A bag of sand originally weighing 144 lb was lifted at a constant rate. As it rose, sand also leaked out at a con-stant rate. The sand was half gone by the time the bag had been lifted to 18 ft. How much work was done lifting the sand this far? (Neglect the weight of the bag and lifting equipment.

Q: B. How rapidly will the water level inside a vertical cylindrical tank if we pump the water out at…

A:

Q: Cocoa butter, which is solid at room temperature and melts at 34°C, has a specific gravity of 0.86.…

A: Given, Cocoa butter, which is solid at room temperature and melts at 34°C has a specific gravity of…

Q: a car braked with a constant deceleration of 20ft/s^2, producing skid marks measuring 350 ft before…

A: Measuring distances in feet and time (starting with the brakes being applied ) in seconds we have…

Q: The side of a cube decreases at a rate of 9 m/sec. Find the rate at which the volume changes, when…

A: Consider the side of a cube which decreases at the rate of 9 m/sec. The objective of the problem is…

Q: If 6 J of work is needed to stretch a spring from 13 cm to 15 cm and another 10 J is needed to…

A:

Q: A ball is thrown vertically upwards with a velocity of 48 ft/s from the top of a building 35 ft…

A: Given that,

Q: To what constant deceleration would a car moving along a straight road be subjected if the car were…

A: The first equation of motion states that, v = u+at, here v is the final velocity, u is the initial…

Q: While John was on a hike, he filled his cylinder canteen, that was 10 in. tall and 6 in. in diameter…

A: Given that the canteen is 10 in. tall and 6 in. diameter. Since John filled the canteen, the initial…

Q: The current in a typical Mississippi River shipping route flows at a rate of 4 mph. In order for a…

A: Let the speed of barge in still water be x miles per hour. Given the speed of river is 4 miles per…

Q: If the work required to stretch a spring 5 feet beyond its natural length is 15 foot-pounds, how…

A: first, we need to find the spring constant  W=∫0a fxdx here we have W=15 and a=5 feet 15=∫05 fxdx…

Q: A car traveling at 42 ft/sec decelerates at a constant 44 feet per second per second. How many feet…

A: Given,A car traveling at 42 ft/sec decelerates at a constant 4 feet per second.i.e., initial…

Q: A 600 gallon brine tank is to be cleared by piping in pure water at 1 gal/min. , and allowing the…

A: Let S be pounds of salt in tank at time t, so: or Rewritting the equation above we get:…

Q: The side of a cube decreases at a rate of 9 m/sec. Find the rate at which the volume changes, when…

A:

Q: A girl flies a kite at a height of 300 ft, the wind carrying the kite horizontally away fromher at a…

A:

Q: a 400 gal tank initially contains 100 gal of brine containing 25 lb of salt. Brine containing 2 lb…

A: A real-life scenario can be described mathematically through a differential equation. By solving the…

Q: The side of a cube decreases at a rate of 9 m/sec. Find the rate at which the volume changes, when…

A: If the rate is decreasing then it will be the negative.

Q: The width of a rectangle is increasing at a rate of 5 cm/sec, while the length increases at 6…

A:

Q: The side of a cube increases at a rate of 10m/sec,then the rate at which the area of the cube…

A:

Q: If a snowball melts so that its surface area decreases at a rate of 2 cm2/min, find the rate at…

A:

Q: A ladder 13 feet long is leaning against the wall. If the base of the ladder is pushed toward the…

A:

Q: A kite 50 ft above the ground is moving horizontally at a rate of 4 ft/s. At what rate is the string…

A: We will be using the trigonometric ratios relating the sides of the triangle formed by strings and…

Q: The intensity of illumination at any point from a light source is proportional to the square of the…

A: Given that The intensity of illumination at any point from a light source is proportionalto the…

Q: An automobile uses gasoline at a rate of 12 kilometres per litre and has a 65 litre tank. How far…

A:

Q: The side of a cube decreases at a rate of 8 m/sec. Find the volume changes, when the side is 6 m. O…

A: Please refer the image.

Q: A 400-gal tank initially contains 100 gal of brine containing 50 lb of salt. Brine containing 1 lb…

A:

Q: with 2.60 moles of oxygen at 39.3 degrees Celcius?

A:

Q: If the radius of a sphere increases at a rate of 1.5 m/sec, then the rate at which the volume of the…

A:

Q: The side of a cube decreases at a rate of 7 m/sec. Find the rate at which the volume changes, when…

A:

Q: 4. A vertical right circular cylindrical tank measures 24 ft high and is 8 ft in diameter. It is…

A: Given:The height of the right circular cylindrical tank is 24 ft and diameter is 8 ft. It is full of…

Q: The side of a cube decreases at a rate of 7 m/sec. Find the rate at which the volume changes, when…

A:

Q: The side of a cube decreases at a rate of 9 m/sec. Find the rate at which the volume changes, when…

A: To find the rate of change of volume

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: A car braked with a constant deceleration of 40 ft/s2, producing skid marks measuring 80 ft before…

A: Deceleration = dv/dt And v = dx/dt where v is the velocity and x is the displacement Hence,…

Q: water pressure requirement at the roof

A: Given : High-rise building is 108 feet tall To find: How much pressure must be available at ground…

Q: A reservoir shaped like a right-circular cone, point down, 20 ft across the top and 8 ft deep, is…

A: Given: A reservoir shaped like a right-circular cone, point down, 20 ft across the top and 8 ft…

Q: At a constant pressure, what temperature must be reached to increase the volume of a 100mL samples…

A:

Q: an ice cube is shrinking uniformly at a rate of 8 cubic inches per hour. when the cube has a volume…

A: We are given the rate of change of volume of ice cube is shrinking uniformly at a rate of 8 cubic…

Q: A car braked with a constant deceleration of 16 fts 2 , producing skid marks measuring 200 ft…

A: Given, deceleration a(t) = 16 ft/sec2. s(0) = 0 ft and s(T) = 200 ft and v(T) = 0. Where T is the…

Q: The volume of a cube is increasing at a rate of 64 in ³/sec. At what rate is the length of each edge…

A:

Q: A 90 kg man lying on a surface of negligible friction shoves a 81 g stone away from himself, giving…

A: Explanation of the answer is as follows

Q: If a snowball melts so that its surface area decreases at a rate of 3 cm2/min, find the rate at…

A: Given information:

Q: The side of a cube decreases at a rate of 10 m/sec. Find the rate at which the volume changes, when…

A: Differentiate volume of cube wrt t

Q: 2. A 20-foot chain with density 4 lb/ft hangs off the roof of a building. How much work is required…

A: Given a 20 foot chain with density 4 lb/ft hangs off the roof of a building.

Q: A kite is 30 ft. high and is moving horizontally at a rate of 10 ft./min. At what rate is the string…

A: Calculate the rate in the following way:-

Q: . A trough has ends shaped like isosceles triangles, with width 3 m and height 4 m, and the trough…

A: Given that a though has ends shaped like isosceles triangle with width 3 m and height 4m and trough…

Q: A truck with a mass of 1500 kg is decelerated at a rate of 5m/s2 . How much force did this require?

A:

Q: An anchor weighing 130lb in water is attached to a chain weighing 4lb/ft in water. Find the work…

A:

Q: A ball is thrown vertically upwards with a velocity of 48 ft/s from the top of a building 35 ft…

A: topic-equations

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.