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

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

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.

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

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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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.
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Answers

Answer: it should be 8

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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:

15

Step-by-step explanation:

1+5=6

6*3=15

Answer:

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Step-by-step explanation:

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Need more information

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Answer:

Step-by-step explanation:

its the first one

Answer:

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

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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.

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:

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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.

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

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Answers

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646 divided by 9 long division with a reimandeir

Answers

Answer:

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Step-by-step explanation:

Hope this helps!

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?
Express your answer as a fraction and a percent

Answers

Answer:

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Step-by-step explanation:

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Answers

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Good luck

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Answers

B=6
.
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.
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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:

Normal temperture: 98.6 degrees Fahrenheit

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Step-by-step explanation:

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Answers

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Answers

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Answers

Answer:

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Answers

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Answers

Step-by-step explanation:

by PT,

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Topic: Pythagoras theorem

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

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Answers

Answer:

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.

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Step-by-step explanation:

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Answers

Answer:

.75 i think

Step-by-step explanation:

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