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Real-Life Applications of Differentiation

Fill in the blank:
In business, __________ is used to find profit and loss for the future of the investment using graphs.

distance

displacement

differentiation

Is the sentence true or false?
Differential equations model are available to control a particular species' population dynamics.

True

False

A stone is dropped into a quite pond and the waves moves in circles. If the radius of the circular wave increases at the rate of 8 cm/sec, find the rate of increase in its area at the instant when its radius is 6 cm?

$2\pi\ \frac{cm^2}{\sec}$

$9\ \frac{cm^2}{\sec}$

$96\pi\ \frac{cm^2}{\sec}$

Is the sentence true or false?
The rate of change of the area of a circle with respect to its radius $r$ when $r=6\ cm$ is $12\pi\ cm^{ }$ .

True

False

A spherical soap bubble is expanding so that its radius is increasing at the rate of 0.02 cm/sec. At what rate is the surface area is increasing when its radius is 5 cm?

$2.1512\ \frac{cm^2}{\sec}$

$6.1512\ \frac{cm^2}{\sec}$

$4.1512\ \frac{cm^2}{\sec}$

Fill in the blank:
__________ is used to calculate the rate of change of distance of a moving body with respect to time.

integration

differentiation

addition

The length x of a rectangle is decreasing at the rate of 5 cm/minute and the width y is increasing at the rate 4 cm/minute. When x=8 cm and y=6 cm then find the rate of change of the area of the rectangle.

6 cm/minute

3 cm/minute

4 cm/minute

Is the sentence true or false?
Temperature variations are calculated by using differentiation.

True

False

Fill in the blank:
The ____________ equation of the same type determines a circuit consisting of an inductance L or capacitor C and resistor R with current and voltage variables.

differential

integral

None of these

Is the sentence true or false?
Newton's second law of motion is used to describe the motion of the pendulum from which a differential equation of second order is obtained.

True

False

Questions

Time

Score

Real-Life Applications of Differentiation

Fill in the blank:In business, __________ is used to find profit and loss for the future of the investment using graphs.

distance

displacement

differentiation

Is the sentence true or false?Differential equations model are available to control a particular species' population dynamics.

True

False

A stone is dropped into a quite pond and the waves moves in circles. If the radius of the circular wave increases at the rate of 8 cm/sec, find the rate of increase in its area at the instant when its radius is 6 cm?

﻿﻿2π cm2sec⁡2\pi\ \frac{cm^2}{\sec}2π seccm2​﻿

﻿9 cm2sec⁡9\ \frac{cm^2}{\sec}9 seccm2​﻿

﻿96π cm2sec⁡96\pi\ \frac{cm^2}{\sec}96π seccm2​﻿

Is the sentence true or false?The rate of change of the area of a circle with respect to its radius ﻿rrr﻿ when ﻿r=6 cmr=6\ cmr=6 cm﻿ is ﻿12π cm12\pi\ cm^{ }12π cm﻿.

True

False

A spherical soap bubble is expanding so that its radius is increasing at the rate of 0.02 cm/sec. At what rate is the surface area is increasing when its radius is 5 cm?

﻿2.1512 cm2sec⁡2.1512\ \frac{cm^2}{\sec}2.1512 seccm2​﻿

﻿6.1512 cm2sec⁡6.1512\ \frac{cm^2}{\sec}6.1512 seccm2​﻿

﻿4.1512 cm2sec⁡4.1512\ \frac{cm^2}{\sec}4.1512 seccm2​﻿

Fill in the blank:__________ is used to calculate the rate of change of distance of a moving body with respect to time.

integration

differentiation

addition

The length x of a rectangle is decreasing at the rate of 5 cm/minute and the width y is increasing at the rate 4 cm/minute. When x=8 cm and y=6 cm then find the rate of change of the area of the rectangle.

6 cm/minute

3 cm/minute

4 cm/minute

Is the sentence true or false?Temperature variations are calculated by using differentiation.

True

False

Fill in the blank:The ____________ equation of the same type determines a circuit consisting of an inductance L or capacitor C and resistor R with current and voltage variables.

differential

integral

None of these

Is the sentence true or false?Newton's second law of motion is used to describe the motion of the pendulum from which a differential equation of second order is obtained.

True

False

Incorrect

Great!

Fill in the blank:
In business, __________ is used to find profit and loss for the future of the investment using graphs.

Is the sentence true or false?
Differential equations model are available to control a particular species' population dynamics.

$2\pi\ \frac{cm^2}{\sec}$

$9\ \frac{cm^2}{\sec}$

$96\pi\ \frac{cm^2}{\sec}$

Is the sentence true or false?
The rate of change of the area of a circle with respect to its radius $r$ when $r=6\ cm$ is $12\pi\ cm^{ }$ .

$2.1512\ \frac{cm^2}{\sec}$

$6.1512\ \frac{cm^2}{\sec}$

$4.1512\ \frac{cm^2}{\sec}$

Fill in the blank:
__________ is used to calculate the rate of change of distance of a moving body with respect to time.

Is the sentence true or false?
Temperature variations are calculated by using differentiation.

Fill in the blank:
The ____________ equation of the same type determines a circuit consisting of an inductance L or capacitor C and resistor R with current and voltage variables.

Is the sentence true or false?
Newton's second law of motion is used to describe the motion of the pendulum from which a differential equation of second order is obtained.