A helium balloon is released at ground level directly under a light hanging 20 m above the ground. The balloon rises at 2 m/sec and is blown horizontally at a rate of 3 m/sec. How fast is the shadow of the balloon moving along the ground after 9 seconds? Please explain the steps

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 ladder 10 feet long is resting against a wall. If the bottom of the ladder is sliding away from…

A: Let the base be x  And the perpendicular be y and length of ladder=10 feet   dxdt=1 feet/sec…

Q: A ladder 10 meters long rests on horizontal ground and leans against a vertical wall. The foot of…

A:

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…

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

Q: a 17 foot tall ladder is leaning against a vertical wall and its base is on level ground. The top of…

A: We have to find at what rate is the top of the ladder sliding down the wall when it is 8 feet above…

Q: A 10​-foot ladder is leaning against a vertical wall​ when Jack begins pulling the foot of the…

A: The given data can be expressed in a right triangle as shown below.

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

A:

Q: The area of a circle is increasing at a rate of 80n square feet per second. How fast is the radius…

A: Since there are multiple questions present, according to company policy we will be answering only…

Q: A 25-foot ladder is leaning against a wall and the base begins to fall away from the wall. When the…

A: A 25-foot ladder is leaning against a wall and the base begins to fall away from the wall. When the…

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

A:

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: First I have draw the graph of given problem and then solved them using Pythagoras theorem. The foot…

Q: A 46 ft ladder is leaning against a vertical wall when Jack begins pulling the foot of the ladder…

A:

Q: A 6-ft-diameter cylindrical tank is filled with water to a height of 10 ft. It is drained such that…

A:

Q: How fast is the area of the circle of the ripples expanding at the instant that the radius of the…

A:

Q: A 17 feet ladder is leaning against a wall. if the bottom of the ladder is pulled along the ground…

A: Given:- A 17 feet ladder is leaning against a wall. if the bottom of the ladder is pulled along the…

Q: Two cars start moving from the same point. One travels south at 48 mi/h and the other travels west…

A:

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: The top of a 22 foot ladder, leaning against a vertical wall, is slipping down the wall at the rate…

A:

Q: A 10 ft ladder leans against a wall. If the top of the ladder slides down the wall at a rate of 2…

A:

Q: A 15-foot teddy bear is leaning against a shelf. The top hand of the teddy bear is sliding down the…

A: Let horizontal distance= x ft , vertical distance= y ft Relation between x and y is: Given that…

Q: A 13-foot ladder is resting against a wall and the bottom is initially 10 feet away from the wall.…

A:

Q: The base of a triangle begins to increase at a rate of 2 inches per minute while the height remains…

A: Consider the following variables, b=base of the triangleh=height of the triangleA=area of the…

Q: A weather balloon is rising vertically at the rate of 5 meters per second. An observer is standing…

A:

Q: A 10-meter ladder is leaning against the wall of a building. It begins to slide down the wall. When…

A: Let l denote the length of the ladder leaning against the wall of a building Let x denote the…

Q: A ladder 13 meters long rests on horizontal ground and leans against a vertical wall. The foot of…

A:

Q: A ladder 10 feet long rests along a vertical wall. If the bottom of the ladder slides away from the…

A: To find the rate of change of the ladder's top changes with wall

Q: A 13-ft ladder is leaning against a wall. If the top of the ladder slips down the wall at a rate of…

A:

Q: A 13 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 4 ft/s, how…

A: Let x be the distance between wall and bottom of ladder and y be the distance of top of ladder from…

Q: A ladder 20 feet long is leaning against the wall of a house. The base of the ladder is pulled away…

A:

Q: Two cars start moving from the same point. One travels south at 84 mi/h and the other travels west…

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 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: A ladder 20 feet long is leaning against a vertical wall. The base of the ladder is pulled away from…

A: First we formulate an equation involving two variables x and y by using  the Pythagorean theorem…

Q: A 15 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 4 ft/s, how…

A:

Q: A 14 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 2 ft/s, how…

A: Firstly we will draw the diagram for given information and then find the required as shown below

Q: A small balloon is released at a point 150 feet away from an observer who is on level ground. If the…

A: we have to find

Q: A 15 foot ladder is resting against a wall. The bottom is initially 10 feet away from the wall and…

A: Let: The length of the ladder be l. The top of the ladder be at a distance of y from the ground. The…

Q: A 15 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 4 ft/s, how…

A:

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

A:

Q: Two cars start moving from the same point. One travels south at 64 mi/h and the other travels west…

A:

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

A: According to the given question,

Q: A light sits on the ground 20 feet away from a very tall wall. A 5-foot-tall person walks toward the…

A:

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 pole that is 74 feet long is leaning against a brick wall. The bottom of the pole is getting…

A: This question is related to rate of change, we will solve it using given information.

Q: a 10-foot ladder is leaning against a vertical wall when Jack begins pulling the foot of the ladder…

A:

Q: A 25 -foot ladder is leaning against a vertical wall​ when Jack begins pulling the foot of the…

A:

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

A: