A right triangle has legs of 6 inches and 8 inches whose sides are changing. The short leg is decreasing by 7 in/sec and the long leg is growing at 6 in/sec. What is the rate of change of the hypotenuse?

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Q: A thin sheet of ice is in the form of a circle. If the ice is melting, at what rate is the radius…

A: Given a thin sheet of ice is in the form of a circle. And the area is 12 square inches.Let the area…

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A: The given data are: Radius of pool= 7 feet Height of pool= 7 feet dVdt=4 cubic feet per minute The…

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Q: A right triangle has legs of 30 inches and 40 inches whose sides are changing. The short leg is…

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Q: In an isosceles right triangle, the hypotenuse is increasing at a rate of 0.1 ft/s. When the area of…

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Q: What is the rate of change of the area?

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Q: A right triangle has legs of 6 inches and 8 inches whose sides are changing. The short leg is…

A: Given, A right triangle has legs of 6 inches and 8 inches whose sides are changing. The short leg is…

Q: The altitude of a triangle is increasing at a rate of 3 cm/minute while the area of the triangle is…

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Q: A ladder 20 feet long leans against a house. What is the rate at the top of a ladder that is moving…

A: Given that ,      A ladder 20 feet long leans against a house. We have to calculate the rate at the…

Q: A 6 foot tall man is walking at a rate of 40 metres per minute directly away from a wall with a…

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Q: The volume of a cube is increasing at the rate of 21 cc/min. At what rate is its surface area…

A: The volume of a cube is increasing at rate, dVdt = 21 cc/min To evaluate: The rate at which the…

Q: A right triangle has legs of 3 inches and 4 inches whose sides are changing. The short leg is…

A: dhdt=7 in/sec , dbdt = -10 in/sec

Q: A light is hung 6 meters above a straight horizontal path. If a man 2 meters tall is walking toward…

A: Decreasing:- We know that if something is decreasing then it is going down.

Q: If we know the rate of growth of a patch of moss, how can we calculate the area the moss covers?

A: The rate of growth of a patch of moss is modeled by a complex function A't, where t is measured in…

Q: Suppose that water is pouring into a swimming pool in the shape of a right circular cylinder at a…

A: Rate of change

Q: When a circular plate of metal is heated in an​ oven, its radius increases at a rate of 0.04…

A: When a circular plate of metal is heated in an​ oven, its radius increases at a rate of  0.04…

Q: A metallic ball with a diameter of 12 cm is covered with a layer of ice, so if the ice begins to…

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Q: A right triangle has legs of 9 inches and 12 inches whose sides are changing. The short leg is…

A: Given: A right triangle has legs of 9 inches and 12 inches whose sides are changing. The short leg…

Q: The radius of a circle is increasing at the rate of 0.7 cm/s.whats is the rate of increase of its…

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Q: When a circular plate of metal is heated in an oven, its radius increases at the rate of 0.01…

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Q: As the base of the ladder slides away from the house, the rate of change of the height of the ladder…

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Q: A rectangle has a length of 10 inches and a width of 4 inches whose sides are changing. The length…

A: Given:A rectangle has a length of 10 inches and a width of 4 inches whose sides are changing. The…

Q: The volume of a cube is increasing at 24 cubic inches per minute. What is the rate of change of its…

A: volume of cube = side3 V= volume  x= side dVdt=24 in3/minutedxdt=? at x=2

Q: A 5​-foot-tall woman walks at 4ft/s toward a street light that is 25ft above the ground. What is the…

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Q: A rectangle's length is increasing at the rate of 5 inches/sec, its width at 2 inches/sec. At what…

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Q: The top of a 25-foot ladder is sliding down a vertical wall at a constant rate of 3 feet per minute.…

A: This question is based on application of differentiation.

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Q: When a circular metal plate is heated in an oven, its radius increases at the rate of 0.02 cm/min.…

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Q: A right triangle has legs of 24 inches and 32 inches whose sides are changing. The short leg is…

A: Given, Measure of two legs of a right triangle: 24 inches, 32 inches. Let x be the short leg and y…

Q: A right triangle has legs of 18 inches and 24 inches whose sides are changing. The short leg is…

A: A right triangle has legs of 18 inches and 24 inches. The short leg is decreasing by 3 in/sec. The…

Q: A right triangle has legs of 33 inches and 44 inches whose sides are changing. The short leg is…

A: to find:- dH/dt.

Q: A right triangle has legs of 27 inches and 36 inches whose sides are changing. The short leg is…

A: Given that  Right triangle has  AB = 27 inches  BC = 36 inches Rate of change of short leg i.e. 27…

Q: Car B starts 30 miles directly east of car A and begins moving west at 90 mph. At the same moment…

A: We construct a triangle as shown below.

Q: A man that is 5 feet tall is walking in a straight line at a rate of 3 ft / s towards a lamp post…

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Q: When a circular plate of metal is heated in an oven, its radius increases at the rate of 0.01 cm…

A: Given:When a circular plate of metal is heated in an oven, its radius increases at the rate of 0.01…

Q: A conical tank (with vertex down) is 10 feet across the top and 12 feet deep. If water is flowing…

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Q: In a right triangle the hypotenuse is increasing at a rate of 0.1 ft/s. When the area of the…

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Q: A body cools at the rate of 0.5°C per second when it is 500°C above the surroundings. what is the…

A:

Q: A 6 foot tall man walks away at the rate of 4 feet per second from the base of the street light 12…

A: Let s be the length of the base of the street light to the shadow, x be the length of the base of…

Q: A rectangle has a length of 12 inches and a width of 6 inches whose sides are changing. The length…

A: The length of a rectangle is l=12 inThe width of a rectangle is w=6 inTo find the rate at width the…

Q: A rectangle has a length of 9 inches and a width of 10 inches whose sides are changing. The length…

A: Length of the rectangle, l =9 inches Width of the rectangle, w = 10 inches The length is increasing…

Q: A right triangle has legs of 33 inches and 44 inches whose sides are changing. The short leg is…

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Q: A spherical balloon is being deflated at the rate of 10 cm/s. What is the rate of change for the…

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Q: A rectangle has a length of 7 inches and a width of 8 inches whose sides are changing. The length is…

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Q: A right triangle has legs of 21 inches and 28 inches whose sides are changing. The short leg is…

A: Length of the legs are 21 inches and 28 inches and the short leg is increasing by 10 in/sec and the…

Q: A right triangle has legs of 18 inches and 24 inches whose sides are changing. The short leg is…

A: Given: A right triangle has legs of 18 inches and 24 inches whose sides are changing. The short leg…

Q: A right triangle has legs of 33 inches and 44 inches whose sides are changing. The short leg is…

A: Given: A right triangle has legs of 33 inches and 44 inches . The short leg is decreasing by 4…

Exponential Growth Model

The relation that represents an exponential function is: