Given the acceleration, initial velocity, and initial position of a body moving along a coordinate line at time t, find the body's position at time t. a=16, v(0) = -14, s(0) = -8

Answers

Answer 1

Answer:

The  position at time t  is  [tex]s(t) = 8t^2 - 14t -8[/tex]

Step-by-step explanation:

From the question we are told that

   The acceleration is  [tex]a = 16[/tex]

   The velocity at t = 0  is  [tex]v(0) = -14[/tex]

    The  position at time t =  0  is [tex]s(0) = -8[/tex]

Generally acceleration is mathematically represented as

     [tex]a(t) = \frac{d v}{dt }[/tex]

=>   [tex]\frac{dv}{dt} = 16[/tex]

=>   [tex]dv = 16 dt[/tex]

integrating both sides we have    

     [tex]\int\limits dv = \int\limits16 dt[/tex]

=>  [tex]v(t) = 16 t + c[/tex]

Now at t = 0  

     [tex]v(0) = 16 * 0 +c = -14[/tex]

=>  [tex]c = -14[/tex]

So

   [tex]v(t) = 16 t -14[/tex]

Generally the position of the body is mathematically represented as

     [tex]s(t) = \int\limits v(t)dt[/tex]

So

    [tex]s(t) = \int\limits 16t - 14 dt[/tex]

So  

    [tex]s(t) = 16 \frac{t^2}{2} - 14t + C[/tex]

Now  at t =  0

     [tex]s(0) = 16 \frac{0^2}{2} - 14(0) + C = -8[/tex]

=>    [tex]C = -8[/tex]

So

   [tex]s(t) = 8t^2 - 14t -8[/tex]

Answer 2

Rate of change of velocity with respect to time is known as acceleration.

Rate of change of displacement with respect to time is known as velocity.

Body position at time t is given by,   [tex]s(t)=8t^{2}-14t-8[/tex]

Data given are, a=16, v(0) = -14, s(0) = -8

Since,  [tex]\frac{dv}{dt}=a\\\\\frac{dv}{dt}=16\\\\dv=16dt[/tex]

Integrating both side

 We get,    [tex]v=16t + C[/tex]

Substituting v(0)=-14 in above equation

We get,   C = -14

  So,   [tex]v=16t-14[/tex]

Since, Rate of change of displacement with respect to time is known as velocity.

        [tex]v=\frac{ds}{dt}\\\\ds=vdt\\\\ds=(16t-14)dt[/tex]

Taking integration on both side

We get,   [tex]s=16\frac{t^{2} }{2}-14t+c[/tex]

Substituting s(0)= - 8 in above equation

We get,   [tex]c=-8[/tex]

So,  [tex]s=16\frac{t^{2} }{2}-14t-8\\\\s(t)=8t^{2} -14t-8\\[/tex]

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Related Questions

What are the six trigonometric functions and how are their values determined using the three sides of a right triangle?

Answers

Explanation:

Six trigonometric functions are ratio of sides with their angle in right angled triangle.

Six trigonometric functions are:

Sinθ = Perpendicular / Hypotenuse

Cosθ = Base / Hypotenuse

Tanθ = Perpendicular / Base

Cotθ = Base / Perpendicular

Secθ = Hypotenuse / Base

Cosecθ = Hypotenuse / Perpendicular

1+6v+4=47

Be quick please :D

Answers

Answer:

1+ 6v + 4 = 47

collect like terms

5 + 6v = 47

Subtract the 5 from both sides

6v = 42

divide 6 from both sides

v = 7


Which is the decimal expansion of 7/22?
0.318
0.318
0.318
0.318

Answers

Answer: B

Step-by-step explanation: Cuz I got a calculator

Hope this helps

The decimal expansion of 7/22 is 0.3181818..., which means that the answer is [tex]0.3\overline{18}[/tex]

Option B is the correct answer.

What is an expression?

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example: so

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

To find the decimal expansion of 7/22, we need to perform a long division:

  0.3181818...

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

22 | 7.0000000

   6.6

   -----

   3.4

   3.3

   ---

     10

      8

      --

      20

      18

      ---

       20

       18

       --

        200

        198

        ---

          20

          22

          --

          -2

Now,

0.3181818 can be written as [tex]0.3\overline{18}[/tex]

Therefore,

The decimal expansion of 7/22 is 0.3181818..., which means that the answer is 0.3181818...

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Which is the best description for the graph below? A graph decreases from (0, 3) to (9, 0). The graph increases everywhere. The graph decreases everywhere. The graph remains constant. The graph increases, then decreases.

Answers

Answer:

the graph decreases everywhere

Step-by-step explanation:

the left side of the line is higher than the right side which means its a negative  slope so it is decreasing

Answer:B

Step-by-step explanation:

A group of 4 children and 8 adults are going to the zoo. Each child tickets cost $10, and each adult tickets cost $15. How much will the group spend on tickets to the zoo?

Answers

Answer:

160

Step-by-step explanation:

4 times 10 is 40

8 times 15 is 120

add 40 plus 120 and get 160

Step-by-step explanation:

4×10+8×15

=40+120

=$160

Sample A weighed 2.96 pounds, sample B weighed 3.8 pounds, and sample C weighed 4.417 pounds. How much more does sample C weigh than sample A? Betty collected another sample. Sample D weighed 0.67 pounds more than sample A. How much more does sample B weigh than sample D? 0.17 0.17 3.63 3.63 0.787 0.787 1.26

Answers

Answer:

4.417 - 2.96 = 1.457

3.8-3.63=0.17

Sample C weighs 1.457 more pounds than Sample A.

Sample B weights 0.17 more pounds than Sample D.

Calculate the volume of the cube ____ cm³

Answers

Answer:

48

Step-by-step explanation:

volume=width×length×hight

2×4×6

48

in a given year, residents of a country spent approximately $54.7 billion on their pets. Of this amount, $17.6 billion wa for veterinarian bills. What percent of the total was spent on veterinary care?

Answers

Answer:

32.176 %

Step-by-step explanation:

(100% / 54.7) x 17.6 = about 32.176 percent

Do the equation yourself for a more precise answer!

What is the inverse of g(x)= 1/x-1 and is it a function? 1/x Yes 1/x +1 Yes 1/x - 1 No 1/y-1 No

Answers

Answer:

Step-by-step explanation:

hello,

[tex]g(x)=\dfrac{1}{x-1}\\\\x=g(g^{-1}(x))=\dfrac{1}{g^{-1}(x)-1} \\ \\g^{-1}(x)-1=\dfrac{1}{x}\\ \\g^{-1}(x)=\dfrac{1}{x}+1=\dfrac{1+x}{x}[/tex]

And this is a function defined for x different from 0.

Thanks

People wait for sales to_______

1. buy the most goods

2. get the best price for a good

Answers

2. get the best price for a good

Canada has a population of 1/10 as large as the United States and Canada population is about 32 million about how many people live in United States explain how many zeros in your answer

Answers

Answer:

Step-by-step explanation: If Canada(C) is 32,000,000 and America is A and C x 10 = A then 32,000,000 x 10 = A

And to multiply any whole number by 10 you just add a zero to the end so

320,000,000  is the answer which is pronounced "Three hundred twenty million" And there is 7 zeros in the answer

hope this helps mark me brainliest

convert 2 2/3 into an improper fraction​

Answers

Answer: 8/3

Step-by-step explanation:

Please and Thank youu

Answers

Answer:

5

Step-by-step explanation:

y = 2x - 3

{ x = 4 }

y = 2(4)-3= 8 - 3 = 5

Roxannee is buying suppliers for a catering job. She bought a piece of salmon for $31.28. If the cost of the salmon was $9.20 per pund, how many pounds did she buy? (Show your work)​

Answers

Answer:

she bought 3.4 pounds

Step-by-step explanation:

Given that x = −2 and y = 5, what is the value of 3x+4y−2

Answers

Answer:

12

Step-by-step explanation:

Note:

x = -2 ; y = 5

Plug in -2 for x and 5 for y.

3(-2) + 4(5) - 2

Remember to follow PEMDAS. First solve for multiplication, then combine:

3 * -2 = -6

4 * 5 = 20

-6 + 20 - 2

Combine like terms:

20 - 6 - 2 = 12

12 is your value.

~

Answer:

12

Step-by-step explanation:

When answering these types of problems make sure you simplify the expression before substituting

In this case it is not necessasry so substitute x for -2 and y for -5. The expression is now ...

3(-2) + 4(5) - 2

Now just add like term

-6 + 20 -2

12

Is the square root of 900 rational

Answers

Answer:

Yes it is rational

Step-by-step explanation:

The square root of 900 is a rational number if 900 is a perfect square. It is an irrational number if it is not a perfect square. Since 900 is a perfect square, it is rational number.

Maya runs 7 miles in 80 minutes. At the same rate, how many miles would she run in 64 minutes?

Answers

Answer:

5.6 miles.

Step-by-step explanation:

7/80=x/64 is our equation

Cross multiply to solve for x

x=7*64/80

x=5.6mi

Hope this helps ^-^

Answer:

5.6 miles

Step-by-step explanation:

Let's set up a proportion using the following setup.

[tex]\frac{miles }{minutes}=\frac{miles }{minutes}[/tex]

We know Maya can run 7 miles in 80 minutes.

[tex]\frac{7miles }{80minutes}=\frac{miles }{minutes}[/tex]

We don't know how many miles she can run in 64 minutes. Let's say she can run x miles in 64 minutes.

[tex]\frac{7miles }{80minutes}=\frac{x miles }{64 minutes}[/tex]

[tex]\frac{7}{80}=\frac{x}{64}[/tex]

We want to solve for x (miles in 64 minutes). Therefore, we must isolate x on one side of the equation.

x is being divided by 64. The inverse of division is multiplication. Multiply both sides of the equation by 64.

[tex]64*\frac{7}{80}=\frac{x}{64}*64[/tex]

[tex]64*\frac{7}{80}=x[/tex]

[tex]64*0.0875=x[/tex]

[tex]5.6=x[/tex]

[tex]x= 5.6 miles[/tex]

Maya can run 5.6 miles in 64 minutes.

You buy a new wheel for your bicycle. Thaw diameter of the bicycle wheel is 22 inches.What is the radius of the bicycle wheel?What is the circumference of the bicycle wheel?What is the area of the bicycle wheel?

Answers

Answer:

R = 11

C ≈ 69.12

A ≈ 380.13

Step-by-step explanation:

R = d ÷ 2

C = 2πr

A = 2πr²

Which of the following is equal to 7.5 × 4? A. (7 × 4) + (0.5 × 7) B. (7 × 4) + (0.5 × 4) C. (7 + 4) × (0.5 + 4) D. (7 × 4) × (0.5 × 4)

Answers

Answer:

012

3

4

5

61

8

9

10 11 12

13 14

OA. 3

OB. 4

C. 5

D. 7

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A ranger in a lookout tower spots two fires on the campground below. Fire A is 75 meters east
and 40 meters south of the tower. Fire B is 37 meters west and 64 meters south of the tower.
If there is a fire hydrant located three-fourths of the way from Fire A to Fire B, find the location
of the fire hydrant relative to the tower.

Answers

Answer:

the fire hydrant is 9 meters west and 58 m south of the tower

Step-by-step explanation:

Fire A and Fire B can be represented as a point in the Cartesian coordinate with the tower as the origin. Fire A is 75 meters east  and 40 meters south of the tower, It can be represented as (75, -40).  Fire B is 37 meters west and 64 meters south of the tower,  It can be represented as (-37, -64).

If a point O(x, y) divides a line segment AB in the ratio n:m, with A([tex]x_1,y_1[/tex]) and B([tex]x_2,y_2[/tex]), the point O(x, y) is at:

[tex]x=\frac{n}{n+m}(x_2-x_1)+x_1\\ \\y=\frac{n}{n+m}(y_2-y_1)+y_1[/tex]

The fire hydrant (x, y) divides Fire A(75, -40) and fire B(-37, -64) in the ratio 3:1(three fourth), hence:

[tex]x=\frac{n}{n+m}(x_2-x_1)+x_1=\frac{3}{4}(-37-75) +75=\frac{3}{4}(-112)+75=-84+75\\x=-9 \\ \\y=\frac{n}{n+m}(y_2-y_1)+y_1=\frac{3}{4}(-64-(-40))+(-40)= \frac{3}{4}(-18)-40=-18-40\\y=-58[/tex]

The fire hydrant is at (-9, -58). That is the fire hydrant is 9 meters west and 58 m south of the tower

The location of the hydrant relative to the tower is [tex]\left(-9, -58 \right)[/tex] meters.

How to locate the coordinates of the hydrant relative to the tower

In this question we should use the vectorial formula for a line segment to determine the coordinates of the hydrant relative to the tower ([tex]\vec C[/tex]), in meters:

[tex]\vec C = \vec A + r\cdot (\vec B - \vec A)[/tex] (1)

Where:

[tex]\vec A[/tex] - Coordinates of the fire A relative to the tower, in meters. [tex]\vec B[/tex] - Coordinates of the fire B relative to the tower, in meters. [tex]r[/tex] - Distance ratio.

Now we determine the location of the hydrant: ([tex]\vec A = (75, -40)\,[m][/tex], [tex]\vec B = (-37, -64)\,[m][/tex], [tex]r = \frac{3}{4}[/tex])

[tex]\vec C = (75,-40) + \frac{3}{4}\cdot [(-37,-64)-(75,-40)][/tex]

[tex]\vec C = (75,-40) + \frac{3}{4} \cdot (-112,-24)[/tex]

[tex]\vec C = (75,-40) + \left(-84, -18\right)[/tex]

[tex]\vec C = \left(-9, -58 \right)\,[m][/tex]

The location of the hydrant relative to the tower is [tex]\left(-9, -58 \right)[/tex] meters. [tex]\blacksquare[/tex]

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Visna had 5 comic books. His brother gave him 4 more comic books. Visna bought some more comic books at the store. Now he has 15 comic books. How many comic books did Visna buy at the store?

Answers

He bought 6 more books

Answer:6

Step-by-step explanation:

5+4+× = 15

9+x=15

15-9=x

X=6

what is (+21) ÷ (+7) =

Answers

Answer:

3

Step-by-step explanation:

If A, B, and C are the vertices of a triangle, find AB + BC + CA.

Answers

Answer:

0

Step-by-step explanation:

When drawing a triangle, note that the vectors can be drawn either in a clockwise or anticlockwise direction. For a triangle with vertices A, B and C, te vectors are AB, BC and CA

In vector notation CA = - AC (length CA is equal to AC but acting in opposite direction to AC)

and AB+BC = AC

To evaluate AB + BC + CA, we will substitute the vector expression above into the given expression and simplify as shown;

= (AB + BC) + CA

= AC + (-AC)

open the parenthesis

= AC-AC

= 0

Hence the sum of the vector expression AB + BC + CA is a zero vector

On Monday Ken spent half of his money on a new game. The next day he earned $12 mowing lawns. He now has #32. How much money did ken have before he bought the game?

Answers

Answer:

Step-by-step explanation:

ken has 64 dollars

What is the volume of a sphere with a radius of 3 inches? 12π cubic inches 24π cubic inches 36π cubic inches 48π cubic inches

Answers

Answer:

The answer is

36π cubic inches

Step-by-step explanation:

Volume of a sphere is given by

[tex]V = \frac{4}{3} \pi {r}^{3} [/tex]

where r is the radius

From the question

r = 3 inches

Substitute the value into the above formula and solve for the volume

That's

[tex]V = \frac{4}{3}( {3})^{3} \pi \\ = \frac{4}{3} \times 27\pi \\ = 4 \times 9\pi[/tex]

We have the final answer as

36π cubic inches

Hope this helps you

-x+7= -6x-13 how do you solve it

Answers

Answer:

-4=x

Step-by-step explanation:

Okay, let's do this step-by-step for the best results!

We need to make sure that common variables can be put together first. If you did not know this, look at PEMDAS.

-x+7=-6x-13

We need to add -x and -6x together. If we do that then you would get,

7=-5x-13

Let's add 13 to 7 now.

20=-5x

Lets divide -5 with 20.

-4=x

I hope this helped!

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{x = - 4}}}}}[/tex]

Step-by-step explanation:

[tex] \sf{ - x + 7 = - 6x - 13}[/tex]

Move 6x to left hand side and change it's sign

[tex] \dashrightarrow{ \sf{ - x + 6x + 7 = - 13}}[/tex]

Move 7 to right hand side and change it's sign

[tex] \dashrightarrow{ \sf{ - x + 6x = - 13 - 7}}[/tex]

Collect like terms

[tex] \dashrightarrow{ \sf{ 5x = - 13 - 7}}[/tex]

Calculate

[tex] \dashrightarrow{ \sf{5x = - 20}}[/tex]

Divide both sides by 5

[tex] \dashrightarrow{ \sf{ \frac{5x}{5} = \frac{ - 20}{5} }}[/tex]

Calculate

[tex] \dashrightarrow{ \sf{x = - 4}}[/tex]

Hope I helped!

Best regards! :D

I need help 2x+y=7 to solve for y

Answers

Answer:

X=7-y over 2

Step-by-step explanation:

Subtract yy from both sides.

2x=7-y2x=7−y

2 Divide both sides by 22.

x=\frac{7-y}{2}x=

​2

​7−y

​​  

The equation solved for y is  y=7-2x.

The given equation is 2x+y=7.

We need to solve the given equation for y.

How to solve an equation?

Solving equations is computing the value of the unknown variable still balancing the equation on both sides. An equation is a condition on a variable such that two expressions in the variable have equal value. The value of the variable for which the equation is satisfied is said to be the solution of the equation. An equation remains the same if the LHS and the RHS are interchanged.

Now, solving the equation for y, we get y=7-2x.

Put x=1, 2, 3, 4,....in the equation and find the y value.

So, put x=1 in equation  y=7-2(1)=5.

Put x=2, we get

y=7-2(2)=3

Verification: Put the ordered pair (1, 5) in the equation and verify.

That is, 5=7-2(1)

⇒5=5

Therefore, the equation solved for y is  y=7-2x.

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what is 12x8 please tell me i need to know :) ")

Answers

Answer:

96

Step-by-step explanation:

10 x 8 = 80

2 x 8 = 16

so 80 + 16 = 96 :)

The equivalent value of the equation is A = 96

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the first number be p = 12

Let the second number be q = 8

Now , A = pq

On simplifying the equation , we get

A = 12 x 8

So , the left hand side of the equation is equated to the right hand side by the value of 12 x 8

On multiplying 12 times 8 , we get

A = 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8

A = 96

Therefore , the value of A = 96

Hence , the expression is A = 96

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Dimensional analysis. An adult mosquito's lifespan is about 16 days. How many minutes is that?

Answers

Answer:

23040 minutes.

Step-by-step explanation:

Its 23040 minutes long because there are 60 minutes in an hour, an 24 hours in a day and 60 times 24 is 1440. Then you multiply 1440 by 16 which equals 23040.

The expression 36 ÷ 6 · 2 + 1 is equal to _____. 4 18 2 13

Answers

Answer:

13

Step-by-step explanation:

We have to use the BODMAS ( Bracket Of Division Multiplication Addition Subtraction) rule here

So first divide

36 ÷ 6 * 2 + 1

6 * 2 + 1

Now multiply

6 * 2 + 1

12 + 1

Now add

12 + 1 = 13

Answer:

13

Step-by-step explanation:

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