(a) Water flows from a storage tank at a rate of 900 – 6t liters per minute. Find the amount of water that flows out of the tank during the first 16 minutes?

Q: A container initially contains 15 L of water in which there is 30 g of salt dissolved. A solution…

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Q: Consider a tank with volume 100 liters containing a salt solution. Suppose a solution with 2…

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Q: A tank contains 1000 liters of brine with 15 kg of dissolved salt. Pure water enters the tank at a…

A: Let x represents the amount of salt after t minutes. Given that, the initial amount of salt is 15…

Q: A submarine started at the surface of the ocean and began diving -15 kilometers per minute towards…

A: Given: Diving speed of submarine, s = 15 km/min, and time of diving, t = 48 min

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 tank initially contains 200 L of fresh water. Brine containing 2.5 N/L of dissolved salt runs into…

A: Let "s" represents the quantity of salt in the tank. dSdt=(8×2.5)-8S200dSdt+0.04S=20   and S(0)=0…

Q: 6. A spherical balloon is being inflated so that its diameter is increasing at a rate of 2 cm/min.…

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Q: A tank contains 1000L of brine with 16kg of dissolved salt. Pure water enters the tank at a rate of…

A: Given: A tank contains 1000L of brine with 16kg of dissolved salt. The pure water enters the tank at…

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: 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: 18. A kite string is paid out at a constant rate of 3 ft/s. If the wind carries the kite…

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

A: Since you have asked multiple questions in a single request, we will be answering only the 1st…

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

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Q: A 20 m tank is full of brine with 40 kg of dissolved salt. Pure water enters the tank at a rate of…

A: In this question, we find the amount of solt when the takl half full. given that  Initial amount of…

Q: Water is leaking from a 2 foot tall rectangular tank at 0.1 cubic foot per hour. Suppose that the…

A: let the height of tank be "h"Volume is given by VdVdt=0.1 cu. ft/hrh=2 ftV= 10 cu. ftdhdt=?

Q: A tank contains 100 gal of brine made by dissolving 80 lb of salt in water. Pure water runs into the…

A: Many real-life problems can be modeled using differential equations. This is one of the significant…

Q: 9. When a particular plate of metal is heated in an oven, its radius increases at the rate of…

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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: a fisherman on a wharf 1.2 meters above the level of still water is pulling a rope tied to a boat at…

A: topic - application of derivatives

Q: a) When a gold plate is heated in order to melt it, initially its area increases at the rate of 67…

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Q: 21. The radius of a spherical balloon is increasing at the rate of 3 centimeters per minute. How…

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

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Q: 5. A spherical balloon is inflated so that its volume is increasing at the rate of 2 m'/min. At what…

A: Let r be the radius of the balloon and D be the diameter.

Q: Water is flowing into a cylindrical tank at the rate of 2 m^3/min. If the radius of the tank is 0.5…

A: Water is flowing into a cylindrical tank at the rate of 2 m3/min.If the radius of the tank is 0.5 m,…

Q: A tank contains 200 liters of fresh water. Brine containing 2 kilograms per liter of salt enters the…

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

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

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

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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: stone dropped into a pond sends out a circular ripple whose radius increases at a constant rate of…

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Q: A tank contains 100 L of water. A salt solution containing 2 kg of salt per liter flow in at the…

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

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Q: The surface area of a cube is increasing at a rate of 15 square meters per hour. At a certain…

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Q: A swarm of bees is spreading from an original region of 1 square mile. The region the swarm occupies…

A: Given that the original region of 1 square mile.  After 1 year area will be 2(1)=2=21 square miles…

Q: 4. Water flowing in a conical tank 20 ft deep and 10 ft across the top at the rate of 15 cu. ft/…

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Q: A ladder 12 meters long rests against a wall. The foot of the ladder is pulled away from the wall at…

A: According to the question we have the diagram

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: The altitude of a triangle is increasing at a rate of 1 cmminwhile the area of the triangle is…

A: Givendhdt=1cm/mindAdt=2cm2/minA=100cm2h=10cm

Q: A tank initially contains 50 gal. of fresh water. Brine (water in which a certain number of pounds…

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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 worker on a scaffolding 85 feet above the ground needs to lift a 115 pound bucket of cement from…

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Q: 23.) A spherical balloon is inflated with gas at the rate of 800 cubic centimeters per minute. How…

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Q: An apple pie with an initial temperature of 170 -C is removed from the oven and left to cool in a…

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Q: A tank contains 200 liters of fresh water. Brine containing 2.5 N/L of dissolved salt runs into the…

A:

Q: 2. Air is leaking from a spherical-shaped advertising balloon at the rate of 26 cubic feet per…

A: Let r be the radius and v be the volume of balloon, Given dvdt=26 cf/minuteswe know…

Q: A 30 m³ tank is full of brine with 40 kg of dissolved salt. Pure water enters the tank at a rate of…

A: Volume of the tank is 30 m3 The tank is full of brine with 40 kg of dissolved salt. Pure water…

Q: Water flows at the rate of 2000 cubic cm per second into a vertical cylindrical tank 120 cm in…

A: Let height of cylindrical tank is "h". Diameter is 120 cm. So, Radius would be r=1202=60 cm Volume…