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CalculusCalculus: An Applied Approach (MindTap Course List)Checkpoint 4 Worked-out solution available at LarsonAppliedCalculus.com At time t = 0, a diver jumps from a diving board that is 12 feet high with an initial velocity of 16 feet per second. The diver’s position function is s = −16 t 2 + 16 t + 12. a. When does the diver hit the water? b. What is the diver’s velocity at impact?BuyFind*arrow_forward*

10th Edition

Ron Larson

Publisher: Cengage Learning

ISBN: 9781305860919

Chapter 2.3, Problem 4CP

Textbook Problem

Checkpoint 4 Worked-out solution available at LarsonAppliedCalculus.com

At time *t* = 0, a diver jumps from a diving board that is 12 feet high with an initial velocity of 16 feet per second. The diver’s position function is *s* = −16*t*^{2} + 16*t* + 12.

**a.** When does the diver hit the water?

**b.** What is the diver’s velocity at impact?

Expert Solution

**(a)**

To determine

**To calculate:** The time when the diver hits the water, when at time

**Given Information:**

At time

**Formula used:**

Zero product law:

If

Where *a, b* belongs to set of real numbers.

**Calculation:**

The position function of the diver is given by

To find the time when the diver hits the water, substitute

Factor out

It can be further si

Expert Solution

**(b)**

To determine

**To calculate:** The velocity at impact when the diver hits the water where the diver's position function is given by

Calculus: An Applied Approach (MindTap Course List)

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The cost C (In dollars) of...Ch. 2.5 - Credit Card Rate The average annual rate r (in...Ch. 2.6 - Checkpoint 1 Worked-out solution available at...Ch. 2.6 - Checkpoint 2 Worked-out solution available at...Ch. 2.6 - Checkpoint 3 Worked-out solution available at...Ch. 2.6 - Checkpoint 4 Worked-out solution available at...Ch. 2.6 - Checkpoint 5 Worked-out solution available at...Ch. 2.6 - Checkpoint 6 Worked-out solution available at...Ch. 2.6 - In Exercises 1-4, solve the equation. 16t2+292=0Ch. 2.6 - In Exercises 1-4, solve the equation. 16t2+88t=0Ch. 2.6 - In Exercises 1-4, solve the equation....Ch. 2.6 - In Exercises 1-4, solve the equation....Ch. 2.6 - In Exercises 5-8, find dy/dx. y=x2(2x+7)Ch. 2.6 - In Exercises 5-8, find dy/dx. y=(x2+3x)(2x25)Ch. 2.6 - In Exercises 5-8, find dy/dx. y=x22x+7Ch. 2.6 - In Exercises 5-8, find dy/dx. y=x2+3x2x25Ch. 2.6 - In Exercises 9 and 10, find the domain and range...Ch. 2.6 - In Exercises 9 and 10, find the domain and range...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises 112,...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises 112,...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises 112,...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises 112,...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises 112,...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises 112,...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises 112,...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises 112,...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises 112,...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises 112,...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises 112,...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises 112,...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Finding Higher-Order Derivatives In Exercises...Ch. 2.6 - Using Derivatives In Exercises 3134, find the...Ch. 2.6 - Using Derivatives In Exercises 3134, find the...Ch. 2.6 - Using Derivatives In Exercises 3134, find the...Ch. 2.6 - Using Derivatives In Exercises 3134, find the...Ch. 2.6 - Velocity and Acceleration A ball is propelled...Ch. 2.6 - Velocity and Acceleration A brick becomes...Ch. 2.6 - Velocity and Acceleration The velocity v (in feet...Ch. 2.6 - Stopping Distance A car is traveling at a rate of...Ch. 2.6 - Derivatives of Polynomial Functions Consider the...Ch. 2.6 - HOW DO YOU SEE IT? The graph shows the position,...Ch. 2.6 - Modeling Data The table shows the sales y (in...Ch. 2.6 - Finding a Pattern Develop a general rule for...Ch. 2.6 - True or False? In Exercises 43 and 44, determine...Ch. 2.6 - True or False? In Exercises 43 and 44, determine...Ch. 2.6 - Project: Cell Phone Subscribers in U.S. For a...Ch. 2.7 - Checkpoint 3 Worked-out solution available at...Ch. 2.7 - Checkpoint 3 Worked-out solution available at...Ch. 2.7 - Checkpoint 3 Worked-out solution available at...Ch. 2.7 - Checkpoint 4 Worked-out solution available at...Ch. 2.7 - Checkpoint 5 Worked-out solution available at...Ch. 2.7 - Checkpoint 4 Worked-out solution available at...Ch. 2.7 - In Exercises 1-6, solve the equation for y....Ch. 2.7 - In Exercises 1-6, solve the equation for y....Ch. 2.7 - In Exercises 1-6, solve the equation for y....Ch. 2.7 - In Exercises 1-6, solve the equation for y....Ch. 2.7 - In Exercises 1-6, solve the equation for y....Ch. 2.7 - In Exercises 1-6, solve the equation for y....Ch. 2.7 - In Exercises 7-9, evaluate the expression at the...Ch. 2.7 - In Exercises 7-9, evaluate the expression at the...Ch. 2.7 - In Exercises 7-9, evaluate the expression at the...Ch. 2.7 - Finding Derivatives In Exercises 1-12, find dy/dx...Ch. 2.7 - Finding Derivatives In Exercises 1-12, find dy/dx...Ch. 2.7 - Finding Derivatives In Exercises 1-12, find dy/dx...Ch. 2.7 - Finding Derivatives In Exercises 1-12, find dy/dx...Ch. 2.7 - Finding Derivatives In Exercises 1-12, find dy/dx...Ch. 2.7 - Finding Derivatives In Exercises 1-12, find dy/dx...Ch. 2.7 - Finding Derivatives In Exercises 1-12, find dy/dx...Ch. 2.7 - Finding Derivatives In Exercises 1-12, find dy/dx...Ch. 2.7 - Finding Derivatives In Exercises 1-12, find dy/dx...Ch. 2.7 - Finding Derivatives In Exercises 1-12, find dy/dx...Ch. 2.7 - Finding Derivatives In Exercises 1-12, find dy/dx...Ch. 2.7 - Finding Derivatives In Exercises 1-12, find dy/dx...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding the Slope of a Graph Implicitly In...Ch. 2.7 - Finding Derivatives Implicitly and Explicitly In...Ch. 2.7 - Finding Derivatives Implicitly and Explicitly In...Ch. 2.7 - Finding Equations of Tangent Lines In Exercises...Ch. 2.7 - Finding Equations of Tangent Lines In Exercises...Ch. 2.7 - Finding Equations of Tangent Lines In Exercises...Ch. 2.7 - Finding Equations of Tangent Lines In Exercises...Ch. 2.7 - Finding Equations of Tangent Lines In Exercises...Ch. 2.7 - Finding Equations of Tangent Lines In Exercises...Ch. 2.7 - Finding Equations of Tangent Lines In Exercises...Ch. 2.7 - Finding Equations of Tangent Lines In Exercises...Ch. 2.7 - Demand In Exercises 43-46, find the rate of change...Ch. 2.7 - Demand In Exercises 43-46, find the rate of change...Ch. 2.7 - Demand In Exercises 43-46, find the rate of change...Ch. 2.7 - Demand In Exercises 43-46, find the rate of change...Ch. 2.7 - Production Let x represent the units of labor and...Ch. 2.7 - HOW DO YOU SEE IT? The graph shows the demand...Ch. 2.7 - Health: U.S. Chickenpox Decline The numbers (in...Ch. 2.8 - Checkpoint 1 Worked-out solution available at...Ch. 2.8 - Checkpoint 2 Worked-out solution available at...Ch. 2.8 - Checkpoint 3 Worked-out solution available at...Ch. 2.8 - Checkpoint 4 Worked-out solution available at...Ch. 2.8 - In Exercises 1-6, write a formula for the given...Ch. 2.8 - In Exercises 1-6, write a formula for the given...Ch. 2.8 - In Exercises 1-6, write a formula for the given...Ch. 2.8 - In Exercises 1-6, write a formula for the given...Ch. 2.8 - In Exercises 1-6, write a formula for the given...Ch. 2.8 - In Exercises 1-6, write a formula for the given...Ch. 2.8 - In Exercises 7-10, find dy/dx by implicit...Ch. 2.8 - In Exercises 7-10, find dy/dx by implicit...Ch. 2.8 - In Exercises 7-10, find dy/dx by implicit...Ch. 2.8 - In Exercises 7-10, find dy/dx by implicit...Ch. 2.8 - Using Related Rates In Exercises 14, assume that x...Ch. 2.8 - Using Related Rates In Exercises 14, assume that x...Ch. 2.8 - Using Related Rates In Exercises 14, assume that x...Ch. 2.8 - Using Related Rates In Exercises 14, assume that x...Ch. 2.8 - Area The radius r of a circle is increasing at a...Ch. 2.8 - Volume The radius r of a sphere is increasing at a...Ch. 2.8 - Area Let A be the area of a circle of radius r...Ch. 2.8 - Volume Let V be the volume of a sphere of radius r...Ch. 2.8 - Volume A spherical balloon is inflated with gas at...Ch. 2.8 - Volume The radius r of a right circular cone is...Ch. 2.8 - Cost, Revenue, and Profit A company that...Ch. 2.8 - Cost, Revenue, and Profit A company that...Ch. 2.8 - Revenue The revenue R from selling x units of a...Ch. 2.8 - Profit The profit P from selling x units of a...Ch. 2.8 - Volume All edges of a cube are expanding at a rate...Ch. 2.8 - Surface Area All edges of a cube are expanding at...Ch. 2.8 - Boating A boat is pulled by a winch on a dock, and...Ch. 2.8 - Shadow Length A man 6 feet tall walks at a rate of...Ch. 2.8 - Air traffic Control An airplane flying at an...Ch. 2.8 - Baseball A (square) baseball diamond has sides...Ch. 2.8 - Air Traffic Control An air traffic controller...Ch. 2.8 - Advertising Costs A retail sporting goods store...Ch. 2.8 - Environment An accident at an oil drilling...Ch. 2.8 - Profit A company is increasing the production of a...Ch. 2.8 - Sales The profit for a product is increasing at a...Ch. 2.8 - HOW DO YOU SEE IT? 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Finding Rates of Change In Exercises 5154, find...Ch. 2 - Finding Rates of Change In Exercises 5154, find...Ch. 2 - Velocity The height s (in feet) at time t (in...Ch. 2 - Velocity A rock is dropped from a tower on the...Ch. 2 - Marginal Cost In Exercises 5760, find the marginal...Ch. 2 - Marginal Cost In Exercises 5760, find the marginal...Ch. 2 - Marginal Cost In Exercises 5760, find the marginal...Ch. 2 - Marginal Cost In Exercises 5760, find the marginal...Ch. 2 - Marginal Revenue In Exercises 6164, find the...Ch. 2 - Marginal Revenue In Exercises 6164, find the...Ch. 2 - Marginal Revenue In Exercises 6164, find the...Ch. 2 - Marginal Revenue In Exercises 6164, find the...Ch. 2 - Marginal Profit In Exercises 65 and 66, find the...Ch. 2 - Marginal Profit In Exercises 65 and 66, find the...Ch. 2 - Marginal Profit The profit P (in dollars) from...Ch. 2 - Population Growth The population P (in millions)...Ch. 2 - Finding Derivatives In Exercises 6990, find the...Ch. 2 - Finding Derivatives In Exercises 6990, find the...Ch. 2 - 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Two individuals are running for mayor of your town. You conduct an election survey a week before the election a...

Essentials Of Statistics

Public Transportation Budget Deficit According to the Massachusetts Bay Transportation Authority (MBTA), the pr...

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

A semicircle with diameter PQ sits on an isosceles triangle PQR to form a region shaped like a two-dimensional ...

Calculus (MindTap Course List)

Find the limit. 35. lims164ss16

Single Variable Calculus

15. In 20l4, the New York Yankees had a team batting average of µ = 245 (actually 0.245 but we will avoid the d...

Statistics for The Behavioral Sciences (MindTap Course List)

24. Dotplot: Sled Dog Racing Make a dotplot for the data in Problem 15 regarding the finish time (number of hou...

Understanding Basic Statistics

Convert each expression in Exercises 25-50 into its technology formula equivalent as in the table in the text. ...

Finite Mathematics

From the list 0, 2, 34, 56, 253, 3, 8, 0.34, 0.23, 67, and 97, identify each of the following. a The natural nu...

Intermediate Algebra

The accompanying data set consists of observations on shower-flow rate (L/min) for a sample of n = 129 houses i...

Probability and Statistics for Engineering and the Sciences

In Exercises 63 to 70, state whether each of the given pairs of sets are equal, equivalent, both, or neither. T...

Mathematical Excursions (MindTap Course List)

In the problems 7-8, find the intercepts and graph the functions 7x+5y=21

Mathematical Applications for the Management, Life, and Social Sciences

Match the differential equation with its direction field (labeled IIV). Give reasons for your answer. 6. y = si...

Single Variable Calculus: Early Transcendentals

True or false
Label each of the following statement as either true or false.
Let and be integers, then .

Elements Of Modern Algebra

In Exercises 11 to 16, supply the missing coordinates for the vertices, using as few variables as possible. ABC...

Elementary Geometry For College Students, 7e

Change each decimal to a percent: 5.19

Elementary Technical Mathematics

Match the following numbers in word form with the numbers in numerical form. 12,743 102,470 11,270 112,743 Elev...

Contemporary Mathematics for Business & Consumers

Prove the following identities. (1+sin)(1sin)=cos2

Trigonometry (MindTap Course List)

Relative Extrema and Points of Inflection In Exercises 71-78, find the relative extrema and the points of infle...

Calculus of a Single Variable

Tractrix Show that the boat in Example 5 is always pointing toward the person.

Calculus: Early Transcendental Functions (MindTap Course List)

In the accompanying figure, m2=68, m8=112, and m9=110. a.Which lines r and s OR l and m must be parallel? _____...

Elementary Geometry for College Students

Find the effective rate corresponding to 1058%/year compounded monthly.

Finite Mathematics for the Managerial, Life, and Social Sciences

Finding Maximum and Minimum Values (a) Let f(x,y)=xy and g(x,y)=x2+y2=4. Graph various level curves of f ad the...

Multivariable Calculus

Finding the Principal Unit Normal Vector In Exercises 47-50, find the principal unit normal vector to the curse...

Calculus (MindTap Course List)

Which is the graph of ?

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

A surface S is parameterized by x = sin u, y = sin v, z = cos v for (u, v) ∈ D, 0 ≤ u ≤ , 0 ≤ v ≤ . A double in...

Study Guide for Stewart's Multivariable Calculus, 8th

In Exercises 49-30, use the information in Figure 9.120. You have been hired to design a network linking Boston...

Mathematics: A Practical Odyssey

The article Vital Dimensions in Volume Perception: Can the Eye Fool the Stomach? (Journal of Marketing Research...

Introduction To Statistics And Data Analysis

Endowment income is a critical part of the annual budgets at colleges and universities. A study by the National...

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

Traditional statistics (means, variances, and hypothesis tests) are not used to evaluate the results from a sin...

Research Methods for the Behavioral Sciences (MindTap Course List)

In exercise 1, the following estimated regression equation based on 10 observations was presented. = 29.1270 +...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Find the required term of each arithmetic sequence. 6,-1,-8,; 15th term

College Algebra (MindTap Course List)

The purpose of an independent-measures t-test is to determine whether the mean difference obtained between two ...

Research Methods for the Behavioral Sciences (MindTap Course List)

Determine the sine, cosine, or tangent functions of the following angels. Round the answers to 5 decimal places...

Mathematics For Machine Technology

Bessels Equation In Problems 16 use (1) to find the general solution of the given differential equation on (0, ...

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

Best Private Colleges. A random sample of 30 colleges from Kiplingers list of the best values in private colleg...

Essentials Of Statistics For Business & Economics

Let L be the language consisting of all strings of the form an , where n=m2 , for some positive integer m. Show...

Discrete Mathematics With Applications

59. The U.S. Coast Guard (USCG) provides a wide variety of information on boating accidents including the wind ...

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)

Exponential Growth Is the graph of exponential growth versus time increasing or decreasing?

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

Fill in the blanks. To find the amount A in an account after t years with principal P and an annual interest ra...

College Algebra

In the following exercises, use direct substitution to obtain an undefined expression. Then, use the method of ...

Calculus Volume 1