A balloon is 20 m horizontally away from an observer. At an instant, the balloon rises vertically at a constant rate. When the balloon is 25m vertically above the ground, the distance between the observer and the balloon changes at 1.25 m /sec. How fast is the balloon rising vertically?

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A: We know that volume of a cube is given by V=a3 here V=volume of cube ,a=edge of cube Rate of change…

Q: A rocket, rising vertically, is tracked by a radar station that is on the ground 5 mi from the…

A: Given that: Rate of increase of distance from radar station = 2000 mi/hDistance between radar…

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: Let y be height of wall upto ladder and x be distance between bottom of wall and bottom of ladder…

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 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.

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A: Given: Since the height is decreasing.     To determine:

Q: A street light is fastened to the top of a 15-ft-high pole. If a 5-ft-tall women walks away from the…

A: In the figure,  AB=15 ft DE=5 ft BD=yDC=xdydt=3 ft/sec

Q: A ladder 10 ft long leans against a building. If the bottom of the ladder slides away from the…

A: Given A ladder 10 ft long leans against a building. If the bottom of the ladder slides away from the…

Q: A spherical drop of liquid evaporates at a rate proportional to its surface area. If a given drop…

A:

Q: The volume of an ice cube is decreasing at a rate of 1.5 cm³/sec. At what rate is a side of the ice…

A: option A is correct detailed solution with explanations given below

Q: A light is hung 15 ft above a straight horizontal path. if a man 6 ft tall is walking away from the…

A: Solution :x=distance from lights=length of shadowlet,height of light,D=15 ftheight of…

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…

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Q: A rope is attached to a boat at water level, and a man on the dock is pulling on the d) rope at the…

A: Draw a schematic diagram of given figure.

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

A:

Q: An airplane at an altitude of 35,000 feet begins descending at a rate of 2,000 feet per minute. How…

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Q: A ladder 20 ft. long leans against a vertical wall. If the top slides downward at the rate of 2…

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

A:

Q: 2) A 5-ft ladder, leaning against a wall, slips so that its base moves away from the wall at a rate…

A:

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

A: Consider the provided information, Let x and y be the traveled by the cars after time t. We can…

Q: A 17 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 3 ft/s, how…

A:

Q: A boat is pulled into a dock by a rope attached to it and passing through a pulley on the dock…

A: This problem is based on the application of differentiation.  First we have to write an equation in…

Q: A 10-ft ladder is leaning against a wall. If the top of the ladder slides down the wall at a rate of…

A: GivenA 10-ft ladder is leaning against wall .{ HereAB is wallAC is ladder }Let the height of the…

Q: A ladder 20 feet long is leaning against an embankment inclined 60 degrees to the horizontal. if the…

A: The ladder is leaning against an embankment inclined 60 degrees to the horizontal has length 20…

Q: The top of a ladder slides down a vertical wall at a rate of 1.5 m/s. At the moment when the bottom…

A:

Q: A kite, at a height of 60 ft. is moving horizontally at a rate of 5ft/sec. away from the boy who…

A: From the given information, draw a picture.

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A: According to Pythagorean theorem , square of the hypotenuse side is equal to sum of the square of…

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: The rate at which bacteria multiply is proportional to the instantaneous Number Present. If the…

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 rests against a vertical wall. If the bottom of the ladder slides away from…

A:

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

A: x2+y2=172=289Differentiate with respect to 't'2xdxdy+2ydydt=0   xdxdt+ydydt=0

Q: A searchlight, 1/2 mi from a straight shore, rotates at the rate of 2 rev/min. How fast is the spot…

A: Let the angle formed by line AB with the line AC is x  in the triangle ABC,   So, from the tangent…

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A:

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A: Let boy is at the point A, and when 100 ft cord is released the kite is at the point C, which is…

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 13 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 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 ladder 5 m long rests against a vertical wall. If the top of the ladder slides down the wall at a…

A:

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

A: Given:-  Ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away…

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

A:

Q: A ladder 20 meters long leans against a wall. If the bottom of the ladder is being pushed towards…

A: Given a ladder 20 meters long leans against a wall. If the bottom of the ladder is being pushed…

Q: Suppose that the hot-air balloon was descending at a rate of 12 ft/sec instead of ascending.…

A:

Q: A kite is flying at a fixed height of 30 ft. If 50 feet of string is out already from the spool,…

A: With the given details, we can draw a triangle . Here,  h is the vertical height at which kite is…

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: A ladder 13 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A: Assume length of ladder be l height be h base be b Given l=13 ft b=5ft dbdt=2ft/sec

Q: A man 7.00 ft tall approaches a street light 16.0 ft above the ground at the rate of 6.00 ​ft/s. How…

A: Given data: The height of the man is CD=7 ft. The height of the street light is AB=16 ft. The rate…

Exponential Growth Model

The relation that represents an exponential function is: