Derivatives to physical systems, Mathematics

Assignment Help:

Derivatives to Physical Systems:

A stone is dropped into a quiet lake, & waves move within circles outward from the location of the splash at a constant velocity of 0.5 feet per second.  Determine the rate at that the area of the circle is increasing when the radius is 4 feet.

Solution:

Using the formula for the area of a circle,

A = πr2

obtain the derivative of both sides of this equation along with respect to time t.

dA/dt = 2πr (dr/dt)

But, dr/dt is the velocity of the circle moving outward which equals  0.5 ft/s and dA /dt  is the  rate  at  which  the  area  is increasing,  that  is the  quantity  to  be determined.   Set r equal to 4 feet, substitute the known values into the equation, and solve for dA /dt.

dA/dt = 2πr(dr/dt)

dA/dt = (2)(3.1416)(4 ft)(0.5 ft/s)

dA/dt = 12.6 ft2/s

Therefore, at a radius of 4 feet, the area is raising at a rate of 12.6 square feet per second.


Related Discussions:- Derivatives to physical systems

Prove that a/b+c-a, a, b,c are in h.p prove that a/b+c-a, b/a+c-b, c/a+b-c ...

a, b,c are in h.p prove that a/b+c-a, b/a+c-b, c/a+b-c are in h.p To prove: (b+c-a)/a; (a+c-b)/b; (a+b-c)/c are in A.P or (b+c)/a; (a+c)/b; (a+b)/c are in A.P or 1/a; 1

Find the equation to the pair of lines - coordinate geometry, 1. Find the n...

1. Find the number of zeroes of the polynomial y = f(x) whose graph is given in figure. 2 Find the circumcentre of the triangle whose vertices are (-2, -3), (-1, 0) and (7,-6).

Math Help, 1. Which of the following is greater than 4.3 x 10^9 a. 2.1 x ...

1. Which of the following is greater than 4.3 x 10^9 a. 2.1 x 10^9 b. 3.2 x 10^9 c. 5.3 x 10^9 d. 7.4 x 10^8 2. Which of the following is less than 6.5 x 10^-5 a. 1.4 x 10

Factorization, factorize the following algebraic expressions

factorize the following algebraic expressions

How many multiplication required to calculate matrix product, (a) Assume th...

(a) Assume that A is a m 1 ×m 2 matrix and B is a m 2 ×m 3 matrix. How many multiplications are required to calculate the matrix product AB? (b) Given that A 1 is a 20 × 50 m

Find out the variance and standard deviation, The probability of a rare dis...

The probability of a rare disease striking a described population is 0.003. A sample of 10000 was examined. Determine the expected no. suffering from the disease and thus find out

Probability, A man enter a lucky draw that requires him to pick five differ...

A man enter a lucky draw that requires him to pick five different integers from 1 through 30 inclusive .he chooses his five number in such a way that the sum of their log base 10 i

Determine the probability of tossing a head, Q. Determine the probability o...

Q. Determine the probability of tossing a head? Let B represent the event of tossing a heads with the nickel in example 2. Find P(B). Solution:   S = {(H, H), (H, T), (T, H

Find how much more space than the toy it will cover, A Solid toy in the for...

A Solid toy in the form of a hemisphere surmounted by the right circular cone of height  2cm  and  diameter  of  the  base  4  cm .If  a right  circular  cylinder circumscribes the

Integral test- harmonic series, Integral Test- Harmonic Series In ha...

Integral Test- Harmonic Series In harmonic series discussion we said that the harmonic series was a divergent series.  It is now time to demonstrate that statement.  This pr

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd