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CalculusCalculus10th Edition

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Chapter 10, Problem 4PS
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Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095

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BuyFindarrow_forward

Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095
Textbook Problem

Flight Paths An air traffic controller spots two planes at the same altitude flying toward each other (see figure). Their flight paths are 20° and 315°. One plane is 150 miles from point P with a speed of 375 miles per hour. The other is 190 miles from point P with a speed of 450 miles per hour.

Chapter 10, Problem 4PS, Flight Paths An air traffic controller spots two planes at the same altitude flying toward each

(a) Find parametric equations for the path of each plane where t is the time in hours, with t = 0 corresponding to the time at which the air traffic controller spots the planes.

(b) Use the result of part (a) to write the distance between the planes as a function of t.

(c) Use a graphing utility to graph the function in part (b). When will the distance between the planes be minimum? If the planes must keep a separation of at least 3 miles, is the requirement met?

(a)

To determine

To calculate: The parametric equations for the path of each plane if

The flight paths are 20° and 315°.

One plane is 150 miles from P with a speed of 375 miles per hour.

The other plane is 190 miles from point P with a speed of 450 miles per hour.

The figure is given below.

Calculus, Chapter 10, Problem 4PS

Explanation

Given:

The flight paths are 20° and 315°.

One plane is 150 miles from P with a speed of 375 miles per hour.

The other plane is 190 miles from point P with a speed of 450 miles per hour.

The given figure is:

Formula used:

Speed formula:

speed=distancetime

Calculation:

Observe from the given figure, that the angle made by one plane with positive x-axis is

90°−20°=70°

Distance of the flight from the point P is 150 miles.

Since t=0 it corresponds to the time when the air traffic controller spots the plane. Hence, the distance covered by the plane with a speed of 375 miles per hour is 375t

(b)

To determine

To calculate: The distance between the planes as a function of t if

The parametric equation of one of the planes:

x1=(150−375t)cos70°y1=(150−375t)sin70°

The parametric equation of another plane:

x2=(190−450t)cos135°y2=(190−450t)sin45°

(c)

To determine

To graph:

The function y=[(190−450t)cos135°−(150−375t)cos70°]2+[(190−450t)sin45°−(150−375t)sin70°]2 and calculate the minimum distance between the planes and find if the planes keep a separation of at least 3miles.

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What do we mean when we say a histogram is skewed to the left? to the right? What is a bimodal histogram? Discu...

Understanding Basic Statistics

Describe the homogeneity of variance assumption and explain why it is important for the independent- measures t...

Statistics for The Behavioral Sciences (MindTap Course List)

Evaluate the limit and justify each step by indicating the appropriate Limit Law(s). 4. limx1(x43x)(x2+5x+3)

Single Variable Calculus

In problems 15-22, simplify by combining like terms. 15.

Mathematical Applications for the Management, Life, and Social Sciences

Consider a disease whose presence can be identified by carrying out a blood test. Let p denote the probability ...

Probability and Statistics for Engineering and the Sciences

In Exercises 78 and 79, use a Venn diagram similar to the one at the left below to shade in the region represen...

Mathematical Excursions (MindTap Course List)

For Problems 1-50, solve each equation. Objective 1 (2n1)+6(n+3)=4(7n11)

Intermediate Algebra

Solve the equations in Exercises 126. (x+1)3+(x+1)5=0

Finite Mathematics

For the limit limx2(x33x+4)=6 illustrate Definition 2 by finding values of that correspond =0.2 and 0.1. Def...

Single Variable Calculus: Early Transcendentals

A coefficient is a number or quantity placed before another quantity, indicating______. (5-2)

Contemporary Mathematics for Business & Consumers

Simplify each power of i. i12

Trigonometry (MindTap Course List)

Divide: +4800240

Elementary Technical Mathematics

Let be the group of nonzero quaternions with the operation of multiplication. Show that the center of is .

Elements Of Modern Algebra

In Exercises 27 to 30, find the area of the figure shown. Given: Pentagon ABCDE with DC-DE- AE=AB=5 BC=12 Find:...

Elementary Geometry For College Students, 7e

Particle Motion Repeat Exercise 103 for the position function given by x(t)=(t1)(t3)2,0t5.

Calculus: Early Transcendental Functions (MindTap Course List)

Using Newton's Method In Exercises 7-16, use Newtons Method to approximate the zero(s) or the function. Continu...

Calculus of a Single Variable

HOME HEALTH-CARE AND EQUIPMENT SPENDING The following table gives the projected spending on home care and durab...

Finite Mathematics for the Managerial, Life, and Social Sciences

In Exercises 13 to 18, describe the line segments as determined, undetermined, or overdetermined. Use the accom...

Elementary Geometry for College Students

Let and g(x) = x + 3. Then (g ∘ h)(x) = ______.

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

Using the Three-Dimensional Coordinate SystemDetermine the location of a point (x,y,z) that satisfies the condi...

Multivariable Calculus

The equation of the tangent plane corresponding to (1, 2) to the surface S parameterized by r(u, v) = (u + v)i ...

Study Guide for Stewart's Multivariable Calculus, 8th

Customer arrivals at a bank are random and independent; the probability of an arrival in anyone-minute period i...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Describe the general concept of sampling error and explain why this concept creates a problem to be addressed b...

Research Methods for the Behavioral Sciences (MindTap Course List)

Consider the following data on y = Number of songs stored on an MP3 player and x = Number of months the user ha...

Introduction To Statistics And Data Analysis

Solve each equation for y and graph the equation. Then check your graph with a graphing calculator. 2x+5y=10

College Algebra (MindTap Course List)

A researcher examines the relationship between the quality of breakfast and academic performance for a group of...

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 for Business & Economics, Revised (MindTap Course List)

Find each base. Round the answers to 2 decimal places when necessary. 54. 4413is 60% of what number?

Mathematics For Machine Technology

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