Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

The area of a square is increasing at a rate of 2 square inches per second. At the time when the area of the square is 1 , what is the rate of change of the perimeter of the square? Round your answer to three decimal places (if necessary).

The area of a square is increasing at a rate of $2$ square inches per second. At the time when the area of the square is $1$ , what is the rate of change of the perimeter of the square? Round your answer to three decimal places (if necessary).

View step-by-step help

View step-by-step help

Find the rate of change of one variable when rate of change of other variable is given

Full solution

Q. The area of a square is increasing at a rate of

2

square inches per second. At the time when the area of the square is

1

, what is the rate of change of the perimeter of the square? Round your answer to three decimal places (if necessary).

Area of Square: Relate the area of the square to its side length. $\newline$ Area of square, $A = s^2$ , where $s$ is the side length. $\newline$ Given $A = 1$ , find $s$ . $\newline$ $s^2 = 1$ $\newline$ $s = 1$
Differentiate Area Formula: Differentiate the area formula with respect to time. $\newline$ $\frac{dA}{dt} = 2s \cdot \frac{ds}{dt}$ $\newline$ Given $\frac{dA}{dt} = 2$ square inches per second, substitute and solve for $\frac{ds}{dt}$ . $\newline$ $2 = 2\cdot 1 \cdot \frac{ds}{dt}$ $\newline$ $\frac{ds}{dt} = 1$ inch per second
Perimeter of Square: Relate the perimeter of the square to its side length. $\newline$ Perimeter, $P = 4s$ $\newline$ Differentiate the perimeter formula with respect to time. $\newline$ rac{dP}{dt} = 4 \times rac{ds}{dt} $\newline$ Substitute $ds/dt$ from Step $2$ . $\newline$ rac{dP}{dt} = 4 \times 1 $\newline$ rac{dP}{dt} = 4 inches per second

More problems from Find the rate of change of one variable when rate of change of other variable is given

Question

What is the volume of a hemisphere with a diameter of

52.5 \mathrm{ft}

, rounded to the nearest tenth of a cubic foot?

\newline

\mathrm{ft}^{3}

Posted 2 months ago

Question

A cylinder has a base radius of

5 \mathrm{~cm}

and a height of

16 \mathrm{~cm}

. What is its volume in cubic

\mathrm{cm}

, to the nearest tenths place?

\newline

V=\square \mathrm{cm}^{3}

Posted 2 months ago

Question

A cylinder has a base diameter of

20 \mathrm{ft}

and a height of

10 \mathrm{ft}

. What is its volume in cubic

\mathrm{ft}

, to the nearest tenths place?

\newline

V=

\mathrm{ft}^{3}

Posted 2 months ago

Question

A cylinder has a base radius of

6

feet and a height of

8

feet. What is its volume in cubic feet, to the nearest tenths place?

\newline

V=

{ }^{3}

Posted 2 months ago

Question

A spherical balloon of radius

3 \mathrm{~cm}

is being pumped by air at a rate of

9

\mathrm{cm}

per second. What is the rate of change of the radius?

\left(V=\frac{4}{3} \pi r^{3}\right)

Posted 2 months ago

Question

The volume of a rectangular prism is

54 \mathrm{ft}^{3}

. Carter measures the sides to be

2.85 \mathrm{ft}

9.32 \mathrm{ft}

2.09 \mathrm{ft}

. In calculating the volume, what is the relative error, to the nearest thousandth.

\newline

Posted 1 month ago

Question

The volume of a rectangular prism is

108 \mathrm{ft}^{3}

. David measures the sides to be

6.14 \mathrm{ft}

3.44 \mathrm{ft}

5.8 \mathrm{ft}

. In calculating the volume, what is the relative error, to the nearest hundredth.

\newline

Posted 1 month ago

Question

The volume of a rectangular prism is

360 \mathrm{~cm}^{3}

. Alex measures the sides to be

9.09 \mathrm{~cm}

4.84 \mathrm{~cm}

8.35 \mathrm{~cm}

. In calculating the volume, what is the relative error, to the nearest hundredth.

\newline

Posted 1 month ago

Question

The volume of a rectangular prism is

504 \mathrm{in}^{3}

. Eric measures the sides to be

6

63

7

76

9

08

in. In calculating the volume, what is the relative error, to the nearest hundredth.

\newline

Posted 1 month ago

Question

The volume of a rectangular prism is

150 \mathrm{in}^{3}

. Alex measures the sides to be

2

8

9

72

4

54

in. In calculating the volume, what is the relative error, to the nearest hundredth.

\newline

Posted 2 months ago