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
lianna [129]
3 years ago
5

Find the length of the following​ two-dimensional curve. r (t ) = (1/2 t^2, 1/3(2t+1)^3/2) for 0 < t < 16

Mathematics
1 answer:
andrezito [222]3 years ago
5 0

Answer:

r = 144 units

Step-by-step explanation:

The given curve corresponds to a parametric function in which the Cartesian coordinates are written in terms of a parameter "t". In that sense, any change in x can also change in y owing to this direct relationship with "t". To find the length of the curve is useful the following expression;

r(t)=\int\limits^a_b ({r`)^2 \, dt =\int\limits^b_a \sqrt{((\frac{dx}{dt} )^2 +\frac{dy}{dt} )^2)}     dt

In agreement with the given data from the exercise, the length of the curve is found in between two points, namely 0 < t < 16. In that case a=0 and b=16. The concept of the integral involves the sum of different areas at between the interval points, although this technique is powerful, it would be more convenient to use the integral notation written above.

Substituting the terms of the equation and the derivative of r´, as follows,

r(t)= \int\limits^b_a \sqrt{((\frac{d((1/2)t^2)}{dt} )^2 +\frac{d((1/3)(2t+1)^{3/2})}{dt} )^2)}     dt

Doing the operations inside of the brackets the derivatives are:

1 ) (\frac{d((1/2)t^2)}{dt} )^2= t^2

2) \frac{(d(1/3)(2t+1)^{3/2})}{dt} )^2=2t+1

Entering these values of the integral is

r(t)= \int\limits^{16}_{0}  \sqrt{t^2 +2t+1}     dt

It is possible to factorize the quadratic function and the integral can reduced as,

r(t)= \int\limits^{16}_{0} (t+1)  dt= \frac{t^2}{2} + t

Thus, evaluate from 0 to 16

\frac{16^2}{2} + 16

The value is r= 144 units

You might be interested in
Please help meeeee please please c
bazaltina [42]

Answer:

the item would cost $9000

8 0
2 years ago
Janna jumped 156in in the long jump competition at the high school track meet . How many feet did Janna jump
Triss [41]
To find the number of feet she jumped you have to divide 156 by 12 because there are 12 inches in a foot

So 156/12 =13
So she jumped 13 feet
5 0
3 years ago
There are 20 student desks
liq [111]

Answer:

It would be 502 inches.

Step-by-step explanation Ok so, Just do 20 x 25.1 that would give you your answer.

You multiply it because there is going to be 20 desk But they are 25.1 inch k?

8 0
3 years ago
A worker at an orchard measures the mass of different numbers of apples. The scatter plot below shows the relationship between t
denis23 [38]

Answer:

0.12

Step-by-step explanation:

Rise/run

4 0
3 years ago
An equation is shown.<br> f(w) = 2<br> +6<br> Find f(-16).
Nikitich [7]

Answer: f(-16) = -26

Step-by-step explanation: Let's substitute:

f(w) = 2w + 6 --> f(-16) = -32 + 6 =

f(-16) = -26
Hope this helps, please consider making me Brainliest.

7 0
1 year ago
Other questions:
  • You and your friend each collect rocks and fossils. Your friend collects three times as many rocks and half as many fossils as y
    12·1 answer
  • X = <br><br> y = <br><br> m ∠ H = <br><br> m ∠ G =
    11·1 answer
  • What is the area of the triangle below
    13·1 answer
  • Nam has a bag of 8 chips numbered 1 to 8. He will perform an experiment to model the theoretical probability of pulling a chip w
    14·2 answers
  • What is the difference of 15 - 18 =
    13·1 answer
  • Find the missing term (x+2)^2=x^2+4x+___
    12·1 answer
  • A fruit company delivers Its fruit in two types of boxes: large and small. A delivery of 5 large boxes and 3 small boxes has a t
    5·1 answer
  • Could someone please tell me the answer
    7·1 answer
  • I NEED HELP!! Please
    9·1 answer
  • One out of every 3 players on a soccer team is new this season. There are 15 player on the team in all. How many players are new
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!