Under certain conditions, cane sugar in water is converted into dextrose at a rate proportional to the amount that is unconverted at any time. If 75 kg at time t = 0, 8 kg are converted during the first 30 minutes, find the amount converted in 2 hours.

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: A 13ft ladder rests against a vertical wall. If the bottom of the ladder is sliding away from the…

A:

Q: The volume of an ice cube is decreasing at a rate of 1.5 cm³/ sec. At what rate is a side of the ice…

A: We know that volume of a cube is given by V=a3 here V=volume of cube ,a=edge of cube Rate of change…

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 culture of yeast grows at a rate proportional to its size. If the initial population is 4000 cells…

A: Let's find.

Q: Water is pumped from a tank at constant rate, and no more water enters the tank. If the tank…

A: To solve the following problem and find the amount of water left at 6:10pm.

Q: A tank contains 300 gal of water and 100 gal of pollutants. Fresh water is pumped into the tank at…

A: Fresh water is pumped into the tank at the rate of 2 gal/min, and the well stirred mixtureleaves at…

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

A: Given data:   The initial value of the mass is mi=50 milligrams. The mass lost after two hours is…

Q: A 10-metre ladder is placed against a vertical wall. Suppose the bottom of the ladder slides away…

A:

Q: A spherical drop of liquid evaporates at a rate proportional to its surface area. If a given drop…

A:

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: The volume of an ice cube is decreasing at a rate of 1.5 cm³/sec. At what rate is a side of the ice…

A: option A is correct detailed solution with explanations given below

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

A:

Q: A 15-foot ladder is leaning against a wall. If we pull the ladder away from the wall at a rate of…

A:

Q: The rate at which bacteria multiply is proportional to the instantaneous N numbers present. If the…

A: Let y(t) represents the number of bacteria present in the culture after t hours. Let the initial…

Q: The rate of growth of a certain cell culture is proportional to its size. In 10 hours a population…

A: The rate of growth of a certain cell culture is proportional to its size. In 10 hours a population…

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

A:

Q: A yeast grows at a rate proportional to its present size. If the original amount doubles in two…

A: Let v(t) be size of yeast at t time Therefore, ds/dt  ∝ s(t) ds/dt  = ks   [k is proportionality…

Q: The height of a triangle is increasing at a rate of 4 cm/s while the area of the triangle is…

A: Let the height, base and area of a triangle be 'h', 'b' and 'A' Given, dhdt=4 cm/sdAdt=56 cm2/s

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

A:

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

A: Percentage : Percentage of the item is 100th part of the number.  It is denoted by x% or written as…

Q: | Suppose that electricity is draining from a capacitor at a rate proportional to the voltage V…

A: The given differential equation is dVdt=-140V, where V is the voltage and t is the time in seconds.…

Q: A 13 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 3 ft/s, how…

A:

Q: A tank contains 1000 liters (L) of a solution consisting of 170 kg of salt dissolved in water. Pure…

A: The rate of change of a quantity with respect to time is the differential of that quantity. In a…

Q: A certain population of microorganisms grows at a rate proportional to the amount present under a…

A: Given that, A certain population of microorganisms grows at a rate proportional to the amount…

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: Under certain conditions, cane sugar in water is converted into dextrose at a rate proportional to…

A:

Q: 6. The mass of a cube in grams is M = x³ + 0.1x*, where x is the length of one side in centimeters.…

A: Explained below

Q: After a long study, three scientists conclude that a eucalyptus tree will grow at a rate of…

A:

Q: A 100 gallon tank is filled with brine containing 60 pounds of dissolved salt. Water runs into the…

A: Form the differential equation of first order and solve to get the answer.

Q: If the base h of a triangle is increasing at a rate of 3 inches per minute while its height h is…

A: Area of a triangle of base b and height h is given as, A=12bh The derivative of area with respect to…

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: The base x of a triangle is decreasing at the rate of 5 in./sec. and the height y of the triangle is…

A: Given Base = x  Height = y Rate of change of base = dx/dt = - 5 in/s Rate of change of height =…

Q: D. A ladder 10 feet long rests against a vertical wall. If the top of the ladder slides down at a…

A: Make a diagram according to the situation.

Q: A 15 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 4 ft/s, how…

A:

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

A:

Q: After a foreign substance is introduced into the blood, the rate at which antibodies are made is…

A: Please see the below picture for detailed solution.

Q: The population of a community is known to increase at a rate proportional to the number of people…

A:

Q: A 200-gal tank is half full of distilled water.At time t = 0, a solution containing 0.5 lb / gal of…

A:

Q: B. A ladder 13 feet long rests against a vertical wall. If the top of the ladder slides down at a…

A:

Q: A freshly brewed cup of coffee has temperature 95°C in a 20°C room. When its temperature is 66°C, it…

A:

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

A: Given that the top ladder slides down a vertical wall at a rate of 0.15m/s. the bottom of the ladder…

Q: Water is drained from a pool at a rate of R(t) = 50e-0.08t gallons per hour. If the drain is left…

A: 625 gal. water drains from the pool.

Q: A tank contains 1000 liters (L) of a solution consisting of 195 kg of salt dissolved in water. Pure…

A: Solution is given below:

Q: A 50L tank initially contains 5L of brine solution where 3kg of salt have been dissolved. At t = 0,…

A: According to the given information,

Q: A solution with 35% ammonia is added at a rate of 5 liters per minute to a vat that initially…

A: Given: A solution with 35% ammonia is added at a rate of 5 liters per minute to a vat that initially…

Q: A culture of bacteria grows at a rate that is proportional to the present number. It is found that…

A:

Q: Consider that sugar dissolves in water at a rate proportional to the amount still un-dissolved.…

A: 50kgs of sugar is present and at 5-hour mark there's only 20kg of sugar is left.

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.