When cane sugar is dissolved in water, it converts to invert sugar overa period of several hours. The amount A(t) of unconverted cane sugar attime t (in hours) satisfies A' = -0.2A . If there are initially 500 g of unconverted cane sugar, how much unconverted cane sugar remains after 5 h?After 10 h?

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

A:

Q: Use differentials to estimate the amount of paint needed (in m3) to apply a coat of paint 0.06 cm…

A: Given information: The diameter of the hemisphere is 52 m that means the radius is 26 m. Formula…

Q: The top of a ladder slides down a vertical wall at a rate of 0.375 m/s. At the moment when the…

A: Let the ladder is k meters. (k=constant) Let the distance of the bottom = x m and distance of the…

Q: A balloon is rising straight up from a level field, at a constant rate of 0.4 m/ sec. Just when the…

A:

Q: A rectangular box has its height increasing at a rate of 1m/s while its volume is decreasing at a…

A: We have to find the  rate of change of length.

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

A:

Q: A potter forms a piece of clay into a cylinder. As he rolls it, the length, L, of the cylinder…

A: Differentiate volume wrt t

Q: A cylindrical tank 24 inches in radius and 2 meters tall initially contains 100 gal of cane juice. A…

A: Please check step 2 for solution.

Q: A tank is initially filled with 1000 gal. of salt solution containing 500 H of salt. Fresh water…

A: Let At the amount of salt at the time t Then the rate of change of the amount of salt dAdt=0lbL.10…

Q: Two parallel sides of a rectangle are being lengthened at the rate of 20 mm/sec, while the other two…

A: Let the sides of rectangle be x and y   since, two parallel sides are increasing at the rate of…

Q: A 200g-tank holds 100 gallons of fresh water upon first. At t = 0, a 5 gal/min salt solution…

A: Given initial quantity of freshwater in the 200-gallon tank = 100 gallons At t=0, salt solution is…

Q: Suppose a liquid is to be cleared of sediment by pouring it through a cone-shaped filter. Assume…

A:

Q: The length of the rectangle is increasing at a rate of 5 cm per second, and its width is decreasing…

A:

Q: A tank initially holds 80 gal of a brine solution containing 1/8 lb of salt per gallon. At t=0,…

A:

Q: At 12:00 p.m. a tank contains 150 g of salt dissolved in 8 L of water. Pure water begins flowing…

A: Since you have asked multiple questions, we will solve the first one for you. If you want any…

Q: The original 24 m edge length x of a cube decreases at the rate of 5 ​m/min.   a. When x=5m, at what…

A:

Q: If an object in linear motion (but with changing velocity) covers As meters in At seconds, then its…

A:

Q: The top of a ladder slides down a vertical wall at a rate of 0.375 m/s. At the moment when the…

A: Let the length of the ladder is L.

Q: A rectangle is expanding such that its length is always 4 times its width. If the width is…

A:

Q: A liquid solution is passing thru a conical filter 2 feet deep and 4/3 feet across the top, into a…

A: We have to find the rate at which the level of the solution in the cylinder rising.

Q: 7. The top of a ladder slides down a vertical wall at a rate of 0.15 m/s. At the moment when the…

A: Given data A ladder slides a vertical wall at rate of 0.15 m/s  find the length of ladder = ?

Q: The population of bacteria in a culture grows at a rate proportional to the number of bacteria…

A:

Q: use differentials to estimate the amount of metal in a cylindrical can that is 12cm high and 8cm in…

A:

Q: The original 24 m edge length x of a cube decreases at the rate of 2 m/min. a. When x = 1 m, at what…

A:

Q: 2. Suppose that the bottom of a conical shaped tank of water has been ruptured. At the instant when…

A:

Q: A particle is moving along the curve y = x². As the particle passes through the point (1,e), its…

A: Given: A particle is moving along the curve y=x2. As the particle passes through the point (1, e),…

Q: 4 THE LENGTH OF A TRIANGLE LL INCREASING ATA RATE OF 8cm/s AND ITS WIDTH IS INCREASING AT A RATE OF…

A: SOLUTION-

Q: The side of the base of a square prism is decreasing at a rate of 7 km/min and the height of the…

A: Surface area of a square prism is given by- A=2a2+4ah where a is side of prism, h is height of…

Q: 10) Air is being pumped into a spherical balloon so that its volume increases at a rate of 100 cm…

A:

Q: The top of a ladder slides down a vertical wall at a rate of 1.5 m/s. At the moment when the bottom…

A:

Q: One side of a right triangle is known to be 20 cm long and the opposite angle is measured as 30 °,…

A: a. let the hypotenuse of the triangle is h. so using the trigonometric ratio formula,…

Q: A spherical snowball is melting in such a way that its diameter is decreasing at rate of 0.2 cm/min.…

A:

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 balloon is rising straight up from a level field, at a constant rate of 0.4 m/ sec. Just when the…

A:

Q: If the area A = s of an expanding square is increasing at the constant rate of 8 square inches per…

A:

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

A: We have given; the rate of change when ladder slides down i.e 0.15m/s The rate of change when it…

Q: There's a tank containing 50 L of a solution into which 10 g of salt is dissolved in. A solution…

A: image is attached

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

A:

Q: A quantity with an initial value of 110 grows continuously at a rate of o.5% per hour. What is he…

A: Given, Initial value of quantity = 110  It is growing continuously at a rate of 0.5%  per hour.  We…

Q: If a ball is thrown vertically upward and with an initial velocity of 10 m/s, it’s velocity at the…

A: To find: The velocity at the highest point reached by the stone. Given: The initial velocity of the…

Q: A potter forms a piece of clay into a cylinder. As he rolls it, the length, L, of the cylinder…

A:

Q: A ladder 5 m long rests against a vertical wall. If the top of the ladder slides down the wall at a…

A:

Q: A tubular metal 3.9 meters long leans against a vertical wall and the other foot of the metal is on…

A:

Q: The top of a ladder slides down a vertical wall at a rate of 0.375 m/s. At the moment when the…

A: form a triangle with given information : let BC = x   dxdt=0.5 AB = y  dydt=-0.375  AC = z  dzdt=0…

Q: When a metal plate is heated, it expands. If the shape of the plate is circular and its radius is…

A: When a metal plate is heated, it expands. If the shape of the plate is circular and its radius is…

Q: A water trough is 10 m long and has a cross-section in the shape of an isosceles trapezoid that is…

A: The volume of water trough = Area × Length Area of trapezium = 12×Sum of parallel sides×height…

Q: A 60-gal tank initially contains 10 gal of fresh water. At t = 0, a brine solution containing 1 Ib…

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.