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

What is the value of the largest consecutive integer, The sum of three cons...

The sum of three consecutive even integers is 102. What is the value of the largest consecutive integer? Three consecutive even integers are numbers in order such as 4, 6, and

Power of x, (x+1/x)^2=3 then value of x^72+x^66+x^54+x^36+x^24+x^6+1 is

(x+1/x)^2=3 then value of x^72+x^66+x^54+x^36+x^24+x^6+1 is

#title, IF YOU HAVE 24 BISCUITS HOW MUCH WHOLE BISCUITS DO YOU HAVE IF YOU ...

IF YOU HAVE 24 BISCUITS HOW MUCH WHOLE BISCUITS DO YOU HAVE IF YOU SHARE FIVE BETWEEN 5 FRIENDS

Permuation and combination, how many words can be formed from letters of wo...

how many words can be formed from letters of word daughter such that word contain 2vowles and 3consonant

Mean value theorem function, Mean Value Theorem : Suppose f (x) is a funct...

Mean Value Theorem : Suppose f (x) is a function which satisfies both of the following. 1. f ( x )is continuous on the closed interval [a,b]. 2. f ( x ) is differentiable on

Calculate moving average, Calculate Moving Average The table given bel...

Calculate Moving Average The table given below represents company sales; calculate 3 and 6 monthly moving averages, for data Months Sales

Estimate weight if telephone pole weighs 11.5 pounds foot, If a telephone p...

If a telephone pole weighs 11.5 pounds per foot, how much does a 32-foot pole weigh? Multiply 11.5 by 32; 11.5 × 32 = 368 pounds.

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