6. A spherical balloon is inflated with gas at the rate of 400 cubic centimeters per minute. How fast is the radius of the balloon increasing at the instant when the radius is 6 centimeters? Leave your answer in terms of T, and make sure to include units with your answer.

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: 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: 4. A baseball diamond is a square 90 ft on a side. A player runs from first base to second base at…

A:

Q: 8. The radius of a sphere is increasing at a rate 4mm/s. How fast is the volume increasing when the…

A: Given that the radius of sphere is increasing at a rate 4mm/s. drdt=4mm/s To find the rate at which…

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 cylindrical tube expands as its radius r and height h increase at the rate of 2 in/min and 4…

A: Basic product rule of differentiation is used.

Q: 25. A 10-foot ladder is placed against a vertical wall. Suppose that the bottom of the ladder slides…

A: Given :-  dx/dt= 3feet/sec  Ladder height= 10feet  Find rate at which ladder is sliding down from…

Q: 7. A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base…

A:

Q: 2. A rope is attached to a boat at water level, and a man on the dock is pulling on the rope at the…

A: Draw the given situation at any time t then using Pythagoras theorem and application of derivative.…

Q: A potter forms a piece of clay into a cylinder. As he rolls it, the length, L, of the cylinder…

A: Differentiate volume wrt t

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: The edge of an expanding cube is changing at the rate of 2.3 cm/s at the instant its edge is 18.3 cm…

A:

Q: 2. A boat is being pulled into a dock by a rope attached to it and passing through a pulley on the…

A:

Q: 8. The spherical balloon is inflating at the rate of 12,000 cm³/min. How fast is its radius changing…

A: Let  V be the volume of a spherical balloon with radius r at any time tGiven: dVdt=12,000 cm3/min…

Q: 1) A baseball diamond is a square whose sides are 90ft long. Suppose that a player running from…

A: Given : Side of Baseball diamond square =90 ft. Drawing the diagram of the whole situation,

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: A man of height  1.9  meters walks away from a 5-meter lamppost at a speed of  2.1  m/s. Find the…

A: Let distance of the man from the pole=x   Let the length of the shadow =y…

Q: 2. A 15 foot ladder is resting against the wall. The bottom is initially 10 feet away from the wall…

A:

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

A:

Q: A spherical balloon is inflated so that its volume is increasing at the rate of 2.7 ft/minl. How…

A:

Q: A man of height 1.8 m walks away from a 5-m lamppost at the speed of 1.2 m/s. Find the rate at which…

A:

Q: 6) A 13 ft ladder is leaning against a wall. If the top of the ladder slips down the wall at a rate…

A:

Q: 2. a) A ladder 10 ft long leans against a vertical wall. If the top of the ladder slides down the…

A: Given:-  a) A ladder 10 ft long leans against a vertical wall. If the top of the ladder slides down…

Q: 2. A street lamp is 5m tall and located 6m from a brick wall. A person who is 2m tall walks away…

A:

Q: #13 The radius of a sphecical blloon is increasing at the cate of 3inches per second, How fast is…

A:

Q: An ice cube that is 3 cm on each side is melting at a rate of 2 cm3 per min. How fast is the length…

A: Given: Length of cube L=3cm Rate of melting =-2cm3

Q: 7. A conical pile is formed by pouring sand at a rate of 30 cm/s. When its base diameter and…

A:

Q: 1. Sand being dumped from a funnel forms a conical pile whose height is always one￾third the…

A:

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: The area of a rectangle remains 30 cm2. One side of the rectangle is expanding at a rate of 1 cm/s.…

A:

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

A:

Q: 2) A person is standing 350 feet away from a model rocket that is fired straight up into the air at…

A:

Q: Suppose the length of the diagonal of a square is increasing at the rate of 2 inches per second. At…

A:

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

A:

Q: 6. The radius of a sphere is increasing at a rate of 4 mm/s. How fast is the volume increasing when…

A:

Q: A man of height 1.9 meters walks away from a 5-meter lamppost at a speed of 1.1 m/s. Find the rate…

A: Given Data: The height of the man is: h=1.9 m The height of the lamppost is: H=5 m The increasing…

Q: An ice cube that is 3 cm on each side is melting at the rate of 2 cubic cm per min. How fast is the…

A:

Q: D. Supposes a circle is expanding in such a way that its radius is growing at a constant rate of 3…

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

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: Two parallel sides of a rectangle are lengthened at a rate of 3 cm/sec, while the other sides are…

A:

Q: 1. How fast is the water level rising in a rectangular fish tank whose base is 20 ft² if the tank is…

A: Give: Area of base is A=20 ft2 Rate with which tank is filling dVdt=0.5 ft3/min. Volume of a…

Q: 2. A ladder 13 ft long rests against a vertical wall. If the bottom of the ladder slides away from…

A:

Q: The radius of a sphere, initially zero, increases at the rate of 6 ft per second. How fast the…

A: Given ,The radius of a sphere , initially zero , increases at the rate of 6 per second.The volume is…

Q: A potter forms a piece of clay into a cylinder. As he rolls it, the length, L, of the cylinder…

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: The radius of an air bubble is increasing at the rate of 1/2 cm/s.At what rate is the volume of the…

A:

Q: Consider that sugar dissolves in water at a rate proportional to the amount still un-dissolved.…

A: 50kgs of sugar is present and at 5-hour mark there's only 20kg of sugar is left.

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