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
Harlamova29_29 [7]
3 years ago
12

(a) The position of a particle at time t is s(t) = t^3 + t. Compute the average velocity over the time interval [7, 12].(b) Esti

mate the instantaneous velocity at t = 7. (Round your answer to the nearest whole number)
Mathematics
1 answer:
ryzh [129]3 years ago
8 0

Answer:

<h2>a) Average velocity = 278 units</h2><h2>b) Instantaneous velocity at t = 7 seconds is 148 units</h2>

Step-by-step explanation:

a) Average velocity is the ratio of displacement to time.

   We have

              s(t) = t³ + t

    t is in between 7 and 12

             s(7) =  7³ + 7 = 350

              s(12) = 12³ + 12 = 1740

    Displacement = 1740 - 350 = 1390

   Time = 12 - 7 = 5

  Displacement =  Average velocity x time

  1390 = Average velocity x 5

  Average velocity = 278 units

b) s(t) = t³ + t

   Differentiating

         v(t) = 3t² + 1

  At t = 7

          v(t) = 3 x 7² + 1 = 148 units

  Instantaneous velocity at t = 7 seconds is 148 units

You might be interested in
Del has 12 less than 3 times the number of comic books as Patrick. Del has at most 57 comic books. What solution represents the
Akimi4 [234]

Answer:

Del has 19 comic book

Step-by-step explanation:

to figure this out we need to take 57 and divide by the 3 given.

57 ÷ 3 = 19

so because we divided 57 by 3 we know the answer is 19

Del has 19 comic books

3 0
2 years ago
Please explain the how you got the answers thanks asap
stich3 [128]

Answer:

a) 90 stamps

b) 108 stamps

c) 333 stamps

Step-by-step explanation:

Whenever you have ratios, just treat them like you would a fraction! For example, a ratio of 1:2 can also look like 1/2!

In this context, you have a ratio of 1:1.5 that represents the ratio of Canadian stamps to stamps from the rest of the world. You can set up two fractions and set them equal to each other in order to solve for the unknown number of Canadian stamps. 1/1.5 is representative of Canada/rest of world. So is x/135, because you are solving for the actual number of Canadian stamps and you already know how many stamps you have from the rest of the world. Set 1/1.5 equal to x/135, and solve for x by cross multiplying. You'll end up with 90.

Solve using the same method for the US! This will look like 1.2/1.5 = x/135. Solve for x, and get 108!

Now, simply add all your stamps together: 90 + 108 + 135. This gets you a total of 333 stamps!

5 0
3 years ago
Cube-shaped blocks are packed into a cube-shaped storage container. ​ The edge length of the storage container is 212 feet. The
igor_vitrenko [27]

Answer:

The volume of cube-shaped block is 0.125 cubic feet.

Step-by-step explanation:

We are given the following in the question:

Edge length of storage container =

2\dfrac{1}{2}\text{ feet}

Edge length of block =

\dfrac{1}{5}\times \text{Edge length of container}

Putting value we get,

Edge length of block =

\dfrac{1}{5}\times 2\dfrac{1}{2}\\\\=\dfrac{1}{5}\times \dfrac{5}{2}\\\\=\dfrac{1}{2}\text{ feet}

Volume of cube-shaped block = Volume of cube

V = \text{(Edge)}^3\\\\V =(\dfrac{1}{2})^3\\\\V = \dfrac{1}{8}\text{ cubic feet}\\\\V = 0.125\text{ cubic feet}

Thus, the volume of cube-shaped block is 0.125 cubic feet.

7 0
2 years ago
an aquarium has a ratio of 5 rays for every 3 sharks. What percent of this grouping of animals are rays
sashaice [31]

Answer:

62.5%

Step-by-step explanation:

Total number of animals in a group= 5+3=8 animals

Number of rays=5

Since we only have 5 rays out of the total 8, to express the number of rays as a percentage of the total animals, we divide the number of rays by the total animals then multiply by 100 to express in percentage as needed in the question

Percentage of rays=\frac {5}{8}\times 100=62.5

Therefore, the percentage is 62.5%

6 0
3 years ago
Find the area of the figure.
AURORKA [14]

Answer:

28.5 united squared

5 0
2 years ago
Read 2 more answers
Other questions:
  • Which expression is equivalent to (xy)z?
    7·1 answer
  • A(n) ______ shows a corner view of a three-dimensional figure.
    14·2 answers
  • RAMON SELLS CARS AND TRUCKS HE HAS ROOM ON HIS LOT FOR 521 VEHICLES. Ramon has 175 more more cars than trucks. How many of each
    6·1 answer
  • For retirement, linda invested $4,000 in an account that pays 7% annual interest, compounded quarterly. find the value of his in
    8·1 answer
  • marcela's dog gained 4.1 kilograms in two months. two months aga the dog's mass was 5.6 kilograms. what is the dog's current mas
    14·2 answers
  • What is the solution to this equation?<br> x-8=15<br><br> A)x=13<br> B)x=17<br> C)x=7<br> D) x=23
    10·1 answer
  • (03.01)
    8·2 answers
  • Is 9y+3=0 a nonlinear ?
    11·2 answers
  • PLEASE HELP!!! ILL GIVE BRAINLIEST !! Which is the correct answer ?
    8·2 answers
  • ERROR ANALYSIS Describe and correct the error in
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!