1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Leona [35]
2 years ago
13

A particle is moving with acceleration a ( t ) = 18 t + 16 . Its position at time t = 0 is s ( 0 ) = 10 and its velocity at time

t = 0 is v ( 0 ) = 16 . What is its position at time t = 8 ?
Mathematics
1 answer:
MatroZZZ [7]2 years ago
3 0

Answer:

s(8)=2186

Step-by-step explanation:

A particle is moving with acceleration modeled by the function:

a(t)=18t+16

We are given that its position s(t) at <em>t</em> = 0 is 10 and that its velocity v(t) at <em>t</em> = 0 is 16.

And we want to find its position at <em>t</em> = 8.

Velocity is the integral of the acceleration. Hence:

\displaystyle v(t)=\int a(t)\, dt=\int 18t+16\, dt

Find the velocity. Remember the constant of integration!

v(t)=9t^2+16t+C

Since v(t) is 16 when <em>t</em> = 0:

(16)=9(0)^2+16(0)+C\Rightarrow C=16

Hence, our velocity is given by:

v(t)=9t^2+16t+16

Position is the integral of the velocity. Hence:

\displaystyle s(t)=\int v(t)\, dt=\int 9t^2+16t+16\, dt

Integrate:

\displaystyle s(t)=3t^3+8t^2+16t+C

s(t) is 10 when <em>t</em> = 10. Hence:

C=10

So, our position function is:

s(t)=3t^3+8t^2+16t+10

The position at <em>t</em> = 8 will be:

s(8)=3(8)^3+8(8)^2+16(8)+10=2186

You might be interested in
The college hiking club is having a fund raiser to buy new equipment for fall and winter outings. The club is selling Chinese fo
PolarNik [594]

Answer:

a)

- the probability she will win the dinner for two is 0.016

- the probability she will not win the dinner for two is 0.984

b)

- Lisa's expected earnings is $0.57

- Money she effectively contributed to the hiking club is $11.43

Step-by-step explanation:

Given the data in the question;

fortune cookies; $1 per cookies

club sold 743

a) Lisa bought 12 cookies. What is the probability she will win the dinner for two?

P( she will win ) = Number of cookies bought / Total number of cookies

P( she will win ) = 12 / 743

P( she will win ) = 0.01615 ≈ 0.016

Therefore,  the probability she will win the dinner for two is 0.016

P( she will not win ) = 1 - P( she will win )

P( she will not win ) = 1 - 0.016

P( she will not win ) = 0.984

Therefore,  the probability she will not win the dinner for two is 0.984

b)  Lisa's expected earnings can be found by multiplying the value of the dinner by the probability that she will win. What are Lisa's expected earnings? (Round your answer to two decimal places.)$

given that value of dinner = $35

P( she will win ) = 0.01615

so

Lisa's earning = $35 × 0.01615

Lisa's earning = $0.57

Therefore, Lisa's expected earnings is $0.57

- How much did she effectively contribute to the hiking club? (Round your answer to two decimal places.)$

Lisa's contribution = Money she paid for cookies - money from expected earnings

Lisa's contribution = ( 12 × $1 ) -  $ 0.57

Lisa's contribution = $12 -  $0.57

Lisa's contribution = $11.43

Therefore, Money she effectively contributed to the hiking club is $11.43

4 0
2 years ago
/viewform?hr submission=Chclk4feKBIQ.
Gennadij [26K]

Answer:

c) .22

Step-by-step explanation:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1-0.95}{2} = 0.025

Now, we have to find z in the Ztable as such z has a pvalue of 1-\alpha.

So it is z with a pvalue of 1-0.025 = 0.975, so z = 1.96

Now, find the margin of error M as such

M = z*\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

In this question:

\sigma = 2.5, n = 500

Then

M = z*\frac{\sigma}{\sqrt{n}}

M = 1.96*\frac{2.5}{\sqrt{500}}

M = 0.22

5 0
3 years ago
-6(y + 15) = -3y + 6<br> What value of y makes the equation true? Enter the answer in the box.
STatiana [176]

Answer:

y = −32

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

5 0
2 years ago
Ivan surveyed 49 randomly selected players from the 134 players of the soccer club teams to see if they wanted the games to be p
nordsb [41]

Twenty-two of the players said that they preferred that the games be played on Saturdays. Ivan correctly determined that the margin of error, E, of his survey using a 99% confidence interval (z*score 2.58) is approximately 18%

Ivan surveyed 49 randomly select

8 0
3 years ago
Read 2 more answers
If XY=24, XZ=22, and JQ=5, find the radius of the circumscribed circle of triangle XYZ.
grandymaker [24]
23 to the 3 because I just took it
3 0
2 years ago
Other questions:
  • I need help with this asap plz
    5·2 answers
  • Anton took out a 20-year loan for $90,000 at an APR of 10.5% compounded monthly, approximately what would be the total cost of h
    6·2 answers
  • Joe Has an 8 foot long board. He needs to cut it into 9 equal length parts.How many feet long should each section of the board b
    10·2 answers
  • Suppose y = f (x) +k what effect does k have on parent funcation
    9·1 answer
  • Depending on the day of the week, a border guard searches every nth person coming across the border. Each Tuesday every 7th pers
    14·1 answer
  • How many yards are in 400 meters
    7·1 answer
  • Find the value if x, will give brainliest !!
    10·1 answer
  • 3x6-2x4 in Bidmas someone please help
    15·1 answer
  • Reflect points please help me
    5·2 answers
  • 6. If you can run 1 mile in 8 minutes, how long will it take to run 4 miles (assuming you can maintain
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!