   Chapter 9, Problem 92RE Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340

Solutions

Chapter
Section Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340
Textbook Problem

Severe weather ice makers Thunderstorms severe enough to produce hail develop when an upper-level low (a pool of cold air high in the atmosphere) moves through a region where there is warm, moist air at the surface. These storms create an updraft that draws the moist air into subfreezing air above 10,000 feet. Data from the National Weather Service indicate that the strength of the updraft, as measured by its speed s in mph, affects the size of the hail according to h =   0.000595 s 1.922 where h is the diameter of the hail (in inches). Find and interpret h(100) and h'(100).

To determine

To calculate: The values of h(100) and h(100) for the function h=0.000595s1.922 where h represents the diameter of a hail and interpret the result.

Explanation

Given Information:

There is an updraft created by thunderstorms due to which the moist air is converted into subfreezing air above 10000 feet. The effects on the size of the hail due to the speed of updraft, represented by s, are measured according to the function, h=0.000595s1.922.

Formula used:

According to the power rule of derivatives,

ddx(xn)=nxn1

Calculation:

Consider the provided diameter function,

h=0.000595s1.922

For h(100), substitute 100 for s in the function,

h=0.000595(100)1.9224.1545

Hence, the value of h(100) is 4.1545 which means that for a 100mph updraft speed, the diameter of hail is 4.15inches.

To find the rate of change, differentiate both sides of the provided function with respect to s,

dhds=dds(0.000595s1

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