As an object cools, its rate of cooling slows. Explain how this follows from Newton’s Law of Cooling.

Q: A body cools at the rate of 0.5°C per second when it is 500°C above the surroundings. What is the…

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Q: A certain radioactive material is known to decay at a rate proportional to the amount present. If…

A: given,     radioactive material is decay at a rate proportional to the amount present .initially 50…

Q: A balloon leaves the ground 30 m from an observer. If it rises at the rate of 2 m/s, how fast is it…

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Q: All edges of a cube are expanding at a rate of 3 centimeters per second. (a) How fast is the surface…

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Q: A freshly brewed cup of coffee has temperature 95°C in a  20°C room. When its temperature is 70°C,…

A: Given that, Initial temperature of coffee is T0=95°C, surrounding temperature is Ts=20°C. Also,…

Q: The mass of caffeine in the bloodstream decreased rapidly at first, and then more slowly.

A: Given statement: The mass of caffeine in the bloodstream decreased rapidly at first, and then more…

Q: A fighter plane 2000 km away is spotted by a gunner in the ground. If it maintains its altitude at…

A: Pythagoras theorem: In a right angle triangle, Hypotenuse2=Base2+Perpendicular2 Differentiation…

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: A golfer takes a swing from a hill twenty feet above the cup with an initial upwards velocity of 32…

A: It is given that, initial upward velocity from the hill is, v=32 feet per second, angle of swing…

Q: 4. What constant acceleration is required to increase the speed of a car from 30 mi/h to 50 mi/h in…

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Q: A freshly brewed cup of coffee has temperature 95 ° C in a 20 ° C When its temperature is 70 ° C it…

A: The temperature of a freshly brewed coffee is 95°C and the temperature of the room is 20°C. When the…

Q: On a certain planet's moon, the acceleration due to gravity is 2.6 m/sec. If a rock is dropped into…

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Q: Initially 100 milligrams of a radioactive substance were present. After 6 hours the mass had…

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Q: If we know the rate of growth of a patch of moss, how can we calculate the area the moss covers?

A: The rate of growth of a patch of moss is modeled by a complex function A't, where t is measured in…

Q: A metallic ball with a diameter of 12 cm is covered with a layer of ice, so if the ice begins to…

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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: After 2 days, 10 grams of a radioactive substance is present. Three days later, 5 grams is present.…

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Q: A train moving with constant acceleration travels (24 m) during the (10th)s of its motion and (18 m)…

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Q: A certain radioactive material is known to decay at a rate proportional to the present amount. If…

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Q: One airplane is approaching an airport from the north at 203 km/hr. a second airplane approaches…

A: Let in the below figure P represents the airport, Q represents the southbound plane and R represents…

Q: A certain bacteria culture grows at a rate proportional to its size. If 10,000 bacteria grow at the…

A: Given: A certain bacteria culture grows at a rate proportional to its size.

Q: How fast is the circumference of a circle changing if the radius is changing at the rate of 3 mm/s?

A: Solution

Q: A rocket lifts off the surface of Earth with a constant acceleration of 20 m/sec2. How fast will the…

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Q: Define Constant acceleration ?

A: The acceleration of a particle or a body is defined as the rate of change of the particle or the…

Q: An object is thrown vertically upward from a point 32 feet above the ground with an initial velocity…

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Q: A weather balloon is rising vertically at the rate of 5 meters per second. An observer is standing…

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Q: All edges of a cube are expanding at a rate of 2 centimeters per second. (a) How fast is the surface…

A: All edges of a cube are expanding at a rate of 2 centimeters per second.

Q: Assume that a snowball melts so that its volume decreases at a rate proportional to its surface…

A: Let V denote the volume and A denote surface area. Rate of melting is proportional to its surface…

Q: A roast turkey is taken from an oven when Its temperature has reached 185F and Is placed on a table…

A: Follow step 2.

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: After 2 days, 10g of radioactive chemical is present. Three days later, 5g is present. How much of…

A: Given:      After  2 days, 10g of radioactive chemical is present. Three days later5 g chemical is…

Q: A population of yeast cells can double in 6 hours. Assume an initial population of 4,000 cells. What…

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Q: A mold grows at a rate that is proportional to the amount present. Initially, there is 5 oz of this…

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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: A water balloon is launched from a platform 96 feet above the ground, with an initial velocity of…

A: The location of the water balloon when hit the ground is (120, 36, 0).

Q: A certain radioactive material is known to decay at a rate proportional to the amount present.…

A: Given a certain radioactive material is known to decay at a rate proportional to the amount present.…

Q: A body cools at the rate of 0.5°C per second when it is 500°C above the surroundings. what is the…

A:

Q: What constant acceleration is required to increase the speedof a car from 30 mih to 50 mih in 5 s?

A: Given: u=30 mihour, v=50 mihour, t=5 second for finding acceleration, first we convert given…

Q: How are the rate constant and the doubling time related?

A: Explanation: The exponential growth function is y(t)=y0ekt where k  is the positive constant rate…

Q: At what rate is the height of the water rising at the instant the tank is half full?

A: To find the rate at water rising

Q: Initially 100 milligrams of a radioactive substance was present. After 6 hours the mass had…

A:

Q: A computerized spin balance machine rotates a 25-inch-diameter tire at 480 revolutions per minute.…

A:

Q: The kinetic energy of an object varies jointly with its mass and the square of its velocity. What…

A: let: Kinetic energy be k Mass be M. Velocity be V The kinetic energy is directly proportional to…

Q: What is the difference between an object with constant acceleration and an object with constant…

A: Solution: The objective is to determine the difference between an object with constant acceleration…

Q: A water balloon is launched from a platform 96 feet above the ground, with an initial velocity of…

A:

Q: What constant acceleration will bring an automobile traveling 60 mph to rest in 160 feet?

A: Explained below

Q: All edges of a cube are expanding at a rate of 6 centimeters per second. (a) How fast is the surface…

A:

Q: A certain bacteria culture is observed to double its amount after two hours it was initially…

A: Let say population is P. So population at time 't' is given by P(t). Assume initial population is P0…