Mathematics College

[Calculus] analyze speed from position. Show steps, please!

Answers

Answer 1

Answer:

Step-by-step explanation:

We are given that the position of a particle is modeled by the function:

[tex]s(t)=2t^3-24t^2+90t+7[/tex]

And we want to find the times for which the speed of our particle is increasing.

In other words, we want to find the times for which our acceleration is positive (a(t)>0).

So first, we will find our acceleration function. We can differentiate twice.

By taking the derivative of both sides with respect to t, we acquire:

[tex]\displaystyle s^\prime(t)=v(t)=\frac{d}{dt}\big[2t^3-24t^2+90t+7\big][/tex]

Differentiate:

[tex]v(t)=6t^2-48t+90[/tex]

This is our velocity function. We can differentiate once more to acquire the acceleration function. Therefore:

[tex]\displaystyle v^\prime(t)=a(t)=\frac{d}{dt}\big[6t^2-48t+90\big][/tex]

Differentiate:

[tex]a(t)=12t-48[/tex]

If our speed is increasing, our acceleration must be positive. So:

[tex]a(t)>0[/tex]

By substitution:

[tex]12t-48>0[/tex]

Now, we can solve for t:

[tex]12t>48\Rightarrow t>4[/tex]

Therefore, the only interval for which the speed of the particle is increasing (i.e. the acceleration is positive) is for all times t>4.

So, our answer is B.

Related Questions

so I have to take my keystone's soon even tho I have only half of the required material learned cuz of corona and I have to pass them to graduate so does anyone know a good app where I can study those topics

Answers

I think I remember one of my teachers said kuta software has free worksheets with answers. Or jus ask me I can help lol

PLEASE ANSWER GIVING 30 POINTS

Answers

Answer:

this is only 15points but ok

Step-by-step explanation:

answer: D)

Answer:

The answer should be 15.

Step-by-step explanation:

[tex]\sqrt[3]{125}[/tex] Factor 125 = [tex]5^{2}[/tex] x 5. Rewrite the square root of the product [tex]\sqrt{5^{2}X5 }[/tex] as the product of square roots. [tex]\sqrt{5^{2} }[/tex] [tex]\sqrt{5}[/tex]. Take the square root of [tex]5^{2}[/tex].

[tex]3[/tex] x [tex]\sqrt[5]{5}[/tex] Multiply 3 and 5 to get 15.

[tex]\sqrt[15]{5}[/tex]

Eugene wanted to make note cards by cutting pieces of paper in half. Before starting he got six more pieces to use. When he was done he had 26 half-pieces of paper. With how many pieces did he
start?

Answers

Answer:

Step-by-step explanation:

26/2 = 13

13 - 6= 7

Answer = 7

Answer is 7
Why?
26/2 = 13
13-6=7

What is the unit rate of store A?

•$0.75 / notebook

•$0.50 / notebook

•$0.80 / notebook

•None of the above

What is the unit rate of store B ?

•$0.60 / notebook

•$0.30 / notebook

•$0.55 / notebook

•None of the above

Which store has the better deal per notebook? *

•Store A

•Store B

•The unit rate is the same at both stores

Answers

STORE B BECAUSE LOW RATES IS BETTER THAN HIGH

Sand for use on icy roads is stored in a conical pile 14.2 m high and with a base diameter of 34.4 m calculate the volume of the pile if one sander can take 6.9 m of sand, how many sanders can be filled from the pile

Answers

Answer:

1. The volume of the pile is 4,399.7719 m^3

2. The number of sanders to be filled from a pile is 638

Step-by-step explanation:

Here, we firstly would calculate the volume of the pile

Mathematically, that will be;

V = 1/3 * pi * r^2 * h

from the question, h = 14.2

Mathematically, r = d/2

r = 34.4/2 = 17.2 m

So the volume will be:

V = 1/3 * 3.142 * 17.2^2 * 14.2

V = 4,399.7719 m^3

To find the number of sanders to be filled,

we simply divide the volume obtained by the volume a sander can take

That will be;

4,399.7719/6.9

= 637.6 which is 638

Use the rules of transformations to compare the graphs of the functions, f(x) =1/x
and g(x) =5/x-1
following options represents the asymptotes of the functions, f(x) and g(x) Select all that apply.
y= -1
y=0
x=-1
y=1
X= 2

Answers

Answer:

first and second

Step-by-step explanation:

asymptote of 1/x is y= 0 and x=0 (buut x=0 isn't on here)

asymptote of 5/x-1 is the same as 1/x-1, so y = -1 and x= 0

you can graph it on desmos

Paula walked on the treadmill for 11 minutes. The machine told her she had a total of 671 strides. What was her rate in strides per minute?

Answers

Answer:

61 strides per minute

Step-by-step explanation:

You just divide 671 by 11

hope this helps:)

Answer:

Step-by-step explanation: All you have to do is divide 671 by 11

Find the Value of “Y”.

Answers

Answer:

Step-by-step explanation:

7x - 28 = 5x + 12 and 5x + 12 + y = 180

The angle (7y - 28) and angle y are supplementary angles which means their sum is 180°

7y - 28 + y = 180 add like terms

8y - 28 = 180 add 28 to both sides

8y = 208 divide both sides by 8

y = 26

Bo, Ryan and Zachary went for a walk. They walked 1/4 miles from school to Bocas House. Then they walked 4/6 miles From Paul’s house to the park. What is the total distance with the boys walked?

Answers

Answer:

Total distance walked by boys = [tex]\frac{11}{12}[/tex] miles

Step-by-step explanation:

Given that:

Distance walked from school to Bocas house = 1/4 miles

Distance walked from Paul's house to the park = 4/6 miles

Total distance walked = [tex]\frac{1}{4}+\frac{4}{6}[/tex]

Total distance walked = [tex]\frac{3+8}{12}[/tex]

Total distance walked = [tex]\frac{11}{12}[/tex] miles

Hence,

Total distance walked by boys = [tex]\frac{11}{12}[/tex] miles

-5/12 - (-9/3)=

Help me please

Answers

Answer:

HOW T.F DO YOU NOT

Step-by-step explanation:

-5/12+3

2 7/12

UST CAUSE

Answer: -5/4

Step-by-step explanation:

A 15-pound bag of apples cost $6.30. At that rate, how much would a 29-pound bag of apples cost?

Answers

thats alot of apples. what does a person need with all if those apples?

Answer:

here,

15 pound bag =$6.30

or, 1 pound bag = 6.30/15

or, 1 pound bag = $0.42

or,29 pound bag = 29 X $ 0.42

or, 29 pound bag = $ 12.18

Hence, a 29 pound bag of apple cost $12.18

You are flying your dragon kite. It's connected to 40yd of string. The kite is directly above the edge of a pond. The edge of the pond is 36yd from where the kite is tied to the ground. How high is the kite above the edge of the pond?

Answers

We have a right triangle with hypotenuse 38 and leg 34.

We want to find the other leg.

We use the Pythagorean Theorem:

Find the slope of the line

Answers

Answer:

1/2 is the slope

Step-by-step explanation:

By using the graph provided, you can count the lines and go up 1 and over 2. Hope this helped!

Assume the random variable x is normally distributed with mean u = 82 and standard deviation o =5. Find the indicated probability

Answers

P(
x86)
P(x < 86) =
(Round to four decimal places as needed

5 Gross Pay is $432. Finat a the social security tax, b the medicare tax and c the
total deductions

Answers

Answer:

Hope this helps!

Step-by-step explanation:

20 to the power of 3 divided by 2

Answers

Answer:

4000

Step-by-step explanation:

20 to the power of 3 is 8000 and 8000/2 is 4000

20^3 = 8000 / 2 = 4000

Which set of ordered pairs represents a function?
{(-3,1), (8, -2), (0,0), (8,6)}
{(-1,-8),(-8, –3), (-8,-7), (4,1)}
{(-3,-8),(-3,-7), (2,-7), (6,-4)}
{(1,-1),(-3,-8), (8, -1),(0,5)}

Answers

Hope this helps ☺️!!!!!

explanation:

whhdhdhdhehehgaahakkabdvdvhabs

GUYS PLS HELP 25 POINTS + BRAINLIEST IF CORRECT ANSWER

Answers

Answer:

B) 50º

Step-by-step explanation:

first we need to find angle MPL. to do this we do 180 - 70 - 60 = 50º. angle KPN is the smae as angle MPL. so angle KPN is 50º.

Answer:

Step-by-step explanation:

your answer is C because when you solve the answer question you get 60 degrees .What I did to get the answer is that I solve each solution answer and that is how I got 60 degrees

Hope this helps:)

Pls mark brainlist

Function or not? {(2,4)(2,-6)(3,-1)}

Answers

function dujdbfhdhfh

Is this a function? Explain with full sentence!
[(3,2) (4,2) (5,2) (3,2)]

Answers

Answer:

yes

Step-by-step explanation:

so i was doing some serching online and i typed what does a function mean and this wat came up an activity or purpose natural to or intended for a person or thing. so as i was thinking this answer fits the description on what i was given from the internet

PLEASE HELP

The vertex of this parabola is at (-2, 1). Which of the following could be its
equation?

Answers

Answer:

A. [tex]x = 4\cdot (y-1)^{2}-2[/tex]

Step-by-step explanation:

From the image attached below statement we understand that a parabola with a horizontal axis of symmetry and whose vertex is centered at [tex]V(x,y) = (h,k)[/tex] is defined by the following expression:

[tex]x-h = C\cdot (y-k)^{2}[/tex] (1)

Where [tex]C[/tex] is the parabola factor, when [tex]C > 0[/tex], the parabola is oriented in the +x direction, otherwise is oriented in the -x direction. Hence, we may conclude that equation of the parabola is of the form:

[tex]x+2 = C\cdot (y-1)^{2}[/tex]

[tex]x = C\cdot (y-1)^{2}-2[/tex], where [tex]C > 0[/tex]

The correct answer is A.

Answer:

Step-by-step explanation:

Hopefully this helps

Mrs. Jones purchased 6.2 pounds of ground beef. She cooked 0.5 of the ground beef. How many pounds of ground beef did she cook?

Answers

Answer:

She cooked 3.1 pounds

Step-by-step explanation:

6.2 x 0.5 = 3.1

One-third of Olivia’s age, increased by 12, is equal to twice her age, decreased by 3. How old is Olivia?

Answers

Answer:

the answer is 9

Step-by-step explanation:

Write the equation that describes the line with slope = 4 and y-intercept = -2 in slope-intercept form.

Answers

Answer:

2 66

Step-by-step explanation:

beacuse ima gansta and you a cracka so whats up with it

What is the combined length of all the buttons longer than 1 inch

Answers

Answer:

Where is the problem to solve?

Step-by-step explanation:

PLEASE HELP!! ITS ALMOST DUE!! ILL MARK BRAINLIEST!!!

Answers

Answer:

25 units should be right

Step-by-step explanation:

prove me wrong

if g(x)= 1- 3/4x find the value of g(-12)

Answers

Answer:

17/16

Step-by-step explanation:

g(-12) = 1+3/48 = 1+1/16

The function of g(x)= 1- 3/4x the value of g(-12) is 1.0625.

Given:

g(x)= 1- 3/4x

g(-12) = 1-3/4x(-12)

g(-12) = 1-3/-48

g(-12) =1.0625

What is function?

The function X to Y assigns exactly one element of Y to each element of X . The set X is called the range of the function and the set Y is called the code interval of the function.

A function is an equation that has only one answer for y for each x. A function specifies exactly one output for each input of a given type. It is common to call either f(x) or g(x) instead of the y function. f(2) means that we should find the value of our function when x is 2.

To learn more about function, refer;

https://brainly.com/question/9554035

#SPJ2

The radius of a circle is 4 kilometers. What is the circle's area?
r=4 km
Use 3.14 for .
square kildmeters
Submit

Answers

Answer:

50.27km

Step-by-step explanation:

divide the circumference by 3.14 ( pi ) to find the diameter of the circle. Half the diameter is the radius. Square the radius and multiply by pi to find the area of the circle.

Answer:

Step-by-step explanation:

Which expressions are equivalent to 16? Select each correct expression

1 to the 16th power
2 to the 4th power
4 to the 2nd power
8 to the 2nd power
16 to the power of 0
16 to the power of 1

Answers

Answer: Choose 2 to the 4th power, 4 to the 2nd power, and 16 to the power of 1

Step-by-step explanation:

When working with exponents, whatever number is the corner of another number, multiply it by itself. For instance, if you have 2 to the 4th power, multiply 2x2x2x2 which is 16. Also there is 4 to the 2nd power which is 4x4 which is also 16. Lastly you have 16 to the power of 1 and anything multiplied by 1 stays the same.

Correct choices are 2 to the 4th power, 4 to the 2nd power, and 16 to the power of 1.

What is an expression?

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

When working with exponents, whatever number is the corner of another number, multiply it by itself.

For instance, if you have 2 to the 4th power, multiply 2x2x2x2 which is 16. Also, there is 4 to the 2nd power which is 4x4 which is also 16. Lastly, you have 16 to the power of 1 and anything multiplied by 1 stays the same.

Therefore, the correct choices are 2 to the 4th power, 4 to the 2nd power, and 16 to the power of 1.

To know more about an expression follow

https://brainly.com/question/723406

#SPJ2

A florist sells 3 roses for a total of $10. Each rose costs the same amount. What is the cost of 12 roses?

A. $9.60
В. $10.40
C. $14.00
D. $15.00

Answers

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

if 3 roses costs 10 dollars

3x4=12 roses.................10x4=40 dollars

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