Algebra and Trigonometry: Structure and Method, Book 2

2000th Edition

ISBN: 9780395977255

Author: MCDOUGAL LITTEL

Publisher: McDougal Littell

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Concept explainers

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

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Question

Chapter 5, Problem 18CR

To determine

To give the letter of the correct answer to find how fast can bill raw in still water.

Expert Solution & Answer

Answer to Problem 18CR

The correct answer is b.

Explanation of Solution

Given that: Bill rowed 30 km upstream against a 2km/h current and back again in a total of 8h.

Formula:

Speed= distance /time

Let speed be x

The speed in the upstream will be (x−2) with a distance of 30 km

Therefore, the total time for upstream will be 30(x−2)....(i)

Similarly for the speed in the downstream will be (x+2) with a distance of 30 km

Therefore, the total time for downstream stream will be 30(x+2).......(ii)

Now , the sum of total time of upstream and downstream will be equal to 8h

Add both the equation (i) and (ii) and equate with total time of 8 hr.

30(x−2)+30(x+2)=8

Take LCM

30(x+2)+30(x−2)(x−2)(x+2)=830x+60+30x−60(x−2)(x+2)=860x(x−2)(x+2)=860x=8(x+2)(x−2)60x−8(x2−4)=0−8x2+60x+32=08x2−60x−32=0

Apply factor

4(2x2−15x−8)=02x2−(16−1)x−8=02x2−16x+x−8=02x(x−8)+1(x−8)=0(2x+1)(x−8)=0

Apply zero product property to find the value of equation.

(2x+1)=02x=−2x=−1/2similarlyx−8=0x=8

x={−1/2,8}

The negative speed is not valid for the answer . So, the swim speed at 8 km/h.

Hence, the correct option is b.

Chapter 5, Problem 17CR

Chapter 5, Problem 1CT

Chapter 5 Solutions

Algebra and Trigonometry: Structure and Method, Book 2

Ch. 5.1 - Prob. 1OE Ch. 5.1 - Prob. 2OE Ch. 5.1 - Prob. 3OE Ch. 5.1 - Prob. 4OE Ch. 5.1 - Prob. 5OE Ch. 5.1 - Prob. 6OE Ch. 5.1 - Prob. 7OE Ch. 5.1 - Prob. 8OE Ch. 5.1 - Prob. 9OE Ch. 5.1 - Prob. 10OE

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