of two observat

Q: A 13ft ladder rests against a vertical wall. If the bottom of the ladder is sliding away from the…

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Q: A 12 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 4 ft/s, how…

A: A 12 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 4ft/s.

Q: each side of a square increases at a rate of 1.5cm/sec .also find the rate at which the area of the…

A: Given,   Each side of a square increases at a rate of 1.5 cm/sec

Q: A man starts walking north at 2 feet per second from a point P. A minute later a woman starts…

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Q: A water tank in the shape of an inverted cone is being filled up with water at a uniform rate of…

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Q: A vertical cylinder is leaking water at a rate of 3 m/sec. If the cylinder has a height of 10 m and…

A: The volume of the cylinder is given by V=πr2h, where V=volume of the cylinder r=radius of the…

Q: The radius of a spherical balloon is decreasing at a rate of in/sec.

A: Radius of balloon = r = 4 inchesDecreasing rate of balloon = drdt = -2πinches/secondVolume of…

Q: The length { of a rectangle is decreasing at a rate of 8 cm/ sec while the width w is increasing at…

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Q: A 14 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 4 ft/s, how…

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Q: 2. One side of a right triangle is known to be 22 cm long and the opposite angle is measured as 60°,…

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Q: The length of the rectangle is increasing at a rate of 5 cm per second, and its width is decreasing…

A: Given that, Let length of the ractangle is L and the width is W and area is A. Then according to the…

Q: 7. A 6ft tall human is walking away from a 20ft lamppost. Given that the length of the shadow of the…

A: Let the distance of the person from the bottom of the light post be x. Let the length of the shadow…

Q: At noon Person A is 15 km east of person b. person A is walking west at 3km/h, and person b is…

A: initially A and B apart 15 km apart that  person A moves towards west at rate (da/dt) = 3 km/hr…

Q: A car is slowing down at the rate 0.8 ft/sec². How far will the car move before it stops if its…

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Q: A hot air balloon rising vertically is tracked by an observer located 3 miles from the lift-off…

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Q: The tangent lines to the graph of f(x) = x2 grow steeper as x increases. At what rate do the slopes…

A: The tangent line of any given function is the line which  touches the curve of function at only one…

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: One side of a right triangle is known to be 20 cm long and the opposite angle is measured as 30°,…

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Q: If f(x) describes the position of an object over time, what is the average velocity on the interval…

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Q: An 8- meter ladder is leaning against a vertical wall. If a the ladder away from the person pulls…

A: Given  Length of the ladder = 8 meter The rate at which ladder is pulled away from the wall =0.7m/s…

Q: A 15-foot ladder is leaning against a mango tree. If the top of the ladder is sliding down the tree…

A: We need to find rate of bottom of ladder moving.

Q: If a snowball melts so that its surface area decreases at a rate of 3 cm2/min, find the rate at…

A: As per our guidelines, we can answer only one question in a single request. Kindly re-post the other…

Q: How fast is the circumference of a circle changing if the radius is changing at the rate of 3 mm/s?

A: Solution

Q: Water is flowing into a cylindrical tank at the rate of 2 m^3/min. If the radius of the tank is 0.5…

A: Water is flowing into a cylindrical tank at the rate of 2 m3/min.If the radius of the tank is 0.5 m,…

Q: 2 Find the slope of the tangent line to у 3 at X = 1 3 - х

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Q: If an object in linear motion (but with changing velocity) covers As meters in At seconds, then its…

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Q: A vertical cylinder is leaking water at a rate of 8m^3/sec. if the cylinder has a height of 10m and…

A: In a vertical cylinder water is leaking at a rate of 8 m3/sec. dVdt=8 Height of the cylinder is 10…

Q: 7. The top of a ladder slides down a vertical wall at a rate of 0.15 m/s. At the moment when the…

A: Given data A ladder slides a vertical wall at rate of 0.15 m/s  find the length of ladder = ?

Q: A 25 ft ladder is leaning against a vertical wall. 25 ft At what rate (with respect to time) is the…

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Q: Under certain conditions, cane sugar in water is converted into dextrose at a rate proportional to…

A: Given: when the initial time t=0 amount of the cane sugar is 75 kg, and the time t=30 minutes amount…

Q: A ladder 14 ft long rests against a vertical wall. Let 0 be the angle between the top of the ladder…

A: Given:

Q: If f(x) = 12x2 - x3, what is the rate of change of f'(x) at (-1, 13)?

A: We know that, the rate of change of f(x)  is (d/dx) {f(x) }.

Q: A flag is raised vertically from a pole at a constant rate of 1m/s. A point B on the ground level…

A: Given: Vertically raising speed of flag at constant rate=1 m/s……1Horizontal distance from flagpole…

Q: An object is thrown vertically upward with an initial velocity of 16 ft/sec from the top of a house…

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Q: What is the tangent line approximation to e* near x = 4?

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Q: The top of a ladder slides down a vertical wall at a rate of 0.675 m/s. At the moment when the…

A: Given,  A ladder slides down a vertical wall at a rate of 0.675 m/s  When the bottom of the ladder…

Q: A car leaves an intersection traveling west. Its position 4 sec later is 18 ft from the…

A: The figure below depicts the rate of change of y and x at time instant t=4 seconds

Q: C. Two cars start moving from the same point. One travels east at 55mi/h and the other travels south…

A: We use Pythagoras theorem

Q: A piece of wire of length 12 cm was cut into two pieces. The first was folded to form an equilateral…

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Q: One side of a right triangle is known to be 20 cm long and the opposite angle is measured as 30 °,…

A: a. let the hypotenuse of the triangle is h. so using the trigonometric ratio formula,…

Q: The length of the horizontal leg of a right triangle is increasing at a rate of 3 ft/sec, and the…

A: Given A right triangle  horizontal leg = 7ft vertical leg = 1ft

Q: A triangle has a base that is decreasing at a rate of 11 cm/s with the height being held constant.…

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Q: Suppose that a car accelerates at a rate of a(t) = t – 7 meters per second. Use the Fundamental…

A: ANSWER :

Q: 1. Two airplanes left airports which are 960 km apart and flew towards each other. One plane flew 32…

A: This is a question of distance and velocity. Based on the general formula of distance and velocity…

Q: 5. Find the slope of the tangent line to the graph of r = 2-2cos e when 0 = に一2

A: We have given equation of graph r=2-2cosθ  We have to find slope of the tangent line to the graph…

Q: As dry air moves upward, it expands and, in so doing, cools at a rate of about 1o C for each…

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Q: A triangle has a base that is decreasing at a rate of 4 cm/s with the height being held constant.…

A: Let b and h be the base and height of the trianglegiven rate at which base is decreasing, dbdt=4cm/s…

Q: Find the equations of the tangent line and the normal line to the graph of the equation at the…

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Q: An observer who is 3km from a launchpad watches a rocket that is rising vertically. At a certain…

A: Rate of change

Q: A car leaves an intersection traveling west. Its position 4 sec later is 21 ft from the…

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