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

Area and surface Are, I cant figure out how to study for my math test

I cant figure out how to study for my math test

Solving an equation problems, Temperature: On one day in Fairfield, Montana...

Temperature: On one day in Fairfield, Montana the temperature dropped 80 degree fahrenheit from noon to midnight. If the temperature at midnight was -21 degree fahrenheit, write an

Discrete mathematics for computing, Everything stored on a computer can be ...

Everything stored on a computer can be represented as a string of bits. However, different types of data (for example, characters and numbers) may be represented by the same strin

How to multiplying rational expressions, how to Multiplying Rational Expres...

how to Multiplying Rational Expressions ? To multiply fractions, or rational expressions, you must multiply the numerators and then multiply the denominators. Here's how it is

#Regular Expression, Find the Regular Grammar for the following Regular Exp...

Find the Regular Grammar for the following Regular Expression: a(a+b)*(ab*+ba*)b.

Probability distributions, Probability Distributions Since the value of...

Probability Distributions Since the value of a random variable cannot be predicted accurately, by convention, probabilities are assigned to all the likely values that the varia

Phase transformations in binary system, Get the Delta H (Enthalpy) and Delt...

Get the Delta H (Enthalpy) and Delta V (Volume) of the both components below and compare by ratio.  You need to use clapeyron equation and also need to draw the graphs. S A LG

Standard basis vectors - calculus, Standard Basis Vectors The vector th...

Standard Basis Vectors The vector that is, i = (1, 0,0) is called a standard basis vector.  In three dimensional (3D) space there are three standard basis vectors, i → = (1

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