Calculate the instantaneous rate of change of the volume, Mathematics

Assignment Help:

Assume that the amount of air in a balloon after t hours is specified by

                                            V (t ) = t 3 - 6t 2 + 35

Calculate the instantaneous rate of change of the volume after 5 hours.

Solution

The first thing that we need to do is get a formula for the average rate of change of the volume.  In this case it is,

 A.R.C. = V (t ) - V (5)/(t-5)= t 3 - 6t 2 + 35 -10 /t - 5  =t 3 - 6t 2 + 25 /t - 5

To calculate the instantaneous rate of change of the volume at t = 5 we only have to pick values of t that are getting closer & closer to t = 5 .  Following is a table of values of t and the average rate of change for those values.

826_tangent 2.png

Thus, from this table it looks like the average rate of change is approaching 15 and thus we can calculate that the instantaneous rate of change is 15 at this point.


Related Discussions:- Calculate the instantaneous rate of change of the volume

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

Coefficients of the equation, If coefficients of the equation ax 2 + bx + ...

If coefficients of the equation ax 2 + bx + c = 0, a ¹ 0 are real and roots of the equation are non-real complex and  a + c (A) 4a + c > 2b (B) 4a + c Please give t

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

Calculus 1, Suppose a Ferris wheel with radius of 12 meters is rotating at ...

Suppose a Ferris wheel with radius of 12 meters is rotating at a rate of 2 rotations per minute. a. How fast is a person rising when the person is 3 meters above the horizontal lin

Applications of markov chains in business, please help me in my assignment,...

please help me in my assignment, explain Applications of Markov Chains in Business.

Surds, solve for x: logx9

solve for x: logx9

Question, Hi I have a maths question related to construction as its a cons...

Hi I have a maths question related to construction as its a construction management course...i could send some example sheets too...could it be done?

What is the objective of lipids metabolism, What is the objective of lipids...

What is the objective of lipids metabolism ? After studying this unit, you will be able to: 1. explain how fatty acids are oxidized for the production of energy, 2. describe

Market testing, what are the dangers of not market testing a product

what are the dangers of not market testing a product

How much do they save if they pay the bill inside 10 days, Oscar's Oil Comp...

Oscar's Oil Company provides customers a 5% discount if they pay their bill within 10 days. The Stevens' oil bill is $178. How much do they save if they pay the bill inside 10 days

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