12. A small balloon is released at a point 150 feet from an observer, who is on level ground. If the balloon goes straight up at a rate of 8 feet per second, how fast is the distance from the observer to the balloon increasing when the balloon is 50 feet high?

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

A: Given  Speed of first car =48 mi/h towards south Speed of second car =20 mi/h towards west

Q: (8) A baseball diamond has the shape of a square with sides of 75 feet long. A player running from…

A:

Q: 21. A ladder 5 m long is leaning against a vertical wall. If a person pulls the bottom of the ladder…

A: Topic:- application of derivatives

Q: A balloon leaves the ground 18m from an observer and rises vertically at 1.25 m/s. How fast is the…

A: "Since you have asked multiple questions,we will solve first question for you. If you want any any…

Q: 8. The volume of a right circular cylinder is 60 cm³ and is increasing at 2 cm³/min at a time when…

A: Given:                                 Volume of a right circular cylinder V…

Q: 13. A plane flying horizontally at an altitude of 1 mi and a speed of 500 mi/h passes directly over…

A:

Q: 2) Water is pouring into an inverted cone at the rate of 8 cubic me- ters per minute. If the height…

A: Given that Height of cone h=12 m radius of its base r=6 m rate of pouring water into cone dVdt=8 m3

Q: 1. The sides of a square decrease in length at rate 2 m/sec. At what rate is the area of the square…

A:

Q: 3. A plane flying horizontally at an altitude of 1 mi and a speed of 500 mi/h passes directly over a…

A:

Q: 2. A fighter plane 2,000 km away is spotted by a gunner in the ground. If it maintains its altitude…

A:

Q: 2. A ladder 10 meters long is leaning against a wall. If the bottom of the ladder is being pushed…

A: Given, A ladder 10 m long is leaning against a wall. Bottom of the ladder is being pushed…

Q: (4) If the population of bacteria in a certain region triples in 50 days. In how many days will be…

A: Assuming the rate of increase is proportional to the number of inhabitants. To find- No. of days in…

Q: 3. A 20 ft ladder is leaning against a wall and begins to slide. How fast is the top of the ladder…

A: A 20ft ladder is leaning against a wall and begins slide.The ladder is 12ft away from the wall and…

Q: 1. A spherical hot air ballooon is bieng inflated at a rate of 1.5 cubic feet per second. a) Find…

A: Given that a spherical hot air balloon is being inflated at a rate of 1.5 cubic feet per second.…

Q: 3. A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a…

A: As per our guideline we are supposed to be answer only one question you can repost other question in…

Q: 9. A man 5 n tall is walking toward a building at the rate of 3 A/sec. If there is a light on the…

A:

Q: Given the question: A tank shaped like a right circular inverted cone with radius 5 meters and…

A:

Q: 3 Two cars start moving from the same point. One travels south at 24 mi/h and the other travels west…

A: Given the data:

Q: A cubic block of ice whose side is 2 inches long is melting at a rate of 1 in^3 per minute. How fast…

A:

Q: wo cars start moving from the same point. One travels south at 16 mi/h and the other travels west at…

A:

Q: 3. A man 6 feet tall walks at a rate of 5 feet per second away from a light that is 15 feet above…

A:

Q: 13. A 10-meter ladder is leaning against a vertical wall with its foot on the same horizontal plane…

A:

Q: 2. A man walks across a bridge at the rate of 5 ft/s as a boat passes directly beneath him at10…

A: From the given data , Man walks across a bridge in one second AC=5 feet and boat passes in one…

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

A:

Q: Two cars start moving from the same point. One travels south at 60 mi /h and the other travels west…

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: 1. A conical paper cup 4 inches across the top and 4 inches deep is full of water. Since there is a…

A: We have been given the cone as in the figure  By the given figure we get r = 2 in. and h = 4 in. We…

Q: 2. Suppose that the bottom of a conical shaped tank of water has been ruptured. At the instant when…

A:

Q: 2. Suppose that a bacteria population is dying off at a rate of 30% per day. How much of the…

A:

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: 17. If the radius of a sphere is increasing at the constant rate of 3 inches per second, how fast is…

A: Given: The radius of the sphere is increasing at the constant rate of 3 inches per second. To find:…

Q: 3) A camera is located on the ground 3000 ft from the spot where a rocket takes off. If the rocket…

A:

Q: 20. A 13 foot ladder leans against a vertical wall. When the ladder is pulled away from the wall at…

A:

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

A:

Q: If the radius of a right circular cylinder is increasing at a rate of 1 inch per minute, and the…

A:

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

A:

Q: 1. A spherical balloon is expanding. If the radius is increasing at the rate of 2 inches per minute,…

A: The given question can be solved as shown in step2.

Q: Ifthe population of bacteria in a certain region triples in 15 days. In how many days will be four…

A: given                                                 dAdt=AK Where, A is population of bacteria. K…

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

A: Given- A kite is flying at a height of 30 feet, if 50 feet of string is out already from the spool…

Q: 44. The dimensions of a rectangular plate are changing so that the plate maintain its rectangular…

A: Let the length of Rectangle =x Let the width of Rectangle =y since,  Area = (length)×(width)…

Q: A circle is inside a square. The radius of the circle is decreasing at a rate of 5 meters per…

A: Let r be the radius of circle ands be the length of the side of squareGiven: drdt=-5 and ds/dt=5Let…

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

A:

Q: 5) If the radius of a right circular cylinder is increasing at a rate of 1 inch per minute, and the…

A: The volume of cylinder is given by the formula V=πr2h. The given values are as follows: r=40 inches,…

Q: 6) A light is 20 meters above a straight horizontal path. If a man 1.65 meters tall is walking away…

A: Given: Height of light is 20 meter. Height of man is 1.65 meters. Rate with which man is walking is…

Q: A rectangle is growing in such a way that when its length is 5 ft and its width is 2 ft, the length…

A:

Q: OH NO!! CERTAIN DOOM: Car A is traveling west at 50 mi/hr and car B is traveling north at 60 mi/hr.…

A:

Q: 1. A tank is shaped like an upside-down pyramid, with a base of 4 meters and a height of 12 meters.…

A:

Q: 4. A trough filled with liquid is 2 m long and has a cross section of an isosceles trapezoid 30 cm…

A: Given: 4) Question is wrong (Some values are missed) 5) dxdt=10 ft/sec, h=100 ft, and l=125 ft