# The equation given that the statement ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071 ### Precalculus: Mathematics for Calcu...

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

#### Solutions

Chapter 1.11, Problem 30E

(A)

To determine

## To find:The equation given that the statement

Expert Solution

The equation is T=kx

### Explanation of Solution

Given:

T varies directly as x

Concept used:

If the quantities x and y are related by an equation

y=kx

For some constant k0

That is y varies directly as x or y is directly proportional to x

The constant k is called constant proportionality

Calculation:

If the quantities P and l are related by an equation

Pαl

P=kl................(1)

For some constant k0

That is P varies directly as l or P is directly proportional to l

The constant k is called constant proportionality

Where P is the period of a pendulum

l is the length of the pendulum

(B)

To determine

### To find:The equation of double the period that the statement

Expert Solution

The equation is l2=4l1

### Explanation of Solution

Given:

P is directly proportional to l

Concept used:

If the quantities x and y are related by an equation

y=kx

For some constant k0

That is y varies directly as x or y is directly proportional to x

The constant k is called constant proportionality

Calculation:

If the quantities P and l are related by an equation

Pαl

P=kl................(1)

For some constant k0

That is P varies directly as l or P is directly proportional to l

The constant k is called constant proportionality

Where P is the period of a pendulum

l is the length of the pendulum

That is

P2=2P1...........................(2)

kl2=2kl1l2=2l1l2=4l1

The new length has to quadruple the first length

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