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

Please help now :)))

Answers

Answer:

c

Step-by-step explanation: there's 3 muffins for every 5 pizza pies and there's  9 which is 3 times the muffins and 15 which is 3 times the pizzas

283.65 + 85.3 =?

Find the sum?

Answers

Answer:

368.95

Step-by-step explanation:

Line up the decimal places to add the numbers:

  283.65

+   85.3

—————

85.3 is the same as 85.30:

  1

  283.65

+   85.30

—————

  368.95

Answer: 368.95

Hope this helps! :)

Answer:

198.35

Step-by-step explanation:

283.65

085.3

_______________

198.35

A store is offering a discount on shorts of 23.4%.The original price of the shirt is $13.24.how much will you have to pay the clerk

Answers

Answer:

Step-by-step explanation:

Hi

Answer:

13.24

Step-by-step explanation:

Your buying a shirt not shorts

Harry bought 25 pens for 1.00. Find the unit rate

Answers

Answer:

4 cents

Step-by-step explanation:

1.00 divied by 25 =0.04 aka 4 cents

The answer is 4 cents because when you divide 1.00 by 25 it equals to 00.4 if you want a picture of the work her you go :)

Hope this helps :)

Determine whether the triangles are similar by AA~, SSS~, SAS~, or not similar.
If the triangles are similar, write a valid similarity statement.​

Answers

Answer:

the AA~ congruency could be used, because

angle w=y,

angle t=z

and angle x is common

Step-by-step explanation:

That was my answer and I got it right :)

The given triangles are not similar.

What is similarity of triangles?

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.

Given a figure of two triangles, ΔWXT and ΔYXZ

Here,

28/35 ≠ 30/38

WX/YX ≠ XT/XZ

We can conclude that, the corresponding sides are not in common ratio, so triangles are not similar.

Hence, The given triangles are not similar.

For more references on similarity in triangles, click;

https://brainly.com/question/25882965

#SPJ5

what is 20 percent of 90?​

Answers

Answer:

18

Step-by-step explanation:

18% hope this helpss

1. Find the point that is a solution for y = 6x + 8
A. (2, 1)
B. (-1,2)
C. (2,4)
D.(-2,4)
Help plz fast.

Answers

An easy way to solve this equation is to plug in the coordinates.

A. 6(2) + 8 ≠ 1

✅ B. 6(-1) + 8 = 2

C. 6(2) + 8 ≠ 4

D. 6(-2) + 8 ≠ 4

1. A business records its net profits for the week by subtracting the operating costs from the revenue. The function P(x) = (140x) – (30x + 1200) represents the profits for one week, where x is the number of products sold. Which statement is true?

a) The slope of the function is 110, and it represents the change in net profit per product sold.
b) The slope of the function is 140, and it represents the initial operating costs of the business
c) The slope of the function is 110, and it represents the initial operating costs of the business.
d) The slope of the function is 140, and it represents the change in net profit per product sold.

Answers

I think answer should be d. Please give me brainlest let me know if it’s correct or not okay thanks bye

5. If AABC = ADEF, find the measure of

Can someone explain me?

Answers

Answer:

Option A) angle B = 67°

Step-by-step explanation:

I'll use " [ " symbol for saying angle.

Alright so ...

since triangle ABC and triangle DEF are congruent

it means [ A = [ D

[ B = [ E

[ C = [ F

here [ A = 78° (which means [ D is also 78°)

and ..[ F = 35° (which means [ C is also 35°)

-->So now all you need to know to find [ B is to know the other two angles in the triangle. and thats where ..

you write.. [ A + [ B + [ C = 180° (angle sum property)

78° + [ B + 35° = 180°

113° + [ B = 180°

[ B = 180 - 113

= 67°

I hope that clears the concept , if you have any questions regarding it I'd love to help .

Jason drove 110 miles in 2 3/4hours. What was Jason’s speed in miles per hour?

Answers

Answer: His MPH is 40

Step-by-step explanation: 100/2.75 = 40. Converting the fraction to decimal form makes this problem much easier.

HELP!!! The probability that a male’s foot is between 10 and 12.5 inches is__
p(10

Answers

Answer:

I suggest you use Socratic, it solves questions like this.

Step-by-step explanation:

Find the diagonal of the box using the Pythagorean Theorem.
PLS HELP ASAP 50 POINTS PLEASE HELP ASAP PLEASEEE!!!! I NEED HELP ASAP
(Image Linked)

Answers

Answer:

26 cm

Step-by-step explanation:

Diagonal of the box using Pythagorean Theorem can be calculated using the formula:

a² + b² + c² = d²

Where,

d = diagonal of the box = ??

a = length = 24 cm

b = width = 8 cm

c = height = 6 cm

Plug in the value into the formula

24² + 8² + 6² = d²

576 + 64 + 36 = d²

676 = d²

√676 = d

d = 26 cm

Graph △RST with vertices R(4, 1), S(7, 3), and T(6, 4) and its image after the glide reflection.

Translation: (x, y)→(x−3, y)
Reflection: in the line y=−1

Answers

Answer:

Step-by-step explanation:

Points R(4,1) S(7,3) T(6,4) after translation

R(4-3, 1) S(7-3, 3) T(6-3, 4)

R'(1, 1) S'(4, 3) T'(3, 4)

Points R'(1, 1) S'(4, 3) T'(3, 4) after reflection

R''(1, -3) S''(4, -5) T''(3, -6)

n
Which number line shows the graph of x2 11?
6
7
8
9
10
11 12 13
14
6
7
8
9
10
11
12
13
14
6
7
8
9
10 11
12 13
14
6
7
8
9
10
11
12
13
14

Answers

Answer:

11

Step-by-step explanation:




A TV store buys TV's for $250 each, and then increases the price by 120%. What is the sales price of a TV at this store?

Answers

Answer:

$300

Step-by-step explanation:

Answer:

$300

Step-by-step explanation:

250 100

 ?    120

(250x120)/100

Is each expression equivalent to 6 * 53? Justify your reasoning.
a. 6 * 50 + 6* 3
b. 10 * 53 -4 53
c. 6 50 + 3
d. 6 * (50 + 3)

Answers

Answer:

a, b, d. Yes c. No

Step-by-step explanation:

a. 6 * 50 + 6* 3  = 6* ( 50 + 3) = 6* 53

Yes

b. 10 * 53 -4*53  = (10 - 4)*53 = 6*53

Yes

c. 6 * 50 + 3  = 303

No

d. 6 * (50 + 3) = 6*53

Yes

Answer:

A, B, D = Yes

C = No

6 * 50 + 6* 3  = 6* ( 50 + 3) = 6* 53

10 * 53 -4*53  = (10 - 4)*53 = 6*53

6 * 50 + 3  = 303

6 * (50 + 3) = 6*53

write equation asap ​

Answers

Answer:

y = 4/3x - 4.5

Step-by-step explanation:

1) find the slope 4/3

2) find the y-intercept

3) done ------>    y = 4/3x - 4.5

Answer:

(5,2)(-1,-6)

Step-by-step explanation:

-6-2/-1-5

-8/-6

=4/3

Y+1=4/3(x+6)

Y+1=4/3x+8

Y=4/3x+7

Please helpp I’ll give brainleist

Answers

Answer:

87 for lo and om is 56

Step-by-step explanation:

Answer:

<LON= 98 Degrees

Step-by-step explanation:

180-55(2)=70

70+28=98

Can anyone please help me with the last question I’m struggling!

Answers

The equation is x=-6

Step-by-step explanation:

In standard form the equation is y=4

And this is a horizontal line so the perpendicular line will be a vertical line of the form x=a

so that is why the equation is x=-6

Answer:

= -5

Step-by-step explanation:

christian has six grades from tests and IXL. they are all weighted equally. if christian grades are 100,96,96,88,70 and 100, what is the current average grade (round to the nearest whole number)

Answers

Answer:

His average grade would be 91.6... (or 92% if you're rounding up)

Step-by-step explanation:

Add 100, 96, 96, 88, 70, and 100 to get 550, then divide by 6 because there are 6 total grades.

CAN SOMEONE PLEASE ANSWER THIS QUESTION ASAP!!

Answers

hi, the solving is in the image, answer is 50 ft

have a nice day :)

Seth has 2 ¾ candy bars to give away. If he gives each person ⅛ of a candy bar, how many people will get candy?

Answers

Answer:

22 people

Step-by-step explanation:

Change 2 3/4 into a fraction, 11/4.

Then divide by 1/8

11/4 x 8/1 = 22

2x + 2y = 4 -x+ 2y = 4​

Answers

Answer:

x = 0, y = 2

Step-by-step explanation:

We can use substitution method to substitute 2y into 2x + 2y = 4.

-x + 2y = 4

2y = 4 + x --- Equation 1

2x + 2y = 4 --- Equation 2

Substitute Equation 1 into Equation 2:

2x + 2y = 4

2x + 4 + x = 4

3x + 4 = 4

Isolate 3x.

3x = 4-4

    = 0

Find x.

x = 0 ÷ 3

x = 0

Substitute x = 0 into Equation 1:

2y = 4 + x

2y = 4 + 0

    = 4

Find y.

y = 4 ÷ 2

y = 2

The answer is Y=2 I’m pretty sure

Which expression is equal to 2xx−2−x+3x+5?

Answers

Answer:

It's the fourth one

Following are the solution to the given expression:

Given:

[tex]\bold{\frac{2x}{x-2}- \frac{x+3}{x+5}}[/tex]

To find:

Expression =?

Solution:

[tex]\to \bold{\frac{2x}{x-2}- \frac{x+3}{x+5}}\\\\\to \bold{\frac{2x(x+5) -(x+3) (x-2)}{(x-2)(x+5)}}\\\\\to \bold{\frac{2x^2+10x -(x^2 -2x+ 3x-6)}{(x-2)(x+5)}}\\\\\to \bold{\frac{2x^2+10x -(x^2 +x-6)}{(x-2)(x+5)}}\\\\\to \bold{\frac{2x^2+10x -x^2 -x+6)}{(x-2)(x+5)}}\\\\\to \bold{\frac{x^2+9x+6}{(x-2)(x+5)}}\\\\[/tex]

Therefore, the answer is "last choice".

Learn more:

brainly.com/question/17079155

Determine the equation of the line passing through the point below having the corresponding
slope.
Point: ( - 25, -9)

Slope: m=1/5

Write your answer as an equation in the form
y = mx + b

Answers

Answer:

y=1/5x-4

Step-by-step explanation:

So, first we're gonna put this into point slope form, (y-y1)=m(x-x1), then we'll convert it. When you plug the numbers in, you get (y+9)=1/5(x+25)

Then, you simplify!

y= 1/5(x+25)-9

y=1/5x+5-9

y=1/5x-4

Hope this helped!

If mZMRT = 133º , then which equation can be used to find g?​

Answers

Answer:

D

Step-by-step explanation:

We know that MRT = 133 which means that is the total. Angle MRN and NRT are what makes the total angle which is 133. To find what each angle is individually, we can add them both together.

(2g - 2) + (4q - 9) = 133

6q - 11 = 133

6q = 144

q = 24

Best of Luck!

D. (2g - 2)+(4g -9) = 133

Because,

Given, angle MRT = 133°

and MRN = 2g - 2 °

and NRT = 4g - 9°

and MRT = MRN + NRT .........(equation (i))

Placing values in equation (i) we get,

133° = (2g - 2)° + (4g - 9)°

=> 133 = (2g - 2) + (4g - 9)

=> (2g - 2) + (4g - 9) = 133

In a survey of 2300 people who owned a certain type of​ car, 460 said they would buy that type of car again. What percent of the people surveyed were satisfied with the​ car?

Answers

Answer:

20%

Step-by-step explanation

let's assume 100% = 2300

x% = 460

100% / x% = 2300/460

460x100/2300 = 20

the answer is 20%

Answer:

The survey shows that 20% of the individuals were satisfied with the car.

Step-by-step explanation:

We are given that 2,300 people were surveyed.We are also given that 460 of those individuals would buy that car again.We need to find the percentage of individuals that were satisfied with the car.

When we need to find the percentage of a population, we can use the following formula:

[tex]\displaystyle \frac{\text{part}}{\text{whole}} \times 100[/tex]

We need to identify the part and the whole in this problem.

We are given that 2,300 people are surveyed, so this is the whole portion.

We are also given that 460 were satisfied, so this is the part portion.

Therefore, we can set up our fraction.

[tex]\displaystyle \frac{460}{2300}[/tex]

Now, let's solve the percentage.

[tex]\displaystyle \frac{460}{2300} \times 100\\\\\frac{2}{100} \times 100 = 20\%[/tex]

Therefore, of those surveyed, 20% of the individuals were satisfied with the car.

Find the 75th term of the following arithmetic sequence 16,25,34,43

Answers

Answer:

[tex]\boxed {\boxed {\sf 682}}[/tex]

Step-by-step explanation:

The nth term of an arithmetic sequence can be found using the following formula.

[tex]a_n=a+d(n-1)[/tex]

where a is the first term, d is the common difference, and n is the term.

First, we should find the common difference.

We can do this by subtracting each term from the term following it. Basically, subtract the first term from the second term, the second from the third, and so on.

[tex]d= a_2-a_1[/tex]

The second term is 25 and the first is 16.

[tex]d= 25-16[/tex]

[tex]d=9[/tex]

Now we know the common difference is 9. We also know the first term is 16 and we are looking for the 75th term.

[tex]d=9 \\a=16 \\n= 75[/tex]

Substitute the values into the formula.

[tex]a_{75}=16+9(75-1)[/tex]

Solve according the PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction).

Solve the parentheses first.

[tex]a_{75}=16+9(74)[/tex]

Multiply next.

[tex]a_{75}=16+666[/tex]

Finally, add.

[tex]a_{75}=682[/tex]

The 75th term in the sequence is 682.

Find the equation of the line that passes through (4,4) and is parallel to y = 2x + 4.
Leave your answer in the form y= mx + c

Answers

Answer:

x,y(0,12)

Step-by-step explanation:

Y=mx+c

4=2X+4

4=2x+4

2x=0

X=0

Y=mx+c

Y=2(4)+4

Y=8+4

Y=12

pls help me it would mean a lot <3

Answers

I believe it would be y=2.5x

Have an amazing day :3

Answer:

The equation of the line will be:

[tex]y\:=\:\frac{2}{5}x[/tex]

Step-by-step explanation:

We know the slope-intercept of a line equation is

[tex]y = mx+b[/tex]

where m is the slope and b is the y-intercept

Given two points on a line graph

(0, 0)(25, 10)

Finding the slope between two points

[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\left(x_1,\:y_1\right)=\left(0,\:0\right),\:\left(x_2,\:y_2\right)=\left(25,\:10\right)[/tex]

[tex]m=\frac{10-0}{25-0}[/tex]

[tex]m=\frac{2}{5}[/tex]

We know that the y-intercept on a line graph can be observed by setting x=0 and checking the corresponding value of y.

From the graph, it is clear

at x = 0, y = 0

Thus, the y-intercept = b = 0

Now, substituting b = 0, and m = 2/5 in the slope-intercept form

[tex]y = mx+b[/tex]

[tex]y\:=\:\frac{2}{5}x+0[/tex]

[tex]y\:=\:\frac{2}{5}x[/tex]

Therefore, the equation of the line will be:

[tex]y\:=\:\frac{2}{5}x[/tex]
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