BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 1, Problem 135RE

a.

To determine

To calculate:For the given information develop equation which relates intensity of illumination I inversely to square of distance d

Expert Solution

Answer to Problem 135RE

The required equation is I=kd2

Explanation of Solution

Given information:

The Intensity of illumination I from a given light is inversely proportional to square of distance d from the given light.

Formula used:

For 2 variables say, x and y , the statement x is directly proportional to y can be written as:

  xαy

Which can be written as:

  x=ky

Where k denotes the proportionality constant.

Similarly the statement x is inversely proportional to y can be interpreted as:

  xα1y

Which can be written as:

  x=k(1y)

Where k denotes the proportionality constant.

Calculation:

AsIntensity of illumination I from a given light is inversely proportional to square of distance d from the given light.

Recall, For 2 variables say, x and y , the statement x is inversely proportional to y can be interpreted as:

  xα1y

Which can be written as:

  x=k(1y)

Where k denotes the proportionality constant.

Hence, this variation can be expressed as follows:

  Iα1d2I=kd2

Where k denotes the proportionality constant.

Hence, the required equation is I=kd2

b.

To determine

To calculate:The constant of proportionality k if the lamp intensity is 1000 candles and the distance is 8 meters.

Expert Solution

Answer to Problem 135RE

The constant of proportionality k if the lamp intensity is 1000 candles and the distance is 8 meters is k=64000 candles per m2

Explanation of Solution

Given information:

The equation found is I=kd2 and the lamp intensity is 1000 candles while the distance from the light is 8 meters

Formula used:

For 2 variables say, x and y , the statement x is directly proportional to y can be written as:

  xαy

Which can be written as:

  x=ky

Where k denotes the proportionality constant.

Similarly the statement x is inversely proportional to y can be interpreted as:

  xα1y

Which can be written as:

  x=k(1y)

Where k denotes the proportionality constant.

Calculation:

AsIntensity of illumination I from a given light is inversely proportional to square of distance d from the given light.

Form a. the required equation is I=kd2 (1)

It is given that the intensity of illumination I=1000 and distance from the light d=8 meters.

Put these values in (1) to get:

  1000=k82k=64*1000k=64000

Hence, the constant of proportionality is k=64000 candles per m2

c.

To determine

To calculate:The intensity of lamp when the distance from the light is 20 meters

Expert Solution

Answer to Problem 135RE

The intensity of lamp when the distance from the light is 20 meters is I=160 candles.

Explanation of Solution

Given information:

The equation found is I=kd2 and the constant of proportionality is k=64000 candles per m2 . Also distance from the light is d=20 meters

Formula used:

For 2 variables say, x and y , the statement x is directly proportional to y can be written as:

  xαy

Which can be written as:

  x=ky

Where k denotes the proportionality constant.

Similarly the statement x is inversely proportional to y can be interpreted as:

  xα1y

Which can be written as:

  x=k(1y)

Where k denotes the proportionality constant.

Calculation:

AsIntensity of illumination I from a given light is inversely proportional to square of distance d from the given light.

Form a. the required equation is I=kd2 (1)

From b. the constant of proportionality is k=64000 candles per m2 (2)

Also, it is given distance from the light is d=20 meters (3)

Put (2) and (3) in (1) to get:

  I=64000202I=64000400I=160

Hence, the intensity of lamp when the distance from the light is 20 meters is I=160 candles.

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