a high temp, and there for is a greater number.

Danielle earns $36.80 for 4 hours of yardwork. MacKenzie earns $50.40 for 6 hours of yardwork.
Who earns more money per hour? How much more? Use the drop-down menus to show your answer.


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earns
Choose...
more per hour.

Answers

Answer:It is Danielle i guess cause she earns 9.2 each hour and MacKenzie gets 8.4 an hour

:)

I need help with this question!!!! Plzz

Answers

Answer:

y=-5x+9

Step-by-step explanation:

Answer:

y = -5x + 9

Step-by-step explanation:

Plug each of the x values into this equation and see if you get the corresponding outputs for y, it should work fine.

PLEASE HELP!!! Rachel plays a game rolling 2 number cubes numbered 1-6. To win the game she must roll an 11. What is the probability that Rachel will win the game?
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Answers

Answer:

The probability that Rachel will win the game p(E) = 1/18 =0.055

Step-by-step explanation:

A gumball machine has 300 red gumballs. If the red gumballs are 75% of the total number of gumballs, how many gumballs are in the gumball machine?

225
275
375
400
BRAINLIST,EXTRA POINTS, 5 STARS, AND HEART

Answers

Answer:

The answer is 400

Step-by-step explanation:

Percent is to 100 as part is to whole.

In this case we have no whole but we have a part, and we have a percentage. 100% is equal to the whole so, 300 divided by 4 is 75 and what you do on the top is what you do on the bottom; 100x4=400

Use distributive property to complete the equivalent expression. Enter your answer in the boxes. 4(y - 3) =

Answers

The answer is 4y-12
Answer: 4y-12


Good luck

I NEED HELP! I WILL MARK YOU AS BRAINLIEST IF YOU ANSWER CORRECTLY! :D

Answers

Answer:

1. Train B is faster

Step-by-step explanation:

Train b travels a greater distance in 2 hours than train A.

Train B travels 250 miles in 2 hours, while Train A travels only 120 miles.

Yolanda writes a 1,500 word essay about the American Revolutionary War.
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Answers

about 4 days if you round

Stem question, can you plz tell me 3 types of natural water vapor other that steam, fog, and clouds, thanks.

Answers

Answer:

Smoke, Condensation, mist

Step-by-step explanation:

<3

Please helppp
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Answers

Answer: [tex]y=\frac{-x}{w-3}[/tex]

Step-by-step explanation:

To solve for y, we want to isolate y.

[tex]w=\frac{3y-x}{y}[/tex]             [multiply both sides by y]

[tex]yw=3y-x[/tex]         [subtract both sides by 3y]

[tex]yw-3y=-x[/tex]      [factor out y]

[tex]y(w-3)=-x[/tex]     [divide both sides by (w-3)]

[tex]y=\frac{-x}{w-3}[/tex]

Now, we know that [tex]y=\frac{-x}{w-3}[/tex].

Evaluate 8x when x = 3.12​

Answers

Answer:

24.96

Step-by-step explanation:

When you do 8 times 3.12, because 8x (8 times x), you would get 24.96.

i need help with this ^

Answers

Answer:

I think it's 3

Step-by-step explanation:

If 2 is c than subtract  it and it's 3?

8. Kim has a fever. Her temperature is 100.5 degrees Fahrenheit. Norr
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Answers

Answer:

1.9 degrees above the normal temperture

Step-by-step explanation:

Normal temperture: 98.6 degrees Fahrenheit

100.5 - 98.6 =  1.9  

The length of the diagonal of a squere is 36 feet. Find the length of the side of the square.
I need help with this pls

Answers

Step-by-step explanation:

by PT,

36^2 = length^2 x length^2

length = 6 feet

Topic: Pythagoras theorem

If you like to venture further, do check out my insta (learntionary) where I regularly post useful math tips! Thank you!

In a two-digit number, the units digit is 5 more that the tenth digit. The number itself is three times the sum of its digits. What is this number?

Answers

Answer:

15

Step-by-step explanation:

1+5=6

6*3=15

Answer:

27

Step-by-step explanation:

A system is described by the equations2x + 3y = 10 4x + By = 20 For what value of B will the system have infinitely many solutions?

Answers

B=6
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B would equal 6 since the first equation is being doubled to get the second equation
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I need help desperately

Answers

Answer:

B is the answer

Step-by-step explanation:

Look at where the decimal is placed and the value of the numbers

PLZ HELP AND PLEASE HURRY 10 POINTS AND BRAINLIST IF RIGHT!!!

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Need more information

My fellow Americans, tonight, I’d like to talk with you about immigration.
For more than 200 years, our tradition of welcoming immigrants from around the world has given us a tremendous advantage over other nations. It’s kept us youthful, dynamic, and entrepreneurial. It has shaped our character as a people with limitless possibilities—people not trapped by our past, but able to remake ourselves as we choose.
–Address to the nation on immigration, President Obama, 2014
Which advantages of immigration does President Obama name in this passage? Check all that apply.
It has helped create new businesses.
It has helped boost the nation’s military.
It has helped shift the nation’s death rate.
It has shaped the character of the country.
It has given us benefits that other countries do not have.

Answers

Answer:

A, D, and E

so basically, It has helped create new businesses. It has shaped the character of the country.  It has given us benefits that other countries do not have.

Answer:

A,D, and E

Step-by-step explanation:

just answered the question

11 coommon factor of​

Answers

1? Isn’t it like a prime number

What is the first step needed to solve 4 over 7 multiplied by x minus 5 equals negative 13? Subtract 13 from both sides Divide both sides by 7 Add 5 to both sides Multiply both sides by 4

Answers

Answer: C) add 5 to both sides

The given equation is

(4/7)x - 5 = -13

To solve this, we follow PEMDAS in reverse undoing each operation. Normally parenthesis is the first thing we look for, but instead we start with subtraction.

So we'll undo subtraction which means we add 5 to both sides

Answer:

C is your answer

Step-by-step explanation:

Please help does anyone know the answer?

Answers

Answer:

.75 i think

Step-by-step explanation:

There are 3.9 milligrams of calcium in a ½ ounce of cooked chicken. How many milligrams are in 6 ounces?

Answers

Answer:

there are 46.80 milligrams in 6 ounces.

Step-by-step explanation:

A local park is in the shape of a square. A map of the park is made with the scale of 1 inch to 200 feet. If one side of the park on the map is one foot long, how long is the side of the park in real life?

Answers

Answer: The side of the park is 2,400 feet long.

Explanation:
Scale is 1in:200ft
One foot = 12in
The fraction 1/200 = 12/x, which is cross multiplication.
1 times x = 1
12 times 200 = 2400
1 times 2400 = 2400
So that one side equals 2,400ft.
& since it’s a square that means all sides are equal no matter which is talking about.
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