Math

CalculusCalculus: An Applied Approach (MindTap Course List)Tides Throughout the day, the depth of water D (in meters) at the end of a dock varies with the tides. The depth for one particular day can be modeled by D = 3.5 + 1.5 cos π t 6 , 0 ≤ t ≤ 24 where t is the time (in hours), with t = 0 corresponding to midnight. (a) Determine dD / dt . (b) Evaluate dD / dt for t = 4 and t = 20, and interpret the meaning of these values in the context of the problem. (c) Find the time(s) when the water depth is the greatest and the time(s) when the water depth is the least. (d) What is the greatest depth? What is the least depth? (e) When is the rate of change of the water depth the greatest? the least?BuyFind*launch*

10th Edition

Ron Larson

Publisher: Cengage Learning

ISBN: 9781305860919

Chapter 8.4, Problem 72E

Textbook Problem

**Tides** Throughout the day, the depth of water *D* (in meters) at the end of a dock varies with the tides. The depth for one particular day can be modeled by

*t* is the time (in hours), with *t* = 0 corresponding to midnight.

(a) Determine *dD*/*dt*.

(b) Evaluate *dD*/*dt* for *t* = 4 and *t* = 20, and interpret the meaning of these values in the context of the problem.

(c) Find the time(s) when the water depth is the greatest and the time(s) when the water depth is the least.

(d) What is the greatest depth? What is the least depth?

(e) When is the rate of change of the water depth the greatest? the least?

Calculus: An Applied Approach (MindTap Course List)

Ch. 8.1 - For each angle, find a coterminal angle such that...Ch. 8.1 - Convert each degree measure to radian measure. a....Ch. 8.1 - Convert each radian measure to degree measure. a....Ch. 8.1 - Find the area of an isosceles right triangle with...Ch. 8.1 - In Exercises 1 and 2, find the area of the...Ch. 8.1 - In Exercises 1 and 2, find the area of the...Ch. 8.1 - In Exercises 36, let a and b represent the lengths...Ch. 8.1 - In Exercises 36, let a and b represent the lengths...Ch. 8.1 - In Exercises 36, let a and b represent the lengths...Ch. 8.1 - In Exercises 36, let a and b represent the lengths...

Ch. 8.1 - In Exercises 36, let a and b represent the lengths...Ch. 8.1 - In Exercises 710, show that the points form the...Ch. 8.1 - In Exercises 710, show that the points form the...Ch. 8.1 - In Exercises 710, show that the points form the...Ch. 8.1 - Finding Coterminal Angles In Exercises 1-6,...Ch. 8.1 - Finding Coterminal Angles In Exercises 1-6,...Ch. 8.1 - Finding Coterminal Angles In Exercises 1-6,...Ch. 8.1 - Finding Coterminal Angles In Exercises 1-6,...Ch. 8.1 - Finding Coterminal Angles In Exercises 1-6,...Ch. 8.1 - Finding Coterminal Angles In Exercises 1-6,...Ch. 8.1 - Finding Conterminal Angles In Exercise 7-10,...Ch. 8.1 - Finding Conterminal Angles In Exercise 7-10,...Ch. 8.1 - Finding Conterminal Angles In Exercise 7-10,...Ch. 8.1 - Finding Conterminal Angles In Exercise 7-10,...Ch. 8.1 - Converting from Degrees to radians In Exercises...Ch. 8.1 - Converting from Degrees to radians In Exercises...Ch. 8.1 - Converting from Degrees to radians In Exercises...Ch. 8.1 - Converting from Degrees to radians In Exercises...Ch. 8.1 - Converting from Degrees to radians In Exercises...Ch. 8.1 - Converting from Degrees to radians In Exercises...Ch. 8.1 - Converting from Degrees to radians In Exercises...Ch. 8.1 - Converting from Degrees to radians In Exercises...Ch. 8.1 - Converting from Degrees to radians In Exercises...Ch. 8.1 - Converting from Degrees to radians In Exercises...Ch. 8.1 - Converting from Degrees to radians In Exercises...Ch. 8.1 - Converting from Degrees to radians In Exercises...Ch. 8.1 - Converting from Radians to Degrees In Exercises...Ch. 8.1 - Converting from Radians to Degrees In Exercises...Ch. 8.1 - Converting from Radians to Degrees In Exercises...Ch. 8.1 - Converting from Radians to Degrees In Exercises...Ch. 8.1 - Converting from Radians to Degrees In Exercises...Ch. 8.1 - Converting from Radians to Degrees In Exercises...Ch. 8.1 - Converting from Radians to Degrees In Exercises...Ch. 8.1 - Converting from Radians to Degrees In Exercises...Ch. 8.1 - Converting from Radians to Degrees In Exercises...Ch. 8.1 - Converting from Radians to Degrees In Exercises...Ch. 8.1 - Analyzing Triangles In Exercises 33-40, solve the...Ch. 8.1 - Analyzing Triangles In Exercises 33-40, solve the...Ch. 8.1 - Analyzing Triangles In Exercises 33-40, solve the...Ch. 8.1 - Analyzing Triangles In Exercises 33-40, solve the...Ch. 8.1 - Analyzing Triangles In Exercises 33-40, solve the...Ch. 8.1 - Analyzing Triangles In Exercises 33-40, solve the...Ch. 8.1 - Analyzing triangles In Exercises 33-40, solve the...Ch. 8.1 - Analyzing Triangles In Exercises 33-40, solve the...Ch. 8.1 - Finding the Area of an Equilateral Triangle In...Ch. 8.1 - Finding the Area of an Equilateral Triangle In...Ch. 8.1 - Finding the Area of an Equilateral Triangle In...Ch. 8.1 - Finding the Area of an Equilateral Triangle In...Ch. 8.1 - Height A person 6 feet tall standing 16 feet from...Ch. 8.1 - Length A guy wire is stretched from a broadcasting...Ch. 8.1 - Arc Length In Exercises 47-50, use the following...Ch. 8.1 - Arc Length In Exercises 47-50, use the following...Ch. 8.1 - Arc Length In Exercises 47-50, use the following...Ch. 8.1 - Arc Length In Exercises 47-50, use the following...Ch. 8.1 - Speed of Revolution A Blu-ray disc can have an...Ch. 8.1 - How do you see it? Determine which angles in the...Ch. 8.1 - Area of a Sector of a Circle In Exercises 53 and...Ch. 8.1 - Area of a Sector of a Circle In Exercises 53 and...Ch. 8.1 - True or False? In Exercises 55-58, determine...Ch. 8.1 - True or False? In Exercises 55-58, determine...Ch. 8.1 - True or False? In Exercises 55-58, determine...Ch. 8.1 - True or False? In Exercises 55-58, determine...Ch. 8.2 - Let (3,1) be a point on the terminal side of , as...Ch. 8.2 - Evaluate each trigonometric function. a. sin56 b....Ch. 8.2 - Evaluate each trigonometric function. a. sin(6) b....Ch. 8.2 - Find the height of a building that casts a 75-foot...Ch. 8.2 - When the object in Example 5 is 4 feet from the...Ch. 8.2 - Solve for in each equation. Assume 02. a. cos=22...Ch. 8.2 - Solve the equation for . sin2+sin=0,02Ch. 8.2 - In Exercises 1-4, simplify the expression. 72+242Ch. 8.2 - In Exercises 1-4, simplify the expression....Ch. 8.2 - In Exercises 1-4, simplify the expression. 6222Ch. 8.2 - In Exercises 1-4, simplify the expression. 9232Ch. 8.2 - In Exercises 5-8, convert the degree measure to...Ch. 8.2 - In Exercises 5-8, convert the degree measure to...Ch. 8.2 - In Exercises 5-8, convert the degree measure to...Ch. 8.2 - In Exercises 5-8, convert the degree measure to...Ch. 8.2 - In Exercises 9-12, solve the equation. x2x=0Ch. 8.2 - In Exercises 9-12, solve the equation. 2x2+x=0Ch. 8.2 - In Exercises 9-12, solve the equation. x22x=3Ch. 8.2 - In Exercises 9-12, solve the equation. x25x=6Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Determining a Quadrant In Exercises 13-18,...Ch. 8.2 - Determining a Quadrant In Exercises 13-18,...Ch. 8.2 - Determining a Quadrant In Exercises 13-18,...Ch. 8.2 - Determining a Quadrant In Exercises 13-18,...Ch. 8.2 - Determining a Quadrant In Exercises 13-18,...Ch. 8.2 - Determining a Quadrant In Exercises 13-18,...Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - 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Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Evaluating Trigonometric Functions In Exercises...Ch. 8.2 - Solving a Right Triangle In Exercises 43-48, solve...Ch. 8.2 - Solving a Right Triangle In Exercises 43-48, solve...Ch. 8.2 - Solving a Right Triangle In Exercises 43-48, solve...Ch. 8.2 - Solving a Right Triangle In Exercises 43-48, solve...Ch. 8.2 - Solving a Right Triangle In Exercises 43-48, solve...Ch. 8.2 - Solving a Right Triangle In Exercises 43-48, solve...Ch. 8.2 - Solving a Trigonometric Equation In Exercises...Ch. 8.2 - Solving a Trigonometric Equation In Exercises...Ch. 8.2 - Solving a Trigonometric Equation In Exercises...Ch. 8.2 - Solving a Trigonometric Equation In Exercises...Ch. 8.2 - Solving a Trigonometric Equation In Exercises...Ch. 8.2 - Solving a Trigonometric Equation In Exercises...Ch. 8.2 - Solving a Trigonometric Equation In Exercises...Ch. 8.2 - Solving a Trigonometric Equation In Exercises...Ch. 8.2 - 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Finding the Period and Amplitude In Exercises...Ch. 8.3 - Finding the Period and Amplitude In Exercises...Ch. 8.3 - Finding the Period and Amplitude In Exercises...Ch. 8.3 - Finding the Period In Exercises 15-20, find the...Ch. 8.3 - Finding the Period In Exercises 15-20, find the...Ch. 8.3 - Finding the Period In Exercises 15-20, find the...Ch. 8.3 - Finding the Period In Exercises 15-20, find the...Ch. 8.3 - Finding the Period In Exercises 15-20, find the...Ch. 8.3 - Finding the Period In Exercises 15-20, find the...Ch. 8.3 - Matching In Exercises 21-26, match the...Ch. 8.3 - Matching In Exercises 21-26, match the...Ch. 8.3 - Matching In Exercises 21-26, match the...Ch. 8.3 - Matching In Exercises 21-26, match the...Ch. 8.3 - Matching In Exercises 21-26, match the...Ch. 8.3 - Matching In Exercises 21-26, match the...Ch. 8.3 - Graphing a Trigonometric Function In Exercises...Ch. 8.3 - Graphing a Trigonometric Function In Exercises...Ch. 8.3 - Graphing a Trigonometric Function In Exercises...Ch. 8.3 - 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Graphical Reasoning In Exercises 63-66, find a and...Ch. 8.3 - Graphical Reasoning In Exercises 63-66, find a and...Ch. 8.3 - Phase Shift In Exercises 67-70, match the function...Ch. 8.3 - Phase Shift In Exercises 6770, match the function...Ch. 8.3 - Phase Shift In Exercises 6770, match the function...Ch. 8.3 - Phase Shift In Exercises 6770, match the function...Ch. 8.3 - Writing an Equation In Exercises 71 and 72, write...Ch. 8.3 - Writing an Equation In Exercises 71 and 72, write...Ch. 8.3 - Biology: Predator-Prey Cycle The population P of a...Ch. 8.3 - Biology: Predator-Prey Cycle The population P of a...Ch. 8.3 - Music When tuning a piano, a technician strikes a...Ch. 8.3 - Health The function P=10020cos5t3 approximates the...Ch. 8.3 - Health For a person at rest, the velocity v (in...Ch. 8.3 - Health After a person exercises for a few minutes,...Ch. 8.3 - Transportation Workers The number W (in thousands)...Ch. 8.3 - Sales The snowmobile sales 5 (in units) at a...Ch. 8.3 - Physics Use the graphs below to answer each...Ch. 8.3 - Think About It Consider the function given by...Ch. 8.3 - Think About It Consider the functions given by...Ch. 8.3 - HOW DO YOU SEE IT? The normal monthly high...Ch. 8.3 - True or False? In Exercises 8588, determine...Ch. 8.3 - True or False? In Exercises 85-88, determine...Ch. 8.3 - True or False? In Exercises 85-88, determine...Ch. 8.3 - True or False? 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Assume...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Differentiating Trigonometric Functions In...Ch. 8.4 - Slope of a Tangent Line In Exercises 41 and 42,...Ch. 8.4 - Slope of a Tangent Line In Exercises 41 and 42,...Ch. 8.4 - Finding an Equation of a Tangent Line In Exercises...Ch. 8.4 - Finding an Equation of a Tangent Line In Exercises...Ch. 8.4 - Finding an Equation of a Tangent Line In Exercises...Ch. 8.4 - Finding an Equation of a Tangent Line In Exercises...Ch. 8.4 - Finding an Equation of a Tangent Line In Exercises...Ch. 8.4 - Finding an Equation of a Tangent Line In Exercises...Ch. 8.4 - Finding an Equation of a Tangent Line In Exercises...Ch. 8.4 - Finding an Equation of a Tangent Line In Exercises...Ch. 8.4 - Implicit Differentiation In Exercises 51 and 52,...Ch. 8.4 - Implicit Differentiation In Exercises 51 and 52,...Ch. 8.4 - Finding Relative Extrema In Exercises 53-62, find...Ch. 8.4 - Finding Relative Extrema In Exercises 53-62, find...Ch. 8.4 - Finding Relative Extrema In Exercises 53-62, find...Ch. 8.4 - Finding Relative Extrema In Exercises 53-62, find...Ch. 8.4 - Finding Relative Extrema In Exercises 53-62, find...Ch. 8.4 - Finding Relative Extrema In Exercises 53-62, find...Ch. 8.4 - Finding Relative Extrema In Exercises 53-62, find...Ch. 8.4 - Finding Relative Extrema In Exercises 53-62, find...Ch. 8.4 - Finding Relative Extrema In Exercises 53-62, find...Ch. 8.4 - Finding Relative Extrema In Exercises 53-62, find...Ch. 8.4 - Finding Second Derivatives In Exercises 6366, find...Ch. 8.4 - Finding Second Derivatives In Exercises 6366, find...Ch. 8.4 - Finding Second Derivatives In Exercises 6366, find...Ch. 8.4 - Finding Second Derivatives In Exercises 6366, find...Ch. 8.4 - Meteorology The normal average daily temperature...Ch. 8.4 - Meteorology The number of hours of daylight D in...Ch. 8.4 - Transportation Workers The number W (in thousands)...Ch. 8.4 - Employment The number W (in thousands) of golf...Ch. 8.4 - Biology Plants do not grow at constant rates...Ch. 8.4 - Tides Throughout the day, the depth of water D (in...Ch. 8.4 - Think About It Rewrite the trigonometric function...Ch. 8.4 - HOW DO YOU SEE IT? 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Transportation Workers The number W (In thousands)...Ch. 8.5 - Cost The temperature T (in degrees Fahrenheit) in...Ch. 8.5 - Water Supply The flow rate R (in thousands of...Ch. 8.5 - Sales In Example 8 in Section 8.4, the sales of a...Ch. 8.5 - HOW DO YOU SEE IT? 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In Problems 15 and 16 determine by inspection at least two solutions of the given first-order IVP. 16. xy=2y,y(...

A First Course in Differential Equations with Modeling Applications (MindTap Course List)

In the following exercises, compute the average value using the left Riemann sums LN for N = 1, 10, 100. How do...

Calculus Volume 2

For the following exercises, use the horizontal line test to determine whether each of the given graphs is one-...

Calculus Volume 1