Let v(t) = 1/π + sin(3t) represent the velocity of an object moving on a line. On the interval [π/2, π], what is the velocity when the acceleration is 3?

Answers

Answer 1

Answer:

[tex]\displaystyle \frac{1}{\pi}\approx0.318[/tex]

Step-by-step explanation:

The velocity of an object moving on a line is given by the function:

[tex]\displaystyle v(t)=\frac{1}{\pi}+\sin(3t),\; \frac{\pi}{2}\leq x\leq\pi[/tex]

And we want to determine the velocity of the object when its acceleration is 3.

So, we will need to determine our acceleration function. Remember that acceleration is simply the derivative of speed. Therefore, our acceleration function a(t) will be:

[tex]\displaystyle a(t)=v^\prime(t)=\frac{d}{dt}[\frac{1}{\pi}+\sin(3t)][/tex]

Differentiate. We will use the chain rule on the second part. Hence, our acceleration function is:

[tex]\displaystyle a(t)=3\cos(3t)[/tex]

We want to find the velocity when the acceleration is 3.

So, let’s set a(t) equal to 3 and determine at what time t our function equals 3. Hence:

[tex]3=3\cos(3t)[/tex]

Divide both sides by 3:

[tex]\cos(3t)=1[/tex]

Take the inverse cosine of both sides.

Remember that cosine is 1 for every 2π. Hence:

[tex]3t=2\pi n[/tex]

Where n is an integer.

Divide both sides by 3. Therefore, our solutions are:

[tex]\displaystyle t=\frac{2\pi n}{3}[/tex]

However, our domain was π/2≤x≤π.

Hence, we can test values of n such that it is within our domain.

Testing for n=0, 1, and 2, we see that:

[tex]\displaystyle t=0, \, t=\frac{2\pi}{3},\, t=\frac{4\pi}{3}...[/tex]

However, the only solution that is within our domain is the second solution.

Hence, the acceleration is 3 when the t is 2π/3.

Therefore, our velocity at that time t is:

[tex]\begin{aligned}\displaystyle v(\frac{2\pi}{3})&=\frac{1}{\pi}+\sin(3(\frac{2\pi}{3}))\\ &=\frac{1}{\pi}+\sin(2\pi)\\&=\frac{1}{\pi}+0\\&=\frac{1}{\pi}\approx 0.318\end{aligned}[/tex]


Related Questions

Use the figure to find the measure of the angle.Explain your reasoning.

Answers

angle2=180-152=28

angle3=28

angle4=152

angle5=152

angle6=28

angle7=28

angle8=152

The values of the marked angles: angle 2, angle 3,  angle 4,  angle 5,  angle 6,  angle 7,  angle 8 are 28°, 28°, 152°, 152°, 28°, 28°, 152°.

What is an angle?

When two lines or rays meet at a point, then the geometrical figure is formed, is called an angle.

Given, angle 1 = 152°

We know, angle 1 + angle 2 is 180°.     (supplementary angles)

Therefore, angle 2 = (180° - 152°) = 28°.

Again, angle 2 = angle 3.             (opposite angles)

Therefore, angle 3 = 28°.

Similarly, angle 1 = angle 4

Therefore, angle 4 = 152°.

Now, angle 1 = angle 5        (corresponding angle)

Therefore, angle 5 = 152°.

Now, angle 2 = angle 6        (corresponding angle)

Therefore, angle 6 = 28°.

Now, angle 3 = angle 7        (corresponding angle)

Therefore, angle 7 = 28°.

Now, angle 4 = angle 8        (corresponding angle)

Therefore, angle 8 = 152°.

Learn more about an angle here: https://brainly.com/question/18129828

#SPJ2

Does the table represent y as a function of x?

Answers

Answer:

yes

Step-by-step explanation:

Determine if the number is a negative or positive integer. Gain 4 yards in the last down.

Answers

Answer:

Positive

Step-by-step explanation:

It's positive because the person is gaining 4 yards, not losing it.

The total source voltage in the circuit is 6-3i V. What is the voltage at the middle source

Answers

Answer:

The voltage at the middle source is [tex](2-4\mathbf{i})\ V[/tex]

Step-by-step explanation:

Voltage Sources in Series

When two or more voltage sources are connected in series, the total voltage is the sum of the individual voltages of each source.

The figure shown has three voltage sources of values:

[tex]2 + 6\mathbf{i}[/tex]

[tex]a + b\mathbf{i}[/tex]

[tex]2 - 5\mathbf{i}[/tex]

The sum of these voltages is:

[tex]V_t=4+a+(6+b-5)\mathbf{i}[/tex]

Operating:

[tex]V_t=4+a+(1+b)\mathbf{i}[/tex]

We know the total voltage is [tex]6-3\mathbf{i}[/tex], thus:

[tex]4+a+(1+b)\mathbf{i}=6-3\mathbf{i}[/tex]

Equating the real parts and the imaginary parts independently:

4+a=6

1+b=-3

Solving each equation:

a = 2

b = -4

The voltage at the middle source is [tex](2-4\mathbf{i})\ V[/tex]

The voltage at the middle source is;

E2 = (2 + 4i) V

From the image, we see the voltage at each point as;

E1 = (2 + 6i) V

E2 = (a + bi) V

E3 = (2 - 5i) V

The given voltages are in series and as such the total voltage will be;

E_t = E1 + E2 + E3

We are told that the total source voltage is (6 - 3i)V. Thus;

(6 - 3i) = (2 + 6i) + (a + bi) + (2 - 5i)

Rearranging gives;

(a + bi) = 6 - 3i - (2 + 6i) - (2 - 5i)

(a + bi) = 6 - 3i - 2 - 6i - 2 + 5i

(a + bi) = 2 - 4i

The middle source voltage is E2 = (a + bi) V. Thus;

E2 = 2 - 4i

Read more at;https://brainly.com/question/8151005

marie wants to know the most popular car for parents. She plans to survey the people shopping at the used car lot from 10:00 a.m. to 11:00 p.m. Which statement below best reflects Marie's plan?
A. Marie's sample is valid.
B. Marie should also survey people entering the grocery stores.
C. Marie's sample is biased.
D. Marie should make sure she surveys both men and women.

Answers

Answer:

C Marie's sample is biased.

Step-by-step explanation:

It is biased because she doesn't know. It is just 1 hour so like there could be like a lot of people at 4-5 and not a lot at 10-11

Hope this helps!

Merry Christmas

Answer:

Give the other person brainliest.

Step-by-step explanation:

The other person is correct.

HELP I WILL RATE !!!!!!!

Answers

No picture, nothing to rate here.

the picture is below

Answers

Answer:

C

Step-by-step explanation:

Calculate the paychecks of the following people. Select the total hours and paycheck.

Answers

Answer:

If the numbers under the days of the week are the hours worked then the answers are Sue-40,$6.75,$270 Jerry-30,$5.15,154.5  Sam-38.75,$8.75,339 Step-by-step explanation:

Just add up the number of hours worked and multiply by the rate.

PLS HELPPPPP!!!!!!!!!!!!!!!!!!
what is 2/5 times 11 in simplest form?

Answers

Answer:

4.4 would you let me know if you need an explanation and pls don't delete.

Hmmmm i think its 5/22

Step-by-step explanation:

So basically how i got it was 2/5*11

And that got me 5/22

I do not think you could simplify this

Either I'm very smooth brain or you can't simplify 5/22

In the sixth grade, 54% of the students are boys. There are 189 boys in the sixth grade. What is the total number of students in sixth grade? A. 54 B. 161 C. 189 D. 350. (explain what did u do to get you're answer )​

Answers

Answer:

D

Step-by-step explanation:

189 boys is 54%

x is 46%(100-54)

Cross multiply:

189*46%=54%*x

86.94=0.54x

x=161

189 boys 161 girls

350 altogether

So D

Hope this helps plz hit the crown :D

4j + 4 =
Next, subtract 4 from both sides.
4j

Answers

Answer:

4j=-4

j=-1

Step-by-step explanation:

Answer:

4j=-4  j=-1

Step-by-step explanation:

Find the sales tax.
Sales Tax
Selling Price Rate of Sales Tax Sales Tax
$60.00
3%
?
The sales tax is $.

Answers

Answer:

57.00

Step-by-step explanation:

welcome

Answer:

1.80

Step-by-step explanation:

60 x .03=1.80

What is the Slope of the slide?

Answers

Answer:

[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Points on line: (1,2) (3,3)

[tex]\frac{2-3}{1-3}[/tex] = [tex]\frac{-1}{-2}[/tex] = [tex]\frac{1}{2}[/tex]

Can some one help please!!!!!!!

Answers

Answer:

yes it's easy

Step-by-step explanation:

y=-2x

it may help you to understand.

Solve for w. You must write your answer in fully simplified form.
19 = -8w

Answers

Answer:

The answer is 11

1. Explain and give the formula for the formula for the following properties for segments in a circle.
a. Segments from Chords:

b. Segments from Secants:

c. Segments from a Secant and Tangent line:

2. Explain what a radian is and how it relates to a degree.


3. Define the following terms.
a. Inscribed Circle of a Triangle:
b. Incenter:
c. Circumscribed Circle of a Triangle:
d. Circumcenter:

Answers

Answer:

see explanation

Step-by-step explanation:

1

(a)

If 2 chords of a circle intersect then the product of the measures of the parts of one chord is equal to the product of the measures of the parts of the other chord.

(b)

If 2 secants are drawn from an external point to a circle then the product of the measures of one secant's external part and the entire secant is equal to the product of the measures of the other secant's external part and that entire secant.

(c)

If a tangent and a secant are drawn from an external point to a circle , then the square of the measure of the tangent is equal to the product of the measures of the secant's external part and the entire secant.

2

A radian is defined as the angle subtended at the centre of a circle by an arc equal to the radius of the circle.

1 revolution = 360° = 2π radians

1 radian = [tex]\frac{360}{2\pi }[/tex] ≈ 57°

3

(a)

An inscribed circle of a triangle is a circle drawn inside a circle so the circle barely touches the sides of the triangle.

(b)

The incentre is at the point of intersection of the triangle's 3 angle bisectors.

(c)

A circumscribed circle of a triangle ( circles drawn around the triangle so that the circle passes through each of the triangles's vertices.

(d)

The circumcentre is at the intersection of the perpendicular bisectors of the triangle's sides.

'

hwo wants brainlist?
567x357+65-76=?

Answers

Answer:

Hewo, Mee

202408

Answer:

202408

Step-by-step explanation:

Find the area of the trapezoid below.
4 cm
3 cm
8 cm

Answers

Answer:

4 + 8 / 2 * 3 = 18

4 + 8 = 12

12 / 2 = 6

6 * 3 = 18

Step-by-step explanation:

*Hope this helps*

Parker grew
2 1/2 inches each year for the past 3 years. How many inches total has Parker grown in the past 3
years?

Answers

Answer:

it will be 7 and 1/2

Step-by-step explanation:

2 and 1/2 x 3=7 and 1/2

Help me pleaseeeeeeeeeeeeeee

Answers

Answer:

the second one

Step-by-step explanation:

Answer:

2nd

Step-by-step explanation:

The 2nd one is the correct one because it is true and that is the best way to get your solution.

Hope this helps:)

Pls mark brainly

Describe the transformation that takes f (x) = x + 1 To g (x) = -x + 4. [ Please No Plagiarism and Will mark brainliest . .​

Answers

Answer:

fliped over y axis and moved up 3

Step-by-step explanation:

fliped over y axis (changed x to -x) and moved up 3 (changed +1 to +4)

Answer:

why did you delete my answer HUH?

Step-by-step explanation:

HURRY ANSWER THIS IM BEING TIMED

Answers

Answer:

D

Step-by-step explanation:

10(4 - 7)/-(4 - 1)

40-70/-4+1

-30/-3

=10

Using the graphing function on your calculator, find the solution to the system
of equations shown below.
2y- 4x= 6
y- 2x=7
A. No solution
B. More than 1 solution
C. x= 4, y=-2
D. X= -1, y= 1

Answers

48 hdjehddhbeebjehrebbrrbrbfbfbfbfbfnfbf

PLZZ SOMEONE GIVE ME THE EQUATION!! You have $20 to buy snacks for yourself and 4 friends. If you buy a bag of chips for each person, and still have $13.75 left, how much did you spend on each bag of chips? ​

Answers

Answer:

1.56

Step-by-step explanation:

Answer:

1.25

Step-by-step explanation:

20-13.75 = 6.25

6.25 / 5 = 1.25

HELP PLEASEEEEEEEEEEEEEEEEEEEEEE ITS A GRADE

Answers

Answer:

as x increases, y increses

the parabola grows wider and taller, meaning that the y and x values will both increase:)

Answer:

B for the first graph (as x increases, y increases), D for the second graph (as x increases, y decreases), D for the third graph (minimum at y = -9), and A for the forth graph (the graph opens up because the a value in the equation is positive)

At a bakery every 4th coustmer recives a free cookie snd every 10th customer recives a free drink. Which customer will be the first to recive a free cookie and a free drink

Answers

Answer:

40th costumer

Step-by-step explanation:

The 40th costumer will receive a free cookie and drink. You need to find factors of 4 and factors of 10. Then when you find 4 and 10 have the same factor that’s your answer. So you do 4,8,16,24,32,36,40,44,48, etc. (counting up by 4) now do it to 10,20,30,40,50,60,70, etc. (counting up by 10) Now you notice that the first number that is the same is 40. So that means the 40th costumer will be the first one to receive a free drink and cookie.

Customer first to receive a free cookie and a free drink is 20th number customer

Given that;

Number of customer received free cookie = 4th

Number of customer received free drink = 10th

Find:

Customer first to receive a free cookie and a free drink

Computation:

Customer first to receive a free cookie and a free drink = LCM of 4 and 10

Customer first to receive a free cookie and a free drink = 20th number customer

Learn more:

https://brainly.com/question/1879445?referrer=searchResults

Given: a∥b, m∠1 = 71º Find m∠5, m∠8

Answers

Step-by-step explanation:

m <5=71

m <8=109

-------------

Answer:

∠5 = 71°

∠8 = 109°

Step-by-step explanation:

∠1 = 71°

∠5 = 71°  (the same as ∠1 = 71°) its a corresponding angle

∠8 = 180 - ∠5

∠8 = 180 - 71

∠8 = 109°

Assuming all model requirements for conducting the appropriate procedure have been​ satisfied, is the mean IQ of the students in the​ professor's statistics class higher than that of the general​ population, 100? Explain what statistical procedure should be used for this research objective.

Answers

Answer:

Step-by-step explanation:

The right statistical procedure is by applying a hypothesis test that uses a single mean. Here, if we are to talk about comparison, it should be between the mean IQ of the students in the class and the national average IQ. The class is not for a comparison between two population means because it is viewed as the sample of the population. That is to say, the required task is to determine if the sample mean is greater than the population mean. We can conclude that this obeys a hypothesis test rather than a confidence interval.

find the values of a,b, or c for y = x^2 - 9x +18 please help!!

Answers

Answer:

It's X^1 = 3, x^2 =6  

Step-by-step explanation:

If 7x-3x+17-x+1=108, what is the value of 4x+x?

Answers

Answer:

150

Step-by-step explanation:

1. combine like terms

7x-3x-1x=3x

17+1=18

2. subtract

108-18=90

3. divide

90/3=30

which means x=30

4. plug it in

4X30+30=150

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Between 1800 and 1900 coal-driven engines multiplied until . . . they were producing energy equivalent to seventy million horse-power; during the first twenty years of the twentieth century, their power-producing capacity more than doubled. So coal wrought the industrial revolution, the greatest revolution in all human history, which transformed social and economic life as radically as the geographical revolution transformed the earth's surface.Robert W. Brure of the Bureau of Industrial Research in America, The Coming of Coal, 1922a) Identify ONE specific example of the environmental influences and consequences of the Industrial Revolution that would support the author's argument.b) Explain ONE specific example of how coal helped power new inventions that would support the author's argument.c) Explain ONE specific example of how mining coal helped transform social and economic life that would support the authors argument. 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