You drove an 800-gal tank truck of waterfrom the base of Mt. Washington to the summit and discovered onarrival that the tank was only half full. You started with a full tank,climbed at a steady rate, and accomplished the 4750-ft elevationchange in 50 min. Assuming that the water leaked out at a steadyrate, how much work was spent in carrying water to the top? Donot count the work done in getting yourself and the truck there.Water weighs 8 lb / U.S. gal.

Q: 4. A boy is flying a kite at a height 150 ft. If the kite moves horizontally away from the boy at…

A: Given query is to find the rate of change of length of string.

Q: 4. A car brakes with constant deceleration of 18 ft / s² producing skid marks that measure 306 feet…

A:

Q: A student with an estimated VO2max of 51 ml/kg/min wants to run 3 miles at 75% of VO2max. How long…

A:

Q: A solution containing at 2 lb of salt per gal is poured at 3 gal per min into a 300-gal tank that…

A:

Q: 4. A 105 kg male needs to work at a MET level of 8 to reach his target heart rate. If he exercises…

A:

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: Suppose there is no snow in a parking lot when snow begins to fall at midnight; From midnight until…

A:

Q: A 3 lb bucket containing 20 lb of water is hanging at the end of a 20 ft rope that weighs 4 oz/ft.…

A: Given that, a 3 lb bucket containing 20 lb of water is hanging at the end of a 20 ft rope that…

Q: How much 15% solder must be added to 25% solder to produce 30.0 g of 18% solder? In a race, car 1…

A: For part 1 of question   let amount of solder be x so according to the statement  15% of x + 25% of…

Q: In a railroad yard a 35,000 kg boxcar moving at 7.3 m/s is stopped by a spring-loaded bumper mounted…

A: We have to find how far does the spring compress (in cm) in stopping the boxcar.

Q: If 6 J of work is needed to stretch a spring from 10 cm to12 cm and another 10 J is needed to…

A:

Q: The skid marks made by an automobile indicated that its brakes were fully applied for a distance of…

A: Given  final velocity=v=0 msdeceleration=a=20ms2Distance cover by the car before  come to stopy=75…

Q: Each side of a square is increasing at a rate of 6 cm/s . Atwhat rate is the area of the square…

A:

Q: In developing a paint line process for an appliance manufacturer, a given component on a conveyor…

A: To Determine: The lenght of the booth. Given: A given component on a conveyor belt passes a given…

Q: A sewage disposal plant has a big concrete holding tank of 100,000-gal capacity. It is % full of…

A: Let M(t) be the mass of the organic material in the tank at time t and Mt=CtVt, where C(t) and V(t)…

Q: Gravel is being dumped from a conveyor belt at a rate of30 ft3/min , and its coarseness is such that…

A:

Q: Suppose that 4 J of work is needed to stretch a spring from its natural length of 32 cm to a length…

A:

Q: A chain lying on the ground is 10 m long and its mass is 60 kg. How much work (in J) is required to…

A:

Q: Find out the lycopene concentration in tomatoes after 4 months of storage at 15°C.

A: 4 months = 16 weeks to find lycopene concentration in tomatoes we need to find the regression line y…

Q: A safety inspector determines that contamination from an abandoned factory site is spreading through…

A:

Q: A weight W is attached to a rope 50 ft long which passes over a pulley at P, 20 ft above the ground.…

A: Given: - A weight W is attached to a rope 50 ft, long which passes over a pulley at P, 20 ftabove…

Q: A ball is being inflated such that the volume is increasing at a constant rate of 100cm3/s How fast…

A: Given  and

Q: If 6 J of work is needed to stretch a spring from 10 cm to 12 cm and another 10 J is needed to…

A: let L is the natural length (actual length) of the spring. Now if the force (f) produces…

Q: A tank initially contains 50 gal. of fresh water. Brine (water in which a certain number of pounds…

A:

Q: The sides of a triangle measuring 40 m, 32 m, and 16 m increase at the rates of 2 m/s, 5 m/s and 3…

A: Area of triangle: If x, y and z are sides of triangle then area A of triangle is given by A = s(s -…

Q: How much work (in J) is required to move a box that weighs 12 kg upward by 55 cm? Use the fact that…

A:

Q: A spherical scoop of ice cream sits on top of a waffle cone. The diameter of the ice cream sphere is…

A: Cone Shaped ice cream scoop: diameter d1 =10 cm (sphere) diameter d2 = 10cm (cone) and height h = 20…

Q: An IV Piggyback of lincomycin containing 5 gms of drug in 175 mL is to be infused over a 1 hour…

A:

Q: Air is being pumped into a spherical balloon so that its volume increases at a rate of 70cm³ /s. How…

A: Volume of the sphere , V =43πr3 ; where , 'r' is the radius of the sphere. Surface Area of the…

Q: A 500 mL IV starts at 9pm and runs at 33gtt/min with a drop factor of 10gtt/mL.  At what time will…

A: Algebra Question

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 rope is attached to the bow of a sailboat coming in for the evening. Assume that the rope is drawn…

A: Given: The rope is drawn in over a pulley 5 feet higher than the bow at the rate of 2 feet per…

Q: A water trough is 800 cm long and a cross-section has the shape of an isosceles trapezoid that is 40…

A:

Q: 31 An ice (ube is slowly melting, losing 3cm3 of water each hour. If it a lways remains a Perfect…

A: Volume of a cube=(side)^3

Q: A car traveling at 60 mi/h (88 ft/s) skids 176 ft after its brakes are suddenly applied. Under the…

A:

Q: A car braked with a constant deceleration of 18 ft/s2, producing skid marks measuring 100 ft before…

A:

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

A:

Q: A car braked with a constant deceleration of 8 ft/s2, producing skid marks measuring 100 ft before…

A: constant deceleration of 8 ft/s2  skid marks measuring 100 ft

Q: The side of a cube is increasing at a rate 9m/s, then the rate at which the volume of the cube…

A: The function f(t) is a rule that associates or fixes a number to the particular point t. The…

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: On the moon, the acceleration due to gravity is 1.6 m/sec2. a) If a rock is dropped into a crevasse,…

A: a) The acceleration due to gravity on the moon is -1.6 m/sec2. Recall that the second derivative of…

Q: A worker on a scaffolding 85 feet above the ground needs to lift a 115 pound bucket of cement from…

A:

Q: How many cubic meters must be hauled from PIT 1 in order to meet the engineer's needs? Round-off to…

A:

Q: The volume of a cube is increasing at a rate of 56 in/sec. At what rate is the length of each edge…

A: Given that the volume of a cube is increasing at a rate 56 in3/sec and the edges are 8 in. long. It…

Q: In developing a paint line process for an appliance manufacturer, a given component on a conveyor…

A: We will find the solution in the following step.

Q: The top of a ladder slides down a vertical wall at a rate of 0.675 m/s. At the moment when the…

A: Given: The top of a ladder slides down a vertical wall at a rate of 0.675 m/s. At the moment when…

Q: A car braked with a constant deceleration of 16 ft/s2, producing skid marks measuring 50 ft before…

A:

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

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.