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

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

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Need more information

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

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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Answer:

Smoke, Condensation, mist

Step-by-step explanation:

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Answer:

1. Train B is faster

Step-by-step explanation:

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

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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.

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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646 divided by 9 long division with a reimandeir

Answers

Answer:

71 R. 7

Step-by-step explanation:

Hope this helps!

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Answers

Answer:

1.9 degrees above the normal temperture

Step-by-step explanation:

Normal temperture: 98.6 degrees Fahrenheit

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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.
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It has helped boost the nation’s military.
It has helped shift the nation’s death rate.
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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

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Answers

Answer:

I think it's 3

Step-by-step explanation:

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

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Answers

Answer: C) add 5 to both sides

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(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.

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C is your answer

Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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1? Isn’t it like a prime number

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Answers

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Step-by-step explanation:

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Step-by-step explanation:

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Answers

Answer:

15

Step-by-step explanation:

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6*3=15

Answer:

27

Step-by-step explanation:

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earns
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Answers

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

:)

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

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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.

1. What are vertical angles?
2. what us the relationship of vertical angles?
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Answers

Answer:

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

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there are 46.80 milligrams in 6 ounces.

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Answer:

B is the answer

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Answer:

Step-by-step explanation:

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Answer:

C

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Answers

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

Explanation:
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Answer:

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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].

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