please please please help. will do anything, anything!!

Please Please Please Help. Will Do Anything, Anything!!

Answers

Answer 1

Hi there! :)

Answer:

2nd choice. f(x) = 4 sin x + 2

Step-by-step explanation:

Recall that the transformations form of a sine function is:

y = ±a sin(b(x-h)) + k

Where:

'a' changes the amplitude

'b' changes the period

'h' is a horizontal shift

'k' is a vertical shift, or a change in the midline.

In this instance, the function has a midline of y = 2, which means an equation representing this must have a 'k' value of 2.

The only equation that contains this value is:

f(x) = 4 sin x + 2.

Answer 2

Answer:

I'm pretty positive the answer is B.   f(x) = 4sinx + 2

Step-by-step explanation:

Since d = 2 and the amplitude is 4 and there is nothing else effecting the function you are going up the graph 2 vertically and the amplitude will just go up and down 4 with you midline being at y = 2.


Related Questions

You are mandated to pick 45 units per hour. You work 8.5 hours a day (minus a 1/2 hour lunch), Monday to Friday. How many units should you be picking each week?

Answers

Answer:

1912.5 units

Step-by-step explanation:

Firstly let us calculate the amount of hours you will have to work in a week.

Since you will have to work Mondays through Fridays, hence you will be working 5 days in a week.

Hence in a week you will work 8.5*5= 42.5 hours in a week

Since in 1 hours you are mandated to pick 45 units

Hence in 42.5 hours you will pick 42.5*45= 1912.5 units

75% letter size paper and 25% legal size paper. What is the ratio of letter size paper to legal size paper

Answers

Answer:

3:1

Step-by-step explanation:

75%=[tex]\frac{75}{100}[/tex]=[tex]\frac{3}{4}[/tex]

25%=[tex]\frac{25}{100}[/tex]=[tex]\frac{1}{4}[/tex]

WHY CAN'T ANYONE HELP ME: ( Two computer disks and three notebooks cost ​$29. ​However, five computer disks and four notebooks cost ​$48. Find the price of each.

Answers

Answer:

Disks = $4 each and Notebooks = $7 each

Step-by-step explanation:

-4(2D + 3N = 29)

3(5D + 4N = 48)

-8D - 12N = -116

15D + 12N = 144

7D = 28

D = $4

2(4) + 3N = 29

8 + 3N = 29

3N = 21

N = $7

A business marketing firm specializes in radio advertising. They hope to show there is a linear relationship between sales and the amount of money a client invests in radio advertising. Which hypothesis test would be most appropriate for addressing this question?

Answers

Answer: Chi-square test

Step-by-step explanation:

A Chi-square test is a test used or applied to check or see if a relationship between two categorical variables. Example

The marketing firm trying to show their client that there is a linear relationship between sales and the amount of money the client has invested in radio advertisements uses chi-square method by comparing the two variables which are Sales made and Amount spent on advert or promotion on radio.

Please help!! Over several years, Stephon gathered data about his age and the time it took him to run two laps on the school track. The scatter plot shows the data he gathered and the line of best fit. The equation of the line of best fit is y = -2.1x + 565.6. Based on the line of best fit, approximately how long will it take Stephon to run two laps on the track when he is 192 months old?

Answers

Answer:

It will take Stephon about A: 163 seconds to run two laps when he is 192 months old.

Step-by-step explanation:

To find 163 seconds all I did was eyeball where 192 months is going to be on the x-axis and lined it up with the provided line of fit, then I ran it across the x-axis to the y-axis and I got around 163 seconds.

Given line of best fit is y = -2.1x + 565.6, where x is age in months and y is time in seconds, it take Stephon 162.4 seconds to run two laps on the track when he is 192 months old

A line of best fit is a straight line that minimizes the distance between it and some data. The line of best fit is used to express a relationship in a scatter plot of different data points.

Given in the question,

x =  age in months

y = time in seconds

Here, age of child is independent and time taken to run two laps is dependent variable.

given line of best fit :  y = -2.1x + 565.6

given y = 192 months

finding the value of y :

y = -2.1x + 565.6 = -2.1 * 192 + 565.6 = 162.4

Learn more about line of best fit here

https://brainly.com/question/29250235

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The resale value of a certain industrial machine decreases over a 8-year period at a rate that changes with time. When the machine is x years old, the rate at which its value is changing is 200(x - 8) dollars per year. By how much does the machine depreciate during the fifth year

Answers

Answer: The machine depreciates during the fifth year by $4000.

Step-by-step explanation:

Given: The resale value of a certain industrial machine decreases over a 8-year period at a rate that changes with time.

When the machine is x years old, the rate at which its value is changing is 200(x - 8) dollars per year.

Then, the machine depreciates A(x) during the fifth year as

[tex]A(x) =\int^{5}_1200(x - 8)\ dx\\\\=200|\frac{x^2}{2}-8x|^{5}_1\\\\=200[\frac{5^2}{2}-\frac{1^2}{2}-8(5)+8(1)]\\\\=200 [12-32]\\\\=200(-20)=-4000[/tex]

Hence, the machine depreciates during the fifth year by $4000.

write and equation to represent the following statement 28 is 12 less thank K. solve for K K =

Answers

Answer:

K = 40

Step-by-step explanation:

As they said that 28 is 12 less than K , it means that you've to add them to get the answer. So , 28 + 12 = 40 which is represented by the variable "K"

Hope it helps and pls mark as brainliest : )

Answer:

Equation : 28 = k - 12

K = 40

Step-by-step explanation:

28 is 12 less than k

Let's create an equation:

[tex]28 = k - 12[/tex]

Now, let's solve:

[tex]28 = k - 12[/tex]

Move variable to L.H.S and change its sign

Similarly, Move constant to R.H.S and change its sign

[tex] - k = - 12 - 28[/tex]

Calculate the difference

[tex] - k = - 40[/tex]

Change the signs on both sides of the equation

[tex]k = 40[/tex]

Hope this helps...

Best regards!!

Angle bisectors AX and of triangle ABC meet at point I. Find angle C in degrees, if AIB = 109.

Answers

Answer:

angle C = 38 degrees

Step-by-step explanation:

Refer to attached figure (sorry, forgot to attach earlier)

Given

AIB = 109

Let

CAX = XAB = x

CBY = YBA = y

XIB = YIA = x+y    ........exterior angles

XIB = YIA = 180-109 = 71   ............ sum of angles on a line

=>

x+y = 71

ACB = 180 - 2x -2y  ................. sum of angles of a triangle

= 180 - 2(x+y)

= 180 - 2(71)

= 180 - 142

= 38

if -2x = -14 what is the value of x

Answers

Answer: x= 7

Step-by-step explanation:

-2x= -14    Divide both sides by -2

x= 7  

check

-2(7) = -14

-14 = -14

Answer:

x = 7

Step-by-step explanation:

-2x = -14

Divide each side by -2

-2x/-2 = -14/-2

x = 7

Points A,B,C and D are midpoints of the sides of the larger square. If the smaller square has area 60, what is the area of the bigger square?

Answers

Answer:

80

Step-by-step explanation:

which quadratic function in standard form has the value a= -3.5, b=2.7, and c= -8.2?

Answers

Answer:

y = -3.5x² + 2.7x -8.2

Step-by-step explanation:

the quadratic equation is set up as a² + bx + c, so just plug in the values

Answer:

[tex]-3.5x^2 + 2.7x -8.2[/tex]

Step-by-step explanation:

Quadratic functions are always formatted in the form [tex]ax^2+bx+c[/tex].

So, we can use your values of a, b, and c, and plug them into the equation.

A is -3.5, so the first term becomes [tex]-3.5x^2[/tex].

B is 2.7, so the second term is [tex]2.7x[/tex]

And -8.2 is the C, so the third term is [tex]-8.2[/tex]

So we have [tex]-3.5x^2+2.7x-8.2[/tex]

Hope this helped!

which is bigger 4 or
[tex] \frac{12}{7} [/tex]


Answers

obviously 4 is bigger coz 12/7 will yeild you 1.71

13. A hole is drilled in a block of wood as shown in the sketch. The hole is 3/4 of

the total depth of the wood. The total depth of the block of wood is 13/16 in.

How deep is the hole?

Hole

Answers

The depth of hole is 0.609 inches.

Given, the total depth of the block of  wood is  [tex]\frac{13}{16}[/tex] inches.

Since the hole is [tex]\frac{3}{4}[/tex] of the total depth, so the depth of the hole will be,

[tex]D=\frac{3}{4} \times\frac{13}{16}[/tex]

Or, [tex]D=\frac{39}{64}[/tex]

[tex]D=0.609375 \ in[/tex]

Hence the depth of hole is 0.609 inches.

For more details follow the link:

https://brainly.com/question/2263981

This function to calculate the area of a rectangle is not very readable. Can you refactor it, and then call the function to calculate the area with base of 5 and height of 6? Tip: a function that calculates the area of a rectangle should probably be called rectangle_area, and if it's receiving base and height, that's what the parameters should be called.

Answers

Answer:

Here is the refactored function:

def rectangle_area(base, height):

   area = base * height

   return area    

print("The area is ", rectangle_area(5,6))

Step-by-step explanation:

The above program has a function rectangle_area that takes two variables base and height as parameters. The function then computes the area of rectangle by multiplying the values of base and height. The result of the multiplication is assigned to the variable area. Then the function returns the resultant area.

print("The area is ", rectangle_area(5,6)) statement calls rectangle_area() method by passing values of base and height i.e. 5 and 6 to compute the area. The output of this program is:

The area is 30

Note that the use of rectangle_area function name describes what the function does i.e. it computes the area of rectangle. By naming the parameters as base and height that clearly depicts that in order to compute rectangle are we need the base and height of rectangle. So this makes the code readable.

Which pair of non-congruent figures must be similar? two squares two parallelograms (not rectangles) two right triangles two isosceles triangles (not equilateral)

Answers

Answer:

The answer is A (Two squares)

Step-by-step explanation:

Any give square will have proportionate side lengths,as they are the same, meaning that if you dilute  one square it will always be proportinate

Answer:

it is a

Step-by-step explanation:

the other person is correct. and I did the test


A father is 60 years old and his son is half his age. How old was the boy when his father was four times his age?

Answers

Hey there! I'm happy to help!

We see that the father is 60 years old, and the son is half of that age, so this means that the son is 30 years old.

We want to see the age the son was at when the father was four times his age. We know that the father is thirty years older than him, so we can write this equation with s representing the age of the son.

s+30=4s   (30 years older than the son is equal to to four times the son's age at the time)

We subtract 30 from both sides.

s=4s-30

We subtract 4s from both sides.

-3s=-30

We divide both sides by -3.

s=10

Therefore, the boy was 10 when his father was four times his age. This is because his father would have been 40 because that is 30 more years than 10, and it is four times ten!

Have a wonderful day! :D

Explain how to find the range of a data set. What is an advantage of using the range as a measure of​ variation? What is a​ disadvantage?

Answers

Answer:

The range is found by subtracting the minimum data entry from the maximum data entry.

Step-by-step explanation:

The range is found by subtracting the minimum data entry from the maximum data entry.

It is easy to compute.

It uses only two entries from the data set.

Find the probability of picking 1 consonant and 4 vowels when 5 letters are picked (without replacement) from a set of alphabet tiles.

Answers

Answer:

Ok, we have a total of 26 letters, and we want to select 5 of them.

Of the 26 letters, 21 are consonants and 5 are vowels.

Suppose that we want to have the consonant in the first selection, so the probability of picking a consonant is equal to the quotient between the number of consonants and the total number of letters.

p = 21/26

now a letter has been selected, so in the set, we have 25 letters left.

In the next 4 selections, we must select vowels.

In the second selection the probability is:

p = 5/25

in the third, the prob is:

p = 4/24 (we already selected one vowel before, so now we only have 4 vowels)

The fourth selection:

p = 3/23

and the last selection:

p = 2/22

The total probability is equal to the product of all the individual proabilities, so we have:

P = (2/22)*(3/23)*(4/24)*(5/25)*(21/26)

Now, remember that we said that the consonant must be in the first place, but it can be in any of the five places, so if we add the permutations of the consonant letter we have:

P = 5*(2/22)*(3/23)*(4/24)*(5/25)*(21/26) =  0.0018

Find the 10th term of the following geometric sequence.
2, 10, 50, 250, ...

Answers

Answer:

3906250

Step-by-step explanation:

We can notice that the ratio is 5. 10/2 = 5

Each term gets multiplied by 5 to get the next term.

250 × 5 = 1250 (5th term)

1250 × 5 = 6250 (6th term)

6250 × 5 = 31250 (7th term)

31250 × 5 = 156250 (8th term)

156250 × 5 = 781250 (9th term)

781250 × 5 = 3906250 (10th term)

The 10th term of the geometric sequence is 3906250.

4, 12, 36,what is 3 other remaining sequence​

Answers

Answer:

108, 324, 972

Step-by-step explanation:

This sequence is multiplying by ✖️3.

4✖️3=12✖️3=36✖️3=108✖️3=324✖️3=972

Hope this helps!

108, 324, 972................

There are 50 mangoes 20 of which are unriped another basket contains 40 mangoes 15 unripe if we take 1 mangoes from each basket Find the probability of getting both are ripe Find the probability of getting both are unripe Find the probability of getting one ripe and one unripe Find the probability of at least one right Find the probability of at least one uripe

Answers

Answer:

probability of getting both are unripe

= 0.15

probability of getting both are ripe

= 0.375

Probability of one ripe and one unripe

=0.234375

Probability of at least one unripe

=0.625

Step-by-step explanation:

50 mangoes 20 of which are unriped in the first basket .

Riped = 50-20= 30

Probability of unripe = 20/50

Probability of unripe= 0.4

Probability of ripe = 30/50

Probability of ripe = 0.6

40 mangoes of which 15 are unripe In the second basket

Number of riped= 40-15= 25

Probability of unriped= 15/40

Probability of unriped= 0.375

Probability of riped= 25/40

Probability of riped= 0.625

probability of getting both are unripe

= 0.4*0.375

probability of getting both are unripe

= 0.15

probability of getting both are ripe

= 0.6*0.625

= 0.375

Probability of one ripe and one unripe

= 0.625*0375

= 0.234375

Probability of at least one unripe

= 1- probability of no unripe

= 1 - probability of both ripe

= 1-0.375

= 0.625

The height of a projectile launched upward at a speed of 32 feet/second from a height of 128 feet is given by the function h(t) = -16t^2 + 32t +128. How long will it take the projectile to hit the ground?

Answers

Answer:

It takes 4 seconds for the projectile to hit the ground

Step-by-step explanation:

The height of the projectile after t seconds is given by the following equation:

[tex]h(t) = -16t^{2} + 32t + 128[/tex]

How long will it take the projectile to hit the ground?

It happens when [tex]h(t) = 0[/tex]

So

[tex]h(t) = -16t^{2} + 32t + 128[/tex]

[tex]-16t^{2} + 32t + 128 = 0[/tex]

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0[/tex].

This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:

[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]\bigtriangleup = b^{2} - 4ac[/tex]

In this question:

[tex]-16t^{2} + 32t + 128 = 0[/tex]

So [tex]a = -16, b = 32, c = 128[/tex]

[tex]\bigtriangleup = 32^{2} - 4*(-16)*(128) = 9216[/tex]

[tex]t_{1} = \frac{-32 + \sqrt{9216}}{2*(-16)} = -2[/tex]

[tex]t_{2} = \frac{-32 - \sqrt{9216}}{2*(-16)} = 4[/tex]

Time is a positive measure, so:

It takes 4 seconds for the projectile to hit the ground

If four times the brother's age is subtracted from three times the sister's age, the difference is 17. Give an equation that represents this statement using bbb as the age of the brother and s as the age of the sister.

Answers

Answer:

3s-4bbb=17

Step-by-step explanation:

brother=4bbb

sister=3s

3s-4bbb=17

PLEASE HELP Which ordered pair is a solution to the system of inequalities?
y< 3x
y< 5

Answers

Answer:

I am pretty sure that it is  C

Step-by-step explanation:

A 1,3 so 3 < 3 no not true

   x,y

B -12,50   50< -36 Also not true

    x  ,  y

C  9  ,  4   4<27 Yes    4< 5 YEPPP

D 4,10   10<12 Yes          10<5 NOOPPPPPEEEE

What is the next number in the series: 4, 5, 9, 25, 89, ___

Answers

Answer:

345

Step-by-step explanation:

1 + 4 = 5

4 + 5 = 9

16 + 9 = 25

64 + 25 = 89

1, 4, 16, and 64 are powers of 4.  The next power of 4 is 256.

256 + 89 = 345

The answer is 345 (don’t ask why)

BRAINLIEST ANSWER GIVEN Without actually solving the​ problem, choose the correct solution by deciding which choice satisfies the given conditions. The length of a rectangle is 2 feet longer than the width. The perimeter is 20 feet. Find the dimensions of the rectangle. Length= ?; width=?

Answers

Answer:

length = 6 feetwidth = 4 feet

Step-by-step explanation:

Perimeter of a rectangle = 2l + 2w

where l is the length

w is the width

The length of the rectangle is 2 feet longer than the width is written as

l = 2 + w

Perimeter = 20feet

So we have

20 = 2( 2 + w ) + 2w

20 = 4 + 2w + 2w

4w = 16

Divide both sides by 4

w = 4

Substitute w = 4 into l = 2 + w

That's

l = 2 + 4

l = 6

length = 6 feetwidth = 4 feet

Hope this helps you

Answer:

w = 4 and L = 10

Step-by-step explanation:

perimeter of a rectangle = 2(l+w)

p = 20

L = 2 + w

w = ?

20 = 2(2 + w + w)

20 = 2(2 + 2w)

20/2 = 2 + 2w

10 = 2 + 2w

10 - 2 = 2w

8 = 2w

w = 8/2 = 4

L = w + 2

L = 4 +2 = 6

w = 4 and L = 10

Applications of exponential functions

Answers

Answer:

a simple interest rate of 4.5%

Witch table represents a linear function ?

Answers

Answer:

If you compute the slope between any two points that must be the same, that's how you can tell if a table represents a linear function.

Remember that the slope between any two points (x1,y1), (x2,y2) is

slope   =  ( y2 - y1 ) / (x2 - x1)

Step-by-step explanation:

If you compute the slope between any two points that must be the same, that's how you can tell if a table represents a linear function.

Remember that the slope between any two points (x1,y1), (x2,y2) is

slope   =  ( y2 - y1 ) / (x2 - x1)

A certain brand of automobile tire has a mean life span of 35,000 miles, with a standard deviation of 2250 miles. Assume the life spans of the tires have a bell-shaped distribution.
(a) The life spans of three randomly selected tires are 34,000 miles, 37,000 miles, and 30,000 miles. Find the z-score that corresponds to each life span. Determine whether any of these life spans are unusual.
(b) The life spans of three randomly selected tires are 30,500 miles, 37,250 miles, and 35,000 miles. Using the Empirical Rule, find the percentile that corresponds to each life span.

Answers

Answer:

Step-by-step explanation:

From the information given:

mean life span of a brand of automobile = 35,000

standard deviation of a brand of automobile = 2250 miles.

the z-score that corresponds to each life span are as follows.

the standard z- score formula is:

[tex]z = \dfrac{x - \mu}{\sigma}[/tex]

For x = 34000

[tex]z = \dfrac{34000 - 35000}{2250}[/tex]

[tex]z = \dfrac{-1000}{2250}[/tex]

z = −0.4444

For x = 37000

[tex]z = \dfrac{37000 - 35000}{2250}[/tex]

[tex]z = \dfrac{2000}{2250}[/tex]

z = 0.8889

For x = 3000

[tex]z = \dfrac{30000 - 35000}{2250}[/tex]

[tex]z = \dfrac{-5000}{2250}[/tex]

z = -2.222

From the above z- score that corresponds to their life span; it is glaring  that the tire with the life span 30,000 miles has an unusually short life span.

For x = 30,500

[tex]z = \dfrac{30500 - 35000}{2250}[/tex]

[tex]z = \dfrac{-4500}{2250}[/tex]

z = -2

P(z) = P(-2)

Using excel function (=NORMDIST -2)

P(z) = 0.022750132

P(z) = 2.28th percentile

For x =  37250

[tex]z = \dfrac{37250 - 35000}{2250}[/tex]

[tex]z = \dfrac{2250}{2250}[/tex]

z = 1

Using excel function (=NORMDIST 1)

P(z) = 0.841344746

P(z) = 84.14th percentile

For x = 35000

[tex]z = \dfrac{35000- 35000}{2250}[/tex]

[tex]z = \dfrac{0}{2250}[/tex]

z = 0

Using excel function (=NORMDIST 0)

P(z) = 0.5

P(z) = 50th percentile

a.  The z score of each life span should be -0.4444, 0.889, and 2.2222.

b.  The percentile of each life span should be 0.0228, 0.8413 and  0.5000.

Given that,

mean life span of 35,000 miles, with a standard deviation of 2250 miles.

The calculation is as follows:

(a)

The z score should be

[tex]Z1 = \frac{34000-35000}{2250} = -0.4444\\\\Z2 = \frac{37000-35000}{2250} = 0.8889\\\\Z3 = \frac{30000-35000}{2250} = -2.2222\\\\[/tex]

The tire with life span of 30000 miles would be considered unusual

(b)

The percentile should be

[tex]Z1 = \frac{30500-35000}{2250} = -2[/tex]

p(Z1 < -2) = NORMSDIST(-2) = 0.0228

[tex]Z2 = \frac{37250-35000}{2250} = 1[/tex]

p(Z2 < 1) = NORMSDIST(1) = 0.8413

[tex]Z3 = \frac{35000-35000}{2250} = 0[/tex]

p(Z3 < 0) = NORMSDIST(0) = 0.5000

Find out more information about standard deviation here:

https://brainly.com/question/12402189?referrer=searchResults

A particle is moving with the given data. Find the position of the particle. a(t) = 2t + 5, s(0) = 6, v(0) = −5

Answers

Answer:

The position of the particle is described by [tex]s(t) = \frac{1}{3}\cdot t^{3} + \frac{5}{2}\cdot t^{2} - 5\cdot t + 6,\forall t \geq 0[/tex]

Step-by-step explanation:

The position function is obtained after integrating twice on acceleration function, which is:

[tex]a(t) = 2\cdot t + 5[/tex], [tex]\forall t \geq 0[/tex]

Velocity

[tex]v(t) = \int\limits^{t}_{0} {a(t)} \, dt[/tex]

[tex]v(t) = \int\limits^{t}_{0} {(2\cdot t + 5)} \, dt[/tex]

[tex]v(t) = 2\int\limits^{t}_{0} {t} \, dt + 5\int\limits^{t}_{0}\, dt[/tex]

[tex]v(t) = t^{2}+5\cdot t + v(0)[/tex]

Where [tex]v(0)[/tex] is the initial velocity.

If [tex]v(0) = -5[/tex], the particular solution of the velocity function is:

[tex]v(t) = t^{2} + 5\cdot t -5, \forall t \geq 0[/tex]

Position

[tex]s(t) = \int\limits^{t}_{0} {v(t)} \, dt[/tex]

[tex]s(t) = \int\limits^{t}_{0} {(t^{2}+5\cdot t -5)} \, dt[/tex]

[tex]s(t) = \int\limits^{t}_0 {t^{2}} \, dt + 5\int\limits^{t}_0 {t} \, dt - 5\int\limits^{t}_0\, dt[/tex]

[tex]s(t) = \frac{1}{3}\cdot t^{3} + \frac{5}{2}\cdot t^{2} - 5\cdot t + s(0)[/tex]

Where [tex]s(0)[/tex] is the initial position.

If [tex]s(0) = 6[/tex], the particular solution of the position function is:

[tex]s(t) = \frac{1}{3}\cdot t^{3} + \frac{5}{2}\cdot t^{2} - 5\cdot t + 6,\forall t \geq 0[/tex]

Answer:

Position of the particle is :

[tex]S(t)=\frac{1}{3}.t^3+\frac{5}{2}.t^2-5.t+6[/tex]

Step-by-step explanation:

Given information:

The particle is moving with an acceleration that is function of:

[tex]a(t)=2t+5[/tex]

To find the expression for the position of the particle first integrate for the velocity expression:

AS:

[tex]V(t)=\int\limits^0_t {a(t)} \, dt\\v(t)= \int\limits^0_t {(2.t+5)} \, dt\\\\v(t)=t^2+5.t+v(0)\\[/tex]

Where, [tex]v(0)[/tex] is the initial velocity.

Noe, if we tale the [tex]v(0) =-5[/tex] ,

So, the velocity equation can be written as:

[tex]v(t)=t^2+5.t-5[/tex]

Now , For the position of the particle we need to integrate the velocity equation :

As,

Position:

[tex]S(t)=\int\limits^0_t {v(t)} \, dt \\S(t)=\int\limits^0_t {(t^2+5.t-5)} \, dt\\S(t)=\frac{1}{3}.t^3+\frac{5}{2}.t^2-5.t+s(0)[/tex]

Where, [tex]S(0)[/tex] is the initial position of the particle.

So, we put the value [tex]s(0)=6[/tex] and get the position of the particle.

Hence, Position of the particle is :

[tex]S(t)=\frac{1}{3}.t^3+\frac{5}{2}.t^2-5.t+6[/tex].

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