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

Dividing using compatible numbers, 4 friends have 235 marbles and want to s...

4 friends have 235 marbles and want to share.How many marbles should each friend receive?

Differentiate quotient rule functions, Example of quotient rule : Let's no...

Example of quotient rule : Let's now see example on quotient rule.  In this, unlike the product rule examples, some of these functions will require the quotient rule to get the de

Integration and differentiation, Integration and Differentiation Diffe...

Integration and Differentiation Differentiation deals along with the determination of the rates of change of business activities or merely the process of finding the derivativ

Find the largest possible positive integer, Find the largest possible posit...

Find the largest possible positive integer that will divide 398, 436, and 542 leaving remainder 7, 11, 15 respectively. (Ans: 17) Ans: The required number is the HCF of the n

Example of linear in - equation - linear algebra, Explain some Examples of ...

Explain some Examples of linear in - Equation, with solution.

Complex numbers, A number of the form x + iy, where x and y are real and na...

A number of the form x + iy, where x and y are real and natural numbers and is called as a complex number. It is normally given by z. i.e. z = x + iy, x is called as the real part

Ratio, number of consonants to the number of letters in the English Alphabe...

number of consonants to the number of letters in the English Alphabet express answer in ratio

Determine the circumference, If Gretta's bicycle has a 25-inch radius wheel...

If Gretta's bicycle has a 25-inch radius wheel, how far will she travel in two turns of the wheel? (π = 3.14) a. 491 in b. 78.5 in c. 100 in d. 157 in d. To determin

Complex number, a ,b,c are complex numbers such that a/1-b=b/1-c=c-1-a=k.fi...

a ,b,c are complex numbers such that a/1-b=b/1-c=c-1-a=k.find the value of k

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