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

Sample of proportion program., help me with how to write sample of proport...

help me with how to write sample of proportion using visual basic

Developing an understanding ones tens and more, DEVELOPING AN UNDERSTANDING...

DEVELOPING AN UNDERSTANDING :  The other day I was showing the children's book '203 Cats' to my 7-year-old niece. She had recently learnt how to write large numerals in her school

Addition of like terms with same signs, Case 1: Suppose we are given...

Case 1: Suppose we are given expressions like 3abc and 7abc and asked to compute their sum. If this is the case we should not worry much. Because adding like exp

Circle, prove the the centre of a circle is twice of reference angle

prove the the centre of a circle is twice of reference angle

Tangents with parametric equations - polar coordinates, Tangents with Param...

Tangents with Parametric Equations In this part we want to find out the tangent lines to the parametric equations given by X= f (t) Y = g (t) To do this let's first r

Find the constant height at which the jet is flying, The angle of ...

The angle of elevation of a jet fighter from a point A on the ground is 600. After a flight of 15 seconds, the angle of elevation changes to 300. If the jet is flying at a speed  o

Parametric equations and polar coordinates, Parametric Equations and Polar ...

Parametric Equations and Polar Coordinates In this part we come across at parametric equations and polar coordinates. When the two subjects don't come out to have that much in

Find out that sets of functions are linearly dependent, Find out if the fol...

Find out if the following sets of functions are linearly dependent or independent.  (a) f (  x ) = 9 cos ( 2 x )    g (  x ) = 2 cos2 (  x ) -  2 sin 2 (  x ) (b) f

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