A substance cools in moving air at a rate proportional to the difference between the temperature of the substance and that of the air. If the substance cools from 100°C to 60°C in 22 minutes and the temperature of the air is 20°C, find the time required when the temperature of the substance is 40°C. O 66 minutes O 44 minutes -44 minutes 88 minutes

Q: Two cars start moving from the same point. One travels south at 60mi/h and the other travels west at…

A:

Q: Each side of square is increasing at rate of 4 cm/s. At what rate is the area of the square…

A:

Q: The width of a rectangle is increasing at a rate of 2 cm/sec, while the length increases at 3…

A: Let's find rate of area increasing when W=4cm and l=10cm.

Q: A 13-foot ladder is placed against a wall. If the top of the ladder is sliding down the wall at 3…

A:

Q: The value of a computer t years after purchase is v(t) = 3000 e -0.35t At what rate is the…

A: Please see the answer in step 2

Q: Two airplanes are flying in the air at the same height: airplane A is flying east at 290 mi h and…

A: Given that:                      Speed of plain A, vA=290 mi/hSpeed of plain B, vB=290 mi/hDistance…

Q: The altitude of a triangle is increasing at a rate of 3 cm/minute while the area of the triangle is…

A:

Q: Suppose that during the first year after its hatching, the weight of a duck increases at a rate…

A: Solution

Q: 2. 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: The value of a computer t years after purchase is v(t) = 4000e , At what rate is the computer's…

A: we need to find rate of change with respect to time of v(t)

Q: A car accelerates constantly from speed 0 m/s to 60 m/s in 30 seconds, remains at this speed for 20…

A: First step is to write down all the data that we have.

Q: Two cars are initially 1000 miles apart on a road that runs East/West. Car A drives 40 miles per…

A: To determine the rate of change of distance between two cars after 10 hours and 20 hours of travel.

Q: The temperature in a laboratory is maintained at 20°C. A warm bath is left to cool down and the rate…

A:

Q: A certain drug breaks down in the human body at a rate of 12% per hour. The initial amount of the…

A:

Q: In physics, the kinetic energy, K, of an object of mass m, moving at a velocity v, is given by the…

A: Given that kinetic energy K for an object of mass m and velocity V is given by K=(1/2)mv2. If mass…

Q: The temperature in a laboratory is maintained at 20°C. A warm bath is left to cool down and the rate…

A:

Q: The population of a city doubles in 50 years. How many years will it be four times as much? Assume…

A:

Q: certain culture of bacteria, the rate of increase is proportional to the numberpresent. (a) If it is…

A: (a) Consider y as the number of bacteria at time t and the rate of change of bacteria can be written…

Q: In, a culture, bacteria increases at the rate proportional to the number of bacteria present. If…

A:

Q: In a liquid culture, the number of bacteria grows at a proportional rate depending on the number of…

A:

Q: The rate at which the body cools is proportional to the difference in temperature of the body and…

A:

Q: A 200-liter tank initially full of water develops a leak at the bottom. Given that 10% of the water…

A:

Q: The velocity v of a falling object is directly proportional to the time t of the fall. If, after 2…

A: What will its velocity be after 3 seconds?

Q: If a snowball melts so that its surface area decreases at a rate of 4 cm2/min, find the rate (in…

A: Let the diameter be D cm and radius be r cm  The surface area S of the the sphere in term of…

Q: 1. If the growth rate of a culture of bacteria is proportional to the number of bacteria present.…

A: Given:  If the growth rate of a culture of bacteria is proportional to the number of bacteria…

Q: The length l of a rectangle is increasing at a rate of 7 cm divided by sec while the width w is…

A: Given:-             The length l of a rectangle is increasing at a rate of 7 cm/ sec while the width…

Q: In a chemical reaction a substance decomposes at a rate proportional to the amount of substance…

A:

Q: The substance decomposed at a rate proportional to the amount resent. What is the half-life of the…

A:

Q: 5) A cup of coffee cools at rate proportional to the difference between the constant room…

A:

Q: In a certain bacteria culture the rate of increase in a number of bacteria is proportional to the…

A: Follow the steps below to solve a differential equation(in terms of x and y) by the variable…

Q: A man rows up a stream 4 ½ hours and finds that it requires only 2 ½ hours down the stream. If he…

A: To find: The rate of current. Given: A person rows up a stream 412 hours and 212 hours to down the…

Q: A man on a wharf is pulling a rope tied to a raft at a rate of 0.6 m/s. If the hands of the man…

A:

Q: The length l of a rectangle is decreasing at a rate of 2 cm divided by sec while the width w is…

A: Given,           dldt=-2cm/s           dwdt=+2cm/s(a) Area, A=lw              dAdt=ddt(lw)…

Q: If a IV fluid bag is Flowing out of a 1.0 liter bag at the rate of 0.4 cc/min how long will it take…

A: Total volume of fluid flowing out =1.0 litre rate of flowing =0.4 cc/min

Q: At what rate is the distance between Jack and Jill changing if Jack is 3 miles from the bakery and…

A: Given:         To determine:

Q: A bacteria culture starts with a population of 1000 bacteria, and after 2 hours, the population grew…

A: Solution and Explanation is given below

Q: 4. One car leaves a given point and travels north at 30 mph. Another car leaves 1 hour later, and…

A:

Q: A certain population of bacteria is known to grow at a rate proportional to the amount present in a…

A: Solve for bacteria after 20 hrs

Q: A snowball melts in such a way that the rate of change in its volume is proportional to its surface…

A:

Q: A boat traveled north by 5 km then turned west. if the speed of the boat is 10 km/hr at what rate…

A: Given that,  the boat traveled north by 5 km then turned west and the speed of the boat is 10 kn/hr…

Q: In a certain bacteria culture the rate of increase in a number of bacteria proportional to the…

A:

Q: The rate at which the body cools is proportional to the difference in temperature of the body and…

A: Given the data

Q: The rate at which yeast cells multiply is proportional to the number present. If the original number…

A: Given, The rate at which yeast cells multiply is proportional to the number present. the original…

Q: A certain type of bacteria is known to grow at the rate proportional to the amount that is present.…

A:

Q: Suppose a block of metal heated to 250°F and then brought into a room that is at 90 ° F at 5 pm. At…

A:

Q: A life raft, set adrift from a sinking ship 150 miles offshore, travels directly toward a Coast…

A: Time , distance and speed is related using a formula time=distancespeed .At the same time , both the…

Q: A puppy weighs 2.0 lb at birth and 3.5 lb 2 months later. If the weight of the puppy during its…

A:

Q: 1. After 2 days, 10 grams of a radioactive substance is present. Three days later, 5 grams is…

A:

Q: Q.3. The rate at which a body cools is proportional to the difference between the temperature of…

A:

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.