. A particle moves on a line away from its initial position so that after t seconds its distance is s = 3t^2+tmeters from its initial position. (a) At what time does the particle have a velocity of 25 m/s? (b) Is the acceleration ever 0? Why or why/not? Explain your answer
pls solve and explain fast​

. A Particle Moves On A Line Away From Its Initial Position So That After T Seconds Its Distance Is S

Answers

Answer 1

Answer:

The velocity of this particle is [tex]25\; {\rm m \cdot s^{-1}}[/tex] at [tex]t = 4\; {\rm s}[/tex].

Acceleration is constantly [tex]6\; {\rm m\cdot s^{-2}}[/tex] (and thus is never [tex]0[/tex].)

Step-by-step explanation:

The distance between the particle and the initial position is the displacement of this particle. Let [tex]x(t)[/tex] denote the displacement (in meters) of this particle at time [tex]t[/tex] (in seconds.) The question states that [tex]x(t) = 3\, t^{2} + t[/tex].

Differentiate displacement [tex]x(t)[/tex] with respect to time [tex]t[/tex] to find the velocity [tex]v(t)[/tex] (in [tex]{\rm m \cdot s^{-1}}[/tex]) of this particle:

[tex]\begin{aligned}v(t) &= \frac{d}{d t}\left[x(t)\right] \\ &= \frac{d}{d t}\left[3\, t^{2} + t\right] \\ &= 6\, t + 1 \end{aligned}[/tex].

Set velocity to [tex]25\; {\rm m\cdot s^{-1}}[/tex] and solve for time [tex]t[/tex] (in seconds):

[tex]v(t) = 25[/tex].

[tex]6\, t + 1 = 25[/tex].

[tex]t = 4[/tex].

Thus, the velocity of this particle is [tex]25\; {\rm m \cdot s^{-1}}[/tex] at [tex]t = 4\; {\rm s}[/tex].

Differentiate velocity [tex]v(t)[/tex] with respect to time [tex]t[/tex] to find the acceleration (in [tex]{\rm m\cdot s^{-2}}[/tex]) of this particle:

[tex]\begin{aligned}a(t) &= \frac{d}{d t}\left[v(t)\right] \\ &= \frac{d}{d t}\left[6\, t + 1\right] \\ &= 6\end{aligned}[/tex].

In other words, the acceleration of this particle is constantly equal to [tex]6\; {\rm m\cdot s^{-2}}[/tex]. Hence, the acceleration of this particle is never [tex]0[/tex].


Related Questions

A farmer sells 7.7 kilograms of apples and pears at the farmer's market.
1
4
of this weight is apples, and the rest is pears. How many kilograms of pears did she sell at the farmer's market?

Answers

Answer:

She sold 5.775 kilograms of pears at the farmer's market.

Step-by-step explanation:

Let's first determine the information that the question gives us, and what we need to find.

Given:

The farmer sold 7.7 kilograms of apples and pears

1/4 of the weight is apples

The rest of the weight is pears

Find:

Kilograms of pears that the farmer sold

Start by finding the fraction of the whole weight that was pears...

[tex]1-\frac{1}{4}=\frac{4}{4}-\frac{1}{4}=\frac{3}{4}[/tex]

Now, find 3/4 of 7.7...

[tex]\frac{3}{4}(7.7)=\frac{23.1}{4}=5.775\ kg[/tex]

She sold 5.775 kilograms of pears at the farmer's market.

What is the next time: 8:30 A.M., 10:00 A.M., 11:30 A.M., _______? A) 1:00 P.M. B) 1:00 A.M. C) 1:30 P.M. D) 1:30 A.M.

Answers

Answer:

A 1 PM

Step-by-step explanation:

Becasue it grows by an hour and a half each time

Answer: Easy. A. 1 pm.

.

Which is the better choice: $1000 deposited for a year at a rate of 4.8% compounded semiannually 19) or at a rate of 4.7% compounded quarterly?

Answers

[tex]~~~~~~ \stackrel{\textit{\Large 4.8\% semiannually}}{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$1000\\ r=rate\to 4.8\%\to \frac{4.8}{100}\dotfill &0.048\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus twice} \end{array}\dotfill &2\\ t=years\dotfill &1 \end{cases}[/tex]

[tex]A=1000\left(1+\frac{0.048}{2}\right)^{2\cdot 1}\implies \boxed{A\approx 1048.58}~~\textit{\Large \checkmark} \\\\[-0.35em] ~\dotfill\\\\ ~~~~~~ \stackrel{\textit{\Large 4.7\% quarterly}}{\textit{Compound Interest Earned Amount}}[/tex]

[tex]A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$1000\\ r=rate\to 4.7\%\to \frac{4.7}{100}\dotfill &0.047\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &1 \end{cases} \\\\\\ A=1000\left(1+\frac{0.047}{4}\right)^{4\cdot 1}\implies \boxed{A\approx 1047.83}[/tex]

X^2 - 2x = 8
Find the value of X

Answers

To find the solutions to the quadratic equations

    ⇒ factor the equation

           [tex]x^2-2x = 8\\x^2-2x-8=0\\(x-4)(x+2) = 0[/tex]

   

Now to find the exact solutions, we have to set 'x - 4' and 'x + 2' equal to 0

     [tex]x - 4 = 0\\x = 4\\\\x + 2 = 0\\x = -2[/tex]

Thus the solution to this problem is -2 and 4

Hope that helps!

   

Answer:

4 and - 2

Step-by-step explanation:

x² - 2x = 8

x² - 2x - 8 = 0

x² + 2x - 4x - 8 = 0

x ( x + 2 ) - 4 ( x + 2 ) = 0

( x + 2 ) ( x - 4 ) = 0

x + 2 = 0

x = - 2

x - 4 = 0

x = 4

The values of x are - 2 and 4.

The length is :____ meters and the width is ____meters.

Answers

Answer:

Length= 8, Width= 4

Step-by-step explanation:

Say the length is l, and the width is w.

We can set l, the length as 2w, as it is double the length.

The perimeter= 2l + 2w= 24

Input l as 2w, get

4w+2w=24

6w=24, w=4.

Length is w*2, so length is 8.

A bird is nested on a tree top that is 14 feet above the ground. The bird looks down at a worm at a 30 angle of depression. How far is the worm from the base of the tree?

Answers

Applying the tangent ratio, the distance of the worm from the base of the tree is: 24.2 ft.

What is the Tangent Ratio?

Tangent ratio is part of the Trigonometry ratios, which is expressed as, tan ∅ = opposite side / adjacent side in a right triangle.

The information given would form a right triangle, where:

Reference angle = ∅ = 30°Opposite side = 14 ftAdjacent side = distance of the worm from the base of the tree = x

Applying the tangent ratio, we would have:

tan 30 = 14/x

x = 14/tan 30

x = 24.2 ft.

Therefore, applying the tangent ratio, the distance of the worm from the base of the tree is: 24.2 ft.

Learn more about tangent ratio on:

https://brainly.com/question/14169279

Use synthetic division to divide:

(2x^4+5x^3-3x^2-x+1) / (x+2)

Answers

Answer:

[tex]2x^3 +x^2 -5x+9 -\frac{17}{x+2}[/tex]

Step-by-step explanation:

See picture for explanation

please answer and use statement reason

Answers

Answer:

x = 15

Step-by-step explanation:

FD and AC are parallel because both are perpendicular to EB. Angle EDF and Angle DCA are congruent because they are corresponding angles. The measure of Angle DCA is also 3x because congruent angles have the same measure.

Now consider Triangle ACD. Because the sum of all three measures of the angles in a triangle add up to 180°.

x + 8x + 3x = 180°

12x = 180°

12x/12 = 180/12

x = 15

Hamilton, NY has 73465 residents, and 12 members on their Board of Trustees. The three districts of Basel, Heights, and Dagonal have the following populations:
Basel: 13,244 Heights: 30, 415 Dagonal: 29,806
Determine the standard quota (to two decimal places) for the Dagonal district.



6) Gotham City is to apportion 16 seats to districts with populations as follows:
North: 785 South: 1,125 East: 1,950 West: 415
Find the standard divisor
What are the standard, lower, and upper quotas for the four districts?

Answers

a) The determination of the standard quota for the Dagonal district is 40.57%.

b) 1. The standard divisor is 267.19 (4,275/16).

2. The standard, lower, and upper quotas for the four districts are as follow:

                                North         South           East         West      

Standard quota     18.36%       26.32%     45.61%       9.71%

Lower quota             18%          26%            45%            9%

Upper quota             18%          26%            46%           10%

What is the quota method of apportionment?

The quota method of apportionment is the use of the standard divisor to round off standard quotas, according to some agreed ground norms.

When the standard quota is rounded down to an integer, it gives the lower quota, and rounding up gives the upper quota.

The standard divisor is calculated as the total population divided by the total number of seats.

The standard divisor gives the average number of people represented by a Board or seat member.

Data and Calculations:

Hamilton, NY Population:

Residents of Hamilton, NY = 73,465

Board Trustee Members = 12

                              Basel         Heights       Dagonal      Total

Population            13,244         30, 415        29,806    73,465

Proportion            18.03%        41.40%         40.57%      100%

Allocation of Board

Seats                         2                  5                 5               12

Gotham City Population:

Number of seats = 16 seats

                              North         South         East         West      Total

Population               785           1,125         1,950        415       4,275

Proportion            18.36%       26.32%     45.61%       9.71%    100%

Allocation of Board

Seats                        3                 4                7              2          16

Learn more about the quota system at https://brainly.com/question/12105335

ΔQRS is a right triangle.

Triangle S R Q is shown. Angle S R Q is a right angle. An altitude is drawn from point R to point T on side S Q to form a right angle.

Select the correct similarity statement.

Answers

Answer:

∆QRS is a right triangle

Step-by-step explanation:

correct similarity statement is RST

Answer:

I think its B

Step-by-step explanation:

Edge 2022

pls i need help asap

what's the area of this figure?

Answers

Answer:

35

area of traingle b xh/2 5x4/2 - 10

area of square lxl - 5x5 -25

add- 35

Answer:

The answer would be 35.

Step-by-step explanation:

The area of the shape would be 35 square centimeters because if we divide the shape into 3 different shapes, a square on the bottom and 2 triangles at the top, we can multiply the square's length and width to get an area of 25. Next, we'll multiply the 2 triangles length of 4 with the width of 5 to get a total area of 20 from both of them, we'll then divide the area of 20 by 2 to get 10. Now add 20 and 10 to get 35.

a large University with over 40,000 took a recent survey in which 31% of the students claimed to exercise at least 3 times a week. A simple random sample of 250 students was selected. b = the proportion of students in the sample who claimed to work out 3 at least 3 times a week. What is the standard deviation of the sampling??

Answers

Answer:

A large university with over 40,000 students recently took a survey in which 31% of the students claimed to exercise at least 3 times a week. A simple random sample …

✓ approximately Normal, because we would expect at least 10 success and 10 failures

Step-by-step explanation:

Please write no more than two paragraphs. Assignment is worth 25 points We have been talking about variables and how they are measured. For this assignment, I have assigned a paper for you to study on the potential impacts of a paleolithic diet on cardiovascular markers in patients with diabetes.

Answers

The impact of a paleolithic diet on cardiovascular markers in patients with diabetes is that it increases the concentration of certain fats in the blood.

What is diabetes?

It should be noted that diabetes simply means a condition when the blood glucose is too high.

In this case, the impact of a paleolithic diet on cardiovascular markers in patients with diabetes is that it increases the concentration of certain fats in the blood. It's simply a risk factor for heart diseases.

Learn more about diabetes on:

https://brainly.com/question/504794

Help picture below problem 9

Answers

Answer:

42 degrees

Step-by-step explanation:

Complimentary angles are two angles whose total is equal to 90 degrees. Since we already know that Angle N measures at 48 degrees, all we have to do is subtract that from 90 degrees to find the measure of Angle I.

90 - 48 = 42

So, the measure of Angle I is 42 degrees! It's pretty easy finding complementary angles once you know how to. I hope this helps! Have a lovely day!! :)

(p.s. I do teaching textbooks too)

Answer:

Step-by-step explanation:

Complementary angles add up to 90°

∠I + ∠N = 90

∠I  + 48 = 90

    ∠I = 90 - 48

∠I = 42°

The Oriental Pearl Tower in Shanghai, China, is a 468-meter high tower with 11 spheres along the tower. Two spheres are larger than the rest and house meeting areas, an observation deck, and a revolving restaurant. The lower of the two larger spheres has a radius of 25 meters, and the higher sphere has a radius of 22.5 meters. What is the approximate total volume of the two largest spheres on the Oriental Pearl Tower?

Answers

The approximate total volume of the two largest spheres on the Oriental Pearl Tower 113105.45 m³.

How to find the volume of a sphere

The volume of the sphere is calculated as follows:

volume = 4 / 3 πr³

where

r = radius

The lower two larger spheres in the tower has a radius of 25 meters and 22.5 meters. Therefore, the total volume of the two largest sphere is as follows:

volume of lower sphere = 4 / 3 × 3.14 × 25³

volume of lower sphere = 196250 / 3

volume of lower sphere = 65416.6666667

volume of lower sphere = 65416.7 m³

volume of higher sphere = 4 / 3 × 3.14 × 22.5³

volume of higher sphere = 143066.25 / 3

volume of higher sphere = 47688.75

volume of higher sphere = 47688.8 m³

The approximate total volume = 65416.7 + 47688.8  = 113105.45 m³

learn more on sphere here: https://brainly.com/question/13833611

Help help help help help help

Answers

Answer:

The total of this whole angle, which is represented by ∠ABD, measures 64°.

We are given that apart of this angle, ∠CBD measures 30°, so that'd mean that the other part of this angle, ∠ABC, would measure 34°.

This is because both angles ABC and CBD combined would equal a total of 64°.

So we set up the equation;

30 + x = 64

-30       -30

x = 34°, therefore ∠ABC = 34°.

Answer:

m∠ABC = 34°

Step-by-step explanation:

Given:

m∠ABD = 64°

m∠CBD = 30°

BC is the angle bisector of ∠ABD, which means that an angle is cut in half into two equal pieces. The line divides an angle into two angles.

∠ABC + ∠CBD = ∠ABD

m∠ABC = m∠ABD - m∠CBD

m∠ABC = 64° - 30°

m∠ABC = 34°

hope this helps!! p.s. i really need brainliest :)

Help!!!
Rationalize the denominator of;
[tex]1) \frac{1}{ \sqrt{7} } [/tex]
[tex]2) \frac{2}{ \sqrt{3} - \sqrt{2} } [/tex]
[tex]3) \frac{ \sqrt{6} + \sqrt{3} }{9 + 2 \sqrt{18} } [/tex]

Answers

Answer:

see below for explanation:-

Step-by-step explanation:

#1

[tex] \displaystyle{ \frac{1}{ \sqrt{7} } }[/tex]

[tex]\displaystyle{ \frac{1}{ \sqrt{7} } \times \frac{ \sqrt{7} }{ \sqrt{7} } }[/tex]

[tex]\displaystyle{ \frac{ \sqrt{7} }{7} }[/tex]

#2

[tex]\displaystyle{ \frac{2}{ \sqrt{3} - \sqrt{2} } }[/tex]

[tex]\displaystyle{ \frac{2}{ \sqrt{3} - \sqrt{2} } \times \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} + \sqrt{2} } }[/tex]

[tex]\displaystyle{ \frac{2( \sqrt{3} + \sqrt{2} }{( \sqrt{3} {)}^{2} - ( \sqrt{ 2 } {)}^{2} } }[/tex]

[tex]\displaystyle{ \frac{2( \sqrt{3} + \sqrt{2} ) }{3 - 2} }[/tex]

[tex]\displaystyle{2( \sqrt{3} + \sqrt{2} )}[/tex]

#3

[tex]\displaystyle{ \frac{ \sqrt{6} + \sqrt{3} }{9 + 2 \sqrt{18} } }[/tex]

[tex]\displaystyle{ \frac{ \sqrt{6} + \sqrt{3} }{ 9 + 2 \sqrt{9 \times 2} } }[/tex]

[tex]\displaystyle{ \frac{ \sqrt{6} + \sqrt{3} }{9 + 6 \sqrt{2} } }[/tex]

[tex]\displaystyle{ \frac{ \sqrt{6} + \sqrt{3} }{3(3 + 2 \sqrt{2}) } }[/tex]

[tex]\displaystyle{ \frac{ \sqrt{6} + \sqrt{3} }{3(3 + 2 \sqrt{2}) } \times \frac{3 - 2 \sqrt{2} }{3 - 2 \sqrt{2} } }[/tex]

[tex]\displaystyle{ \frac{3 \sqrt{6} - 2 \sqrt{12} + 3 \sqrt{3} - 2 \sqrt{6} }{3( {3}^{2} - (2 \sqrt{2} {)}^{2} ) } }[/tex]

[tex]\displaystyle{ \frac{ \sqrt{6} - 4 \sqrt{3} + 3 \sqrt{3} }{3(9 - 8)} }[/tex]

[tex]\displaystyle{ \frac{ \sqrt{6} - \sqrt{3} }{3} }[/tex]

Kaseem had 1/4 box of candy. He ate 1/2 of the candy. What fraction of the box did Kaseem eat? Show all work.

Answers

Answer:

1/8

Step-by-step explanation:

So he had 1/4 of a candy box and he ate 1/2 of it. 1/2 of 1/4 is 1/8 because 1/4 × 1/2 =1/8

PLEASE HELP ME WITH THIS QUESTION

Answers

Answer:

The second option, 1,008 cm²

Step-by-step explanation:

   This shape has 5 sides to solve for with reguards to surface area.

   Let us solve for them all.

[1 & 2 - the triangles]

12 * 9 = 108 cm²

-> I am not going to divide since we have 2 congruent triangles

[3 - the bottom side]

25 * 12 = 300 cm²

[4 - the side facing away]

25 * 9 = 225 cm²

[5 - the side facing up]

25 * 15 = 375 cm²

   Now we will add them together for the total.

108 + 300 + 225 + 375 = 1,008 cm²

             The surface area for the triangular prism shown is 1,008 cm².

Answer:

Your answer would be:
C.) 1,350 cm2

Volume = 0.5 x b x h x length

0.5 x (25 x 12) x 9 =
0.5 x 300 x 9 =
= 1,350 cm2




Step-by-step explanation:

Have a great rest of your day
#TheWizzer

Find the slope of the line that passes through (56, 49) and (-18, 35).

Answers

Answer:

[tex]\displaystyle \frac{7}{37}[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{-y_1 + y_2}{-x_1 + x_2} = m \\ \\ \frac{-49 + 35}{-56 - 18} = m \hookrightarrow \frac{-14}{-74} = m \\ \\ \boxed{\frac{7}{37} = m}[/tex]

I am joyous to assist you at any time.

Sam has a small paper delivery business. His parents require him to to save $1 every $5 he earns. If he made $200, how much would he need to save

Answers

I believe it would be $40
If not message me and i’ll try to help

please help me solving this question please i want all solve please help​

Answers

The correct answer is:
David= 8
Raveena = 64
Hamid = -4

Modern Electronics offers a one-year monthly installment plan for a big screen TV. The payment for the first month is 882, and then it increases by 4% each month for the rest of the year. Which expression can be used to find the total amount paid in the first 12 months?

Answers

✿————✦————✿

Answer: A

[tex]62=\frac{12(1.04^{12}-1) }{1.04-1}[/tex]

✿————✦————✿

The volume of a rectangular prism is
3,000 cm?. If the width of the prism is 10 cm
and the height is 15 cm, what is the length
of the prism in centimeters?

Answers

Answer:

To find the volume of a rectangular prism, multiply the length, width, and height. The unit for measuring the volume of a rectangular prism is cubic units, i.e., cm3, mm3, in3, m3, etc.

Step-by-step explanation:

hope it helps

Find the volume of the
following triangular prism.

height: 2cm
length: 5cm
width: 3.5cm

A. 17.5cm3
B. 35cm3
C. 42.5cm3
D. 45cm3

Answers

Most likely it’s A because we’re talking about the volume here

Mia drew a scale drawing of a game room. The air hockey table is 6 inches wide in the
drawing. The actual air hockey table is 4 feet wide. What scale factor does the drawing use?
Simplify your answer and write it as a fraction.

Answers

Answer:

8x

Step-by-step explanation:

The drawing of the air hockey table is 1/8th the size of the actual air hockey table so the scale factor the drawing uses is 8x

logariths, please help​

Answers

Answer:

{ - 2 , 8 }

Step-by-step explanation:

[tex]log_{4}[/tex] ( x² - 6x ) = 2

4² = ( x² - 6x )

x² - 6x - 16 = 0

- 6 = - 8 + 2

- 16 = - 8 * 2

( x - 8 )( x + 2 ) = 0 ⇒ [tex]x_{1}[/tex] = - 2 , [tex]x_{2}[/tex] = 8

{ - 2 , 8 }

Solve for p.

3(p + 4) = 48
A. 13

B. 12

C. 14

D. 19

Answers

Step-by-step explanation:

3 ( p + 4 ) = 48

3p + 12 = 48

3p = 48 - 12

3p = 36

p = 36 ÷ 3

p = 12...

Ms.Wiz spent 58 dollars on a pair of jeans at old navy.A week later,the store ran a sale and all jeans were 35% off.if she had waited a week,how much would she had paid for the jeans

Answers

Answer:

$37.70

Step-by-step explanation:

56*.65

pls mark brainliest

Element X is a radioactive isotope such that every 81 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 1800 grams, how much of the element would remain after 28 years, to the nearest whole number?

Answers

Answer:

1426

Step-by-step explanation:

this question has been asked before and answered incorrectly but people corrected them in the comments.

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