2. A 16-foot ladder rests against a vertical wall. The bottom of the ladder begins sliding at a rate of 3 ft/sec. Find the rate at which the top of the ladder is sliding down the wall at time t = 2 seconds if the bottom of the ladder began 5 feet away from the wall.

Q: 3. A light is hung 15 ft above a straight horizontal path. If a man 2 ft tall is walking away from…

A:

Q: 2. Sand is being dropped at the rate of 10ft.3/min into a conical pile. If the height of the pile is…

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: 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: 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: The top of a ladder slides down a vertical wall at a rate of 0.375 m/s. At the moment when the…

A: Let the ladder is k meters. (k=constant) Let the distance of the bottom = x m and distance of the…

Q: 2. A 13-foot ladder is leaning against a vertical wall when Jack begins pulling the foot of the…

A:

Q: 11. If a snowball melts so that its surface area decreases at a rate of 1 cm/min, find the rate at…

A:

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:

Q: The sides of a square increase in length at a rate of 3 m/sec. a. At what rate is the area of the…

A: lets the size of square is l so the rate of change of length = dl/dt = 3 m/sec area of square = l2…

Q: The sides of a square increase in length at a rate of 5 m/sec. a. At what rate is the area of the…

A: We apply chain rule of differentiation. Area of the square is: A= s2.  Where s is the side of 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 balloon is rising vertically over a point A on the ground at the rate of 15 ft/sec. A point B on…

A: Let the distance of the balloon from point B be denoted as p. The balloon, points A and B form a…

Q: 11. The top of a ladder slides down a vertical wall at a rate of 0.15 m/s. At the moment when 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: A car is slowing down at the rate 0.8 ft/sec². How far will the car move before it stops if its…

A:

Q: A cone-shaped tank of water is leaking water at a constant rate of 3 m³/hour. If the base radius of…

A: Using volume  of cone and applications of derivative idea we solve this

Q: 1. If the radius of a spherical balloon is increasing at the rate of 3 cm/s, which of the following…

A: We are only allowed to solve one question at a time so we will answer only the first question.…

Q: A light is on the top of a 12 ft tall pole and a 5 ft 6 inches tall person is walking away from the…

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: A vertical cylinder is leaking water at a rate of 8m^3/sec. if the cylinder has a height of 10m and…

A: In a vertical cylinder water is leaking at a rate of 8 m3/sec. dVdt=8 Height of the cylinder is 10…

Q: A perfectly spherical balloon is losing volume at a rate of 3 in3 per sec. How fast is the balloon’s…

A:

Q: A    26    foot    ladder    is    sliding    down    a    vertical    wall.        The    base…

A: This question can be solved using the concept of rate of change of physical quantities.

Q: A spherical balloon is inflated at a rate of 10 cm3>min. At what rate is the diameter of the…

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: udent is walk

A: Here it is given that,  A student is walking towards the foot of a flagpole 20 meters high at the…

Q: The sides of a square increase in length at a rate of 3 m/sec. a. At what rate is the area of the…

A: let the side of the square is a meter, and the area is A given that da/dt=3m/sec a. a=15m area of…

Q: A 50 feet ladder is leaning against a wall of a building. Suppose the base of the ladder slides away…

A:

Q: A weather balloon is rising vertically at the rate of 2 m/sec. An observer is standing on the ground…

A: The diagram of the given question will be as follows Given: dydt=2 m/s To find: dxdt

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:

Q: 4. A street light is at the top of a 16 ft pole. A 6 ft tall woman walks along a straight path away…

A:

Q: A funnel in the shape of an inverted cone is 30 cm deep and has a diameter across the top of 20 cm.…

A: Geometry

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

A:

Q: 14. If a snowball melts so that its surface area decreases at a rate of 1 cm2/min, find the rate at…

A: To find the rate

Q: A triangle has a base that is decreasing at a rate of 11 cm/s with the height being held constant.…

A:

Q: If the base h of a triangle is increasing at a rate of 3 inches per minute while its height h is…

A: Area of a triangle of base b and height h is given as, A=12bh The derivative of area with respect to…

Q: a. If a snowball melts so that its surface area decreases at a rate of 1 cm²/min, find the rate at…

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: If a spherical balloon is being filled with air at a constant rate of 2 cm³/s, at what rate is the…

A: Let r be the radius of the balloon in cm and V be the volume in cm3. The variable t stands for time…

Q: 1. A man on a wharf, whose hand is 8.2 m above the level of the water surface is pulling a rope tied…

A:

Q: against

A:

Q: 4. Water is running out of a conical tank 3 m across the top and 4 m deep at the rate of 2 m3 /min.…

A: given  h = 4 m  (Note: measurement of h is always taken from bottom) r = (3 ÷ 2 ) = 1.5 m dVdt = 2…

Q: A 15-ft ladder is leaning against a wall. If the bottom is pulled away from the wall at a rate of 3…

A:

Q: The top of a ladder slides down a vertical wall at a rate of 0.125m/s. At the moment when the bottom…

A:

Q: The top of a ladder slides down a vertical wall at a rate of 0.375 m/s. At the moment when the…

A: form a triangle with given information : let BC = x   dxdt=0.5 AB = y  dydt=-0.375  AC = z  dzdt=0…

Q: A weather balloon is rising vertically at the rate of 10ft/s. An observer is standing on the ground…

A: Given: -

Q: The top ladder slides down a vertical wall at a rate of 0.15m/S. At what moment when the bottom of…

A: Given that the top ladder slides down a vertical wall at a rate of 0.15m/s. the bottom of the ladder…

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: Given: The top of a ladder slides down a vertical wall at a rate of 0.675 m/s. At the moment when…

Q: 1 A 5 m ladder is leaning against a wall of a house. The bottom of the ladder is pulled away from…

A: Let the bottom of the ladder is x meters away from the wall and the top of ladder is at distance y…