Water leaks from a tank at a rate of 2 + 5t liters/hour (L/h), where t is the number of hours after 7 am. How much water is lost between 9 and 11 am?

Q: A factory produces bicycles at a rate of 95 + 3t2 − t bicycles per week (t in weeks). How many…

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Q: # 3) Each side of a square is increasing at a rate of 6cm/s. At what rate is the area of the square…

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Q: The length of a rectangle is increasing at a rate of 4 cm/s and its width is increasing at a rate of…

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Q: A robotic machine fills containers with an acid solution at the rate of 90 + 2t milliliters (mL) per…

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Q: A vehicle purchased for $32500 depreciates at a constant rate of 4%. Determine the approximate value…

A: Solving

Q: An oral medication is absorbed into the bloodstream at the rate of 4e-0.04 milligrams per minute,…

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Q: A freshly brewed cup of coffee has temperature 95°C in a 20°C room. When its temperature is 63°C, it…

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Q: The volume V, in liters, of air in the lungs during a five-second respiratory cycle is approximated…

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Q: The length of a rectangle is increasing at a rate of 9 cm/s and its width is increasing at a rate of…

A: Explained below

Q: A robotic machine fills containers with an acid solution at the rate of 80 + 4t milliliters (mL) per…

A: Solution ) given function = 80 + 4t When t=0 or when no solution put into a container f(0) = 80 +…

Q: A stalk of corn grows from a height of 1 foot to a height of 7 feet in 2 months. What is its average…

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Q: An oral medication is absorbed into the bloodstream at the rate of 3e−0.04t milligrams per minute,…

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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 tank contains 7000 L of pure water. Brine that contains 35 g of salt per liter of water is pumped…

A:

Q: An object is moving so that it's velocity after t hours is v(t)=te^-t^2 mph. How far does it travel…

A: Hey the equation of velocity that you have written is v(t)=t·e-t2mph following is the solution to…

Q: Water flows from the bottom of a storage tank at a rate of r(t)=350– 5t litres per minute, where…

A: Given that the water flow from the bottom of a storage tank at a rate, rt=350-5t,  0≤t≤80

Q: At 9 p.m., a cylinder containing 240 liters of brine in which 12kg of salt is dissolved. Brine…

A: We will find how much salt in the cylinder is by 9.30

Q: The length of a rectangle is increasing at a rate of 3 cm/s and its width is increasing at a rate of…

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Q: A Sire starts in the levening. By midnight, 135 acres have already burned. From midnight on, the…

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Q: The volume V, in liters, of air in the lungs during a five-second respiratory cycle is approximated…

A: Given: The volume V, in liters, of air in the lungs during a five-seconds respiratory cycle is…

Q: The number of bacteria in a culture is growing at a rate of 2500e2t/5 per unit time t. Find the…

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Q: The length of a rectangle is increasing at a rate of 4 cm/s and its width is increasing at a rate of…

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Q: Water is pouring into a swimming pool. After t hours, there are 2t – vt gallons in the pool. At what…

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Q: 1. If the motor on a motorboat is started at t = 0 and the boat consumes gasoline at the rate of 6 –…

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Q: The length of a rectangle is increasing at a rate of 3 cm/s and its width is increasing at a rate of…

A: Consider the given situation, Let the length of the rectangle be ‘l’ and breadth be ‘b’.Area of…

Q: The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of…

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Q: A balloon has just been inflated. Calculate the instantaneous rate of change by which the area…

A: Introduction: A geometric shape with a sphere-like appearance. In three dimensions, the sphere is…

Q: An oral medication is absorbed into the bloodstream at the rate of  4e−0.04t  milligrams per…

A: Find the total amount of medication absorbed within the first 20 minutes

Q: Water flows from the bottom of a storage tank at a rate of r(t) = 400 - 8t liters per minute, where…

A: Let A(t) be the amount of water flows at time t. Rate of change of water flow,      r(t) =…

Q: Water flows from the bottom of a storage tank at a rate of r(t) = 400 – 8t liters per minute, where…

A: Application of integration

Q: The length of a rectangle is increasing at a rate of 6 cm/s and its width is increasing at a rate of…

A: Area = length x width A = L x W

Q: The length of a rectangle is increasing at a rate of 3 cm/s and its width is increasing at a rate of…

A: We know for rectangle, Area (A) = Length (l) × width (w) So, rate of change of area, (dA/dt) =…

Q: A rocket rising from the ground has a velocity of v(t)=2,000 te-t/180 ft/s, after t seconds. How far…

A: Given thatThe velocity of the rocket rising from the ground is

Q: The length of a rectangle is increasing at a rate of 7 cm/s and its width is increasing at a rate of…

A: Given, length of rectangle is increasing at a rate of  7 cm/s width of rectangle is increasing at a…

Q: A vehicle purchased for $29800 depreciates at a constant rate of 8%. Determine the approximate value…

A: cost price of vehicle=$29800 Constant rate of depreciates =8% per year We have to find the…

Q: on the moon, the acceleration of a free falling object is a(t) = -1.6 meters per second per second.…

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Q: A spherical balloon is deflated at a rate of 10 cm3 s-1. Find the rate change of the surface area…

A: given: A spherical balloon is deflated at a rate of 10 cm3s-1. we have to find the rate change of…

Q: Water is pumped out of a holding tank at a rate of 3-3e-0.5t liters/minute, where t is in minutes…

A:

Q: Water flows from the bottom of a storage tank at a rate of r(t) = 4(50 − t)e −0.05t liters per…

A: Given:  rt=450-te-0.05t    , 0≤t≤50    1 We need to find the amount of water that flows from the…

Q: A wound is healing in such a way that t days since Monday, the area of the wound has been decreasing…

A: topic - application of derivatives

Q: A robotic machine fills containers with an acid solution at the rate of 90 + 2t milliliters (mL) per…

A:

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

A:

Q: Water flows from the bottom of a storage tank at a rate of r(t) = √(400 − 4t) liters per minute,…

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Q: Water flows into an empty reservoir at a rate of 3000 + 20t L per hour(t is in hours). What is the…

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Q: The volume of a cube increases at the rate of 59m3/sec The rate at which the side of the cube…

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Q: 13-foot ladder is leaning against a wall. If we pull the ladder away from the wall at a rate of 4…

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Q: The volume of a cube is decreasing at a rate of 420 mm³ /s. What is the rate of change of the cube's…

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Q: The diameter of a spherical balloon that is being filled with air is increasing at the rate of 3…

A: the volume of the sphere is given by ..............(1)

Q: ng the shore and 60 meters from the sh mps into the water and swims from the second and swim at a…

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Q: The length of a rectangle is increasing at a rate of 5 cm/s and its width is increasing at a rate of…

A: We have to find

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.