22) A conical reservoir is losing water at the rate of 12 cubic feet per minute. If the radius is % the height, how fast is the height changing at the instant the reservoir is 50 feet deep?

Q: 7. A triangle with a base of 20 inches has a height that is decreasing at a rate of 3 inches per…

A:

Q: 3. The radius of a spherical balloon is increasing at the rate of 2 cm per minute. How fast is the…

A:

Q: Water is poured into a conical paper cup at the rate of 3/2 in/sec (similar to Example 4 in Section…

A: I will use the formula V=13πr2h and differentiation method to solve this problem.

Q: Suppose you have a square that is 300 ft on each side.  Also suppose the length is increasing at the…

A: Given that a square that is 300 ft on each side and the length is increasing at the rate 3ft/sec,…

Q: 1. Water is flowing at the rate of 2 m3/min into a tank in the form of an inverted cone having an…

A: It is given that the cone has altitude 16 m and radius 4 m. That is, hcone=16,rcone=4. Let r and h…

Q: a)How quickly is the water leaving the barrel over the first two seconds? b)Will the water drain…

A: The solution is given below in the next step:

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: A water trough is 10 m long and has a cross-section in the shape of an isosceles trapezoid that is…

A: Given: The trough is being filled with water at the rate of 0.3 m3/min, dVdt=0.3 m3/min

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: if water rises 1/2 inch in 3/7 of a week in a water reservoir, at what rate is the water rising per…

A:

Q: A conical water tank 6 meters in altitude and 3 meters across the top is being emptied at the rate…

A: Using the chain rule :

Q: Suppose the water in Example 4 is poured in at the rate of cubic inches per second. How fast is the…

A: Below is the solutions:-

Q: 1. Water is poured into a conical tank 6 m across the top and 8m deep at the rate of 10 How fast is…

A: To find: The rate of water level rising when water in the tank is 5 m deep. Formula used: The volume…

Q: 17. The base of a triangle is increasing at a rate of 2in/min. If the altitude is always twice the…

A:

Q: An equilateral triangle initially has sides of length 20 ft when each vertex moves toward the…

A: We have given an equilateral triangle intially has sides of length 20ft and each vertex moves toward…

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 trough whose cross section is an equilateral triangle is 6 m long and 2 m wide across the top. If…

A: Solve by diagram and using formulas of equilateral triangle

Q: An inverted conical tank with a height of 6 feet and a diameter of 4 feet that was filled with water…

A: It is given that, the height and diameter of the conical tank is 6 feet and 4 feet, respectively.Let…

Q: 17. A man of height 1.8 m walks away from a 5-m lamppost at a speed of 1.2 m/s (Figure 9). Find the…

A:

Q: 2. A tank with a shape of a cone is 20 feet deep and has a diameter of 10 feet at the top. Water is…

A: Given; Diameter = 10 feet  Height = 20 feet

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: Water is discharged from an inverted cone-shaped tank with a height of 12 meters and a radius of 6…

A: Given: The height of the inverted cone-shaped tank, h = 12m. Also, its radius, r = 6m. From the…

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: If the sides of an equilateral triangle are increasing at a rate of 6 m/min. How fast is the area of…

A:

Q: 7. The top of a ladder slides down a vertical wall at a rate of 0.15 m/s. At the moment when the…

A: Given data A ladder slides a vertical wall at rate of 0.15 m/s  find the length of ladder = ?

Q: 3. The radius of a cylinder is increasing at a rate of 4cm/sec. The surface area remains constant at…

A: Given

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: An isosceles triangular water trough is 5 meters long, 3 meters across the top, and 2 meters deep is…

A: Where we see the application of derivatives to solve the given problem

Q: A conical reservoir is losing water at the rate of 12 cubic feet per minute. If the radius is % the…

A: Let the height of the conical reservoir be h. Then the radius will be = h/4 Therefore we get the…

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

A:

Q: A mold grows at a rate that is proportional to the amount present. Initially there is 6oz of this…

A: The amount of mold at time 0 is m0. The amount of mold present after t hours is m. The rate of…

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: A piece of wire of length 12 cm was cut into two pieces. The first was folded to form an equilateral…

A:

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

A:

Q: A conical water tank 7 meters in altitude and 3 meters across the top is being emptied at the rate…

A: From the given problem the representative diagram is shown as below: Let the radius of the cone is…

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: If the area A = s of an expanding square is increasing at the constant rate of 8 square inches

A:

Q: (5) A conical water tank with vertex down has a radius of 10 ft at the top and is 24 ft high. If…

A: we know that, the volume of conical shape, V = 1/3πr^2h  so after defernciate this, we will solve…

Q: 2. The radius of a sphere is decreasing slowly at the rate of 2 cm/week. How fast is the volume…

A: Consider the given information. The volume of the sphere is defined as, V=43πr3

Q: The volume of a cube is increasing at the rate of 1200 cm³ / min at the instant its edges are 20 cm…

A:

Q: 1. A 50-cm high trough filled with liquid is 200 cm long and has a cross-section of an isosceles…

A: As per our guidelines we are supposed to answer only one question. I am solving the first one Kindly…

Q: 5. A conical tank (with vertex down) is 20 feet across the top and 24 feet deep. If water is flowing…

A: A conical tank is 20 feet across the top and 24 feet deep. If water is flowing into the tank at a…

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

A:

Q: Water is poured into a conical paper cup at the rate of 3/2 in/sec (similar to Example 4 in Section…

A: Let the volume of conical paper cup be V in³, radius be r in, height be h in  Given dV/dt=(3/2)…

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: 5. The area of an equilateral triangle is decreasing at a rate of 4 sq. cm. per minute. Find the…

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

Q: 2. The diagonal of a square increases at the rate of 3 m/sec. How fast is the area changing when the…

A: Let the length of diagonal be y. so that, Now, Length of the side of a square be x. Using the…