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CalculusCalculus: An Applied Approach (MindTap Course List)10th Edition

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Chapter 8.4, Problem 67E
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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Meteorology The normal average daily temperature in degrees Fahrenheit for a city is given by

T = 55 − 21   cos   2 π ( t − 32 ) 365 where t is the time (in days), with t = 1 corresponding to January 1. Find the expected date of

(a) the warmest day. (b) the coldest day.

(a)

To determine

To calculate: The expected date of the warmest day from the function of the normal average daily temperature for a city T=55−21cos2π(t−32)365, where t is the time in days and t=1 means January 1.

Explanation

Given Information:

The normal average daily temperature for a city is given by,

T=55−21cos2π(t−32)365

Where t is the time in days.

Formula used:

Cosine differentiation rule:

ddx[cosu]=−sinududx

General power rule of differentiation:

ddx[xn]=nxn−1

Calculation:

Consider the provided function:

T=55−21cos2π(t−32)365

Differentiate the above function using Cosine and general power rules of differentiation.

T′=ddt[55]−ddt[21cos2π(t−32)365]=0−((−21sin2π(t−32)365)(2π365))=42π365sin2π(t−32)

(b)

To determine

To calculate: The expected date of the coldest day from the function of the normal average daily temperature for a city T=55−21cos2π(t−32)365, where t is the time in days and t=1 means January 1.

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Elementary Geometry for College Students

Polar coordinates of the point with rectangular coordinates (5, 5) are: (25, 0)

Study Guide for Stewart's Multivariable Calculus, 8th

Finding Terms of a Power Series SolutionIn Exercises 7 and 8, the solution of the differential equation is a su...

Multivariable Calculus

ProofIn Exercises 4752, prove the poverty of the cross product. u(vw)=(uv)w

Calculus (MindTap Course List)

Finding an Indefinite Integral In Exercises 39-46, find the indefinite integral. (1ti+jt3/2k)dt

Calculus

limx(12)x2= a) 0 b) 1 c) d) does not exist

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

In the EAI sampling problem (see Figure 7.5), we showed that for n = 30, there was .5034 probability of obtaini...

Statistics for Business & Economics, Revised (MindTap Course List)

Solve each of the following equations using the addition principle of equality. Check each answer. y78=38

Mathematics For Machine Technology

The accompanying summary statistics for a measure of social marginality for samples of youths, young adults, ad...

Introduction To Statistics And Data Analysis

Graph each polynomial function. f(x)=x4+18x232

College Algebra (MindTap Course List)

The mean cost to repair the smoke and fire damage that results from home fires of all causes is 11,389 (HomeAdv...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Define, compare, and contrast the experimental, nonexperimental, and quasi-experimental research strategies, an...

Research Methods for the Behavioral Sciences (MindTap Course List)

Define a main effect for one factor and an interaction between factors, and be able to identify main effects an...

Research Methods for the Behavioral Sciences (MindTap Course List)

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