As a bicyclist moving at 6m/s passes a point, a balloon 8m directly above him rises at the rate of 2m/s. How fast is the distance between the balloon and the cyclist chang ing after 3sec.?

Q: The sides of a square are increasing at the rate of 2 inches per minute. How fast is the Area…

A: Given The side of square is increasing at rate of 2inches per minute.  The area of a square with…

Q: A submarine started at the surface of the ocean and began diving -15 kilometers per minute towards…

A: Given: Diving speed of submarine, s = 15 km/min, and time of diving, t = 48 min

Q: A rabbit is traveling at a pace of 250 meters per hour. How fast is the rabbit  traveling in…

A: Given:    Distance = 250 meter per hour

Q: Due north, Seokjin is walking towards the most famous spot in a park at a rate of 1.3 meters per…

A:

Q: A ball is thrown straight down from the top of a 220-footbuildingwith an initial velocity of −22…

A: Use the position function, s(t)=-16t2+v0t+s0 and substitute v0 and s0 with -22 and 220,…

Q: . An airplane flying on a straight flight path will be exactly above a radar tracking station, which…

A:

Q: A small balloon is released at a point 60 feet away from an observer, who is on level ground. If the…

A:

Q: A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks from the spotlight…

A:

Q: A 5 foot girl is walking toward a 20- foot lamppost at the rate of 6 feet per second. How fast is…

A:

Q: The sides of an equilateral triangle are increasing at a rate of 12 inches per minute. At what rate…

A: Area of equilateral triangle A=/--3/4 a2 Here a = side of the equilateral triangle Differentiate A…

Q: A stone is dropped from the edge of a roof, and hits the ground with a velocity of -110 feet per…

A:

Q: Two buses are driving along parall freeways that are 5 miles apart, one heading east and the other…

A: We have to find rate at which the distance between the buses is changing when they are 13 miles…

Q: The top of a ladder 30 meters long leans against a vertical wall, and the lower end rests on a level…

A: Let the height of wall corresponding to the ladder lean at any instant be denoted as h. Let the…

Q: A baseball diamond is a square with side 90ft. A batter runs toward first base at 25 feet per…

A: Assume x = distance batter has run at time t andD = distance from second base to the batter attime…

Q: If the diagonal of a cube is increasing at a rate of 3 cubic inches per minute, how fast (in…

A: We will find the rate of increase of side of cube.

Q: A man 6 feet tall walks at a rate of 5 feet per second away from the light that is 15 feet above the…

A: Consider the given:

Q: A spotlight on the ground is shining on a wall 24m away. If a woman 2m tall walks from the spotlight…

A: Here we use the application of derivative

Q: A spotlight on the ground shines on a wall of a building 20 feet away. If a man 6ft tall walks from…

A:

Q: A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks from the spotlight…

A: Let, a be the spotlight and “ed” be the wall on which the spotlight shines.Therefore, “ad” is the…

Q: The length of a rectangle is increasing at the rate of 2 feet per second, while the width is…

A: Let length = x feet and width = y feet  Given that dx/dt= 2 and dy/dt= 1

Q: Each side of a square is increasing at a rate of 6 cm/s. At  what rate is the area of the square…

A:

Q: A lady 1.65 meters tall walks towards a lamp post 2.65 meters high at a speed of 1.5 m/s. How fast…

A: Given: Height of lady=1.65 m Height of lamp post=2.65 m Speed of lady=1.5 m/s To find: Shadow of…

Q: The base of a 13 foot ladder that is leaning against a wall begins to slide away from the wa When…

A: It is given that, length of the ladder x = 13 feet,  The distance between the foot of the ladder and…

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.

Q: Two children, who are 224 meters apart, startwalking toward each other at the same instant at rates…

A: Two children are 224 meters apart. They start walking toward each other at the same instant at rates…

Q: A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks from the spotlight…

A:

Q: A parallelogram of rectangular surfaces has a square base and its volume is always 108 cubic…

A: Given information

Q: A spotlight on the ground shines on a wall 10 m away. If a man 3 m tall walks from the spotlight…

A:

Q: Each side of a square is increasing at a rate of 3 cm/s. At what rate is the area of the square…

A: Let the length of side of square be' a '

Q: The sides of the square are increasing at a rate of 3 cm per second . When the sides are 5cm long ,…

A:

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…

A:

Q: A ladder 20 feet long rests against a vertical wall. If the bottom of the ladder slides away from…

A:

Q: An LRT train 6 meters above the ground crosses a street at a speed of 9 m/sec, at the instant that a…

A: Given: An LRT train 6 meters above the ground crosses a street at a speed of 9 m/sec, at the instant…

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 30-foot ladder is leaned up against a 2-story building with 8-foot floors. The bottom of the…

A: Consider the diagram below with marked information: Speed of change in base is 6 feet per second.

Q: A baseball diamond is a square with side 90 feet. A batter hits the ball and runs to first base with…

A: This question is based on application of  differentiation and Pythagoras theorem, We will solve it…

Q: The top of a 18 foot ladder, leaning against a vertical wall, is slipping down the wall at the rate…

A:

Q: A man 6 feet tall walks at a rate of 2 feet per second away from a light pole that is 16 feet high.…

A: From the figure substitute value of BE, AE, AD and AC in equation (1)

Q: A stone is dropped from the edge of a roof, and hits the ground with a velocity of -105 feet per…

A: Given,           A stone is dropped from the edge of a roof, and hits the ground with            a…

Q: A man, running 3 meters per second in an open field, runs east for 30 seconds, then turns north.  If…

A: Since the man ran 3m/s east for 90 sec so he is 90 m from the searchlight. Consider the diagram…

Q: An airplane travels 1950 km against the wind in 3 hours and 2340 km with the wind in the same amount…

A: Given Data: The distance covered by the aeroplane while travelling against the wind is: d1=1950 km…

Q: A man that is 6 feet tall walks towards a light that is 20 feet above the ground at a rate of 5 feet…

A: Given:      Height of man =6 feet     Height of light =20 feet     Rate of walk by man dxdt=5 ft/sec…

Q: A spacecraft is launched from the surface of a 6.7 x 1024 kg planet. If the spacecraft is moving at…

A:

Q: A 6-foot-tall man walks away at the rate of 4 ft/sec from the base of a street light 12 feet above…

A: dx/dt​=4.  given.    Distance of tip= y+x…

Q: The volume of a cube is increasing at the rate of 2 cubic inches per minute. How fast is the surface…

A:

Q: A 22-foot ladder is leaning against a building. If the bottom of the ladder is sliding along the…

A: Leader is leaning against wall at AC=22 ft. Distance of the ladder from the wall is x=15 ft. Let the…

Q: The base of a 20-foot ladder is sliding toward a wall at a rate of 1.5 feet per second. How fast is…

A: We solve the above problem.