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

Describe independent events in maths, Describe Independent Events in maths?...

Describe Independent Events in maths? Events are independent if the outcome of one event does not affect the outcome of the second event. If A represents one independent event

Example of identify the pre-requisites, Ravi is a teacher of Class 4 in a m...

Ravi is a teacher of Class 4 in a municipal school in Delhi. When the new school year started, he opened the textbook and started teaching the children how to write 4-digit numbers

Hasse diagram, The digraph D for a relation R on V = {1, 2, 3, 4} is shown ...

The digraph D for a relation R on V = {1, 2, 3, 4} is shown below (a) show that (V,R) is a poset. (b) Draw its Hasse diagram. (c) Give a total order that have R.

If the squared difference of the zeros find the value of p, If the squared ...

If the squared difference of the zeros of the quadratic polynomial x 2 + p x + 45 is equal to 144 , find the value of p.

Describe the sample of exponents , Describe the Sample of Exponents ? I...

Describe the Sample of Exponents ? Imagine, for example, that you are the P.E. coach at your school, and you need to divide one of your classes into teams. Your team has 45 stu

Work in volume problems, Work : It is the last application of integr...

Work : It is the last application of integral which we'll be looking at under this course. In this section we'll be looking at the amount of work which is done through a forc

Logarithm, I need help with one logarithm problem

I need help with one logarithm problem

What do you mean by transient state, What do you mean by transient state an...

What do you mean by transient state and steady-state queueing systems If the characteristics of a queuing system are independent of time or equivalently if the behaviour of the

Fraccions, multiply 9/19 times 95/7

multiply 9/19 times 95/7

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