Boyle's law says that the product of a gas's pressure, P (atm), and volume, V (m'), is constant. Determine the rate at which the volume of a gas changes when its pressure is 20, its volume is 40, and its pressure is decreasing at a rate of 3 atm per minute.

Q: A tank initially holds 100 gallons of brine solution containing 20 lbs. of salt. At t = 0, fresh…

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

Q: 17 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 fluid is being pumped from a cylinder into a rectangular prism with a square base. The base has…

A:

Q: Initially a tank holds 100 gal of a brine solution containing 4 lb of salt. At t = 0, brine…

A: Solution :-

Q: Consider a tank with volume 100 liters containing a salt solution. Suppose a solution with 2…

A:

Q: A ladder 10 meters long rests on horizontal ground and leans against a vertical wall. The foot of…

A:

Q: A 40 gal tank initially contains 11 gal of fresh water. At t = 0, a brine solution containing 1.2 lb…

A: Given: The initial volume of water v(0)=11 gallons The initial amount of salt s(0)=1.2 lb Since rate…

Q: A spherical balloon is deflating and its radius r is decreasing at the rate of 5 mm per minute.…

A:

Q: A cube is heated in such a way that the volume increases at a rate of 1 mm/s. The rate of change of…

A: A cube is heated in way that volume increases at the rate of 1mm/s. the side of the cube is 7mm…

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

A: Area of rectangle = Length * Width

Q: Suppose a snowball remains spherical while it melts, with the radius r shrinking at 4 inch(es) per…

A: Let r be the radius of the snowball at any time t. The radius r is decreasing at the rate of 4 in/hr…

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: Water is poured into a conical tank 6 m across the top and 8 m deep at the rate of 10 m3min. How…

A:

Q: 2. A ladder 10 meters long is leaning against a wall. If the bottom of the ladder is being pushed…

A: Given, A ladder 10 m long is leaning against a wall. Bottom of the ladder is being pushed…

Q: A 20 m tank is full of brine with 40 kg of dissolved salt. Pure water enters the tank at a rate of…

A: In this question, we find the amount of solt when the takl half full. given that  Initial amount of…

Q: A spherical snowball is melting in such a way that its volume is decreasing at a rate of 2 cm / min.…

A: Given-  dVdt=-2cm3/min (negative sign indicates that it is decreasing). To find- The rate of radius…

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

A:

Q: A tank contains 100 gal of brine made by dissolving 80 lb of salt in water. Pure water runs into the…

A: Many real-life problems can be modeled using differential equations. This is one of the significant…

Q: A bacteria culture starts with 4 bacteria and grows at a rate proportional to its size. After 2…

A:

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

A:

Q: The height of a rectangular box is 10 in. Its length increases at the rate of 2 in./sec; its width…

A: Volume of rectangular box = l b hwhere, l = length of boxb= width of boxh = height of boxRate of…

Q: A tank initially holds 80 of brine solution containing 1/8 b of salt per gallon. At t-0. another…

A:

Q: The tank shown in the figure was filled with 100 liters of substance A in a concentration of 10g /…

A: Given: The tank having 100 liters of substance A in a concentration of 10g / L. Material A is fed…

Q: The radius of a spherical balloon is increasing at the rate of 2 cm per minute. How fast is the…

A: Let r be the radius of spherical ballon

Q: An inverted pyramid is being filled with water at a constant rate of 55 cubic centimeters per…

A: Given: dVdt==55, side length b0=4 and height h0=11. To find: dhdt, when h=2.

Q: A tank contains 5001 of a solution consisting of 30 kg of salt dissolved in water. Pure water umped…

A:

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

A:

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 tank with a capacity of 400 gal originally contains 150 gal of water with 25 lb of salt in…

A:

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

A: Here, the amount of the clay is fixed. dVdt=0...(1) Now, the volume of the cylinder is given by:…

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: A tank contains 200 liters of fresh water. Brine containing 2 kilograms per liter of salt enters the…

A:

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

A: Given: when the initial time t=0 amount of the cane sugar is 75 kg, and the time t=30 minutes amount…

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 tank contains 40 L of solution containing 2g of substance per liter. Salt water containing 3g of…

A: Initially there is 40*2 = 80 grams Let Q be the amount of substance in the tank and dQ/dt be the…

Q: A tank contains 80 gallons of pure water. A brine solution with 2lb/gal of salt enters at 2 gal/min,…

A: Given: r1=2 galsmin., r2=2 galsmin.,  c1=2 lbsgal,, v0=80 gallons, x0=0

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: The volume of a cube decreases at a rate of 0.3 3ft/min. What is the rate of change of the side…

A: Let the length of each side of the cube be a ft. Find the volume of the cube. Differentiate the…

Q: A spherical snowball is melting so that its diameter is decreasing at rate of 0.2 cm/min. At what is…

A: Solution:

Q: Consider a rectangular metal box without a top lid which, because of being heated, is increasing in…

A:

Q: vulcanizing shop has a trapezoidal drum that is 5 meters long, 1.5 meter wide at the top, 1 meter…

A: Solution of the problem as follows

Q: A right circular cylinder has a 4 inch diameter and is filling with water at a constant rate.  The…

A: Consider the volume of right circular cylinder V. Differentiate it w.r.t time t.…

Q: A spherical snowball is melting so that its diameter is decreasing at rate of 0.2 cm/min. At what is…

A:

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

A:

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

A:

Q: A 30 m³ tank is full of brine with 40 kg of dissolved salt. Pure water enters the tank at a rate of…

A: Volume of the tank is 30 m3 The tank is full of brine with 40 kg of dissolved salt. Pure water…

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

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.