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

probability: complying with this treatment, A national study found that tr...

A national study found that treating people appropriately for high blood pressure decreased their overall mortality rate by 20%. Treating people adequately for hypertension has bee

Arc length with vector functions - three dimensional space, Arc Length with...

Arc Length with Vector Functions In this part we will recast an old formula into terms of vector functions.  We wish to find out the length of a vector function, r → (t) =

Percentage, 7 is what percent of 105?.

7 is what percent of 105?.

Tangent, Tangent, Normal and Binormal Vectors In this part we want to ...

Tangent, Normal and Binormal Vectors In this part we want to look at an application of derivatives for vector functions.  In fact, there are a couple of applications, but they

Fraction, Ask question #Minimum 100 words accepted

Ask question #Minimum 100 words accepted

Standard conventions in game theory, Standard conventions in game theory ...

Standard conventions in game theory Consider the given table: Y   3 -4 X -2 1

Evalute right-hand limit, Evaluate following limits. Solution ...

Evaluate following limits. Solution Let's begin with the right-hand limit.  For this limit we have, x > 4  ⇒          4 - x 3   = 0      also, 4 - x → 0  as x → 4

Algebra, Manuel is a cross-country runner for his school’s team. He jogged ...

Manuel is a cross-country runner for his school’s team. He jogged along the perimeter of a rectangular field at his school. The track is a rectangle that has a length that is 3 tim

Definition and fact of the shape of a graph, Definition 1.   Given any ...

Definition 1.   Given any x 1  & x 2   from an interval  I with x 1 2  if f ( x 1 ) 2 ) then f ( x ) is increasing on I. 2.   Given any x 1  & x 2  from an interval

Prove sum of squares any two sides equal twice square, Prove that in any tr...

Prove that in any triangle the sum of the squares of any two sides is equal to twice the square of half of the third side together with twice the square of the median, which bisect

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