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

Profit and loss, a man buy car at rs.50 and sells it at gain of 14% find ...

a man buy car at rs.50 and sells it at gain of 14% find the sp

What are factor trees explain, What are Factor Trees explain? In algebr...

What are Factor Trees explain? In algebra, we often need to factor a number into its prime factors. One way to do this is to use a factor tree. This is a network of numbers, st

Determine the probability of given question, Q. Assume a birthday is equall...

Q. Assume a birthday is equally likely to occur in each of the 365 days. In a group of 30 people, what is the probability that no two have birthdays on the same day? Solution:

Number line, I need to graph rational numbers on the number line Point A-.6...

I need to graph rational numbers on the number line Point A-.60, point B-1/4, point C-.4,point D-7/8

Example of set theory, Suggest me the solution: Consider the given unive...

Suggest me the solution: Consider the given universal set T and its subjects C, D and E T = {0, 2, 4, 6, 8, 10, 12} C = {4, 8,} D = {10, 2, 0} E = {0} Find out

SHARES AND DIVIDEND, i am a student of class 10 and need help for making my...

i am a student of class 10 and need help for making my project on shares and dividend

Definition of natural exponential function, Definition of Natural exponenti...

Definition of Natural exponential function:   The natural exponential function is f( x ) = e x   where, e= 2.71828182845905........ . Hence, since e > 1 we also know that e x

Chi square distribution, Chi Square Distribution Chi square was first ...

Chi Square Distribution Chi square was first utilized by Karl Pearson in 1900. It is denoted by the Greek letter χ 2 . This contains only one parameter, called the number of d

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