. A man starts walking north at 4 ft/s from a point P. Five minutes later a woman starts walking south at 5 ft/s from a point 500 ft due east of P. At what rate are the people mov- ing apart 15 min after the woman starts walking?

Q: 3. A light is hung 15 ft above a straight horizontal path. If a man 2 ft tall is walking away from…

A:

Q: Coffee is draining out of a conical filter at a rate of 2.25 in3>min. If the cone is 5 in tall…

A: Given: The change in volume for the filter is -2.25 in3/min The change in volume for the coffee pot…

Q: If a snowball melts so that its surface area decreases at a rate of 8 cm2/min, find the rate (in…

A:

Q: 4. The distance travelled by a man driving at the rate of 60 kph

A:

Q: A kite is flying at a height of 40 ft. A boy is flying it so that it is moving horizontally at a…

A: Given: Kite is moving horizontally at a rate of 3 ft per sec. To determine: The rate at which the…

Q: A helicopter takes o from a point 80 m away from an observerlocated on the ground, and rises…

A: Thus when the helicopter is 60 m above the ground the elevation angle of theobserver’s line of sight…

Q: A 50 feet ladder is leaning against a wall of a building. Suppose the base of the ladder slides away…

A: Rate of change

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: 01/Water poured into a conical tank through a faucet, this tank has a base radius of 5 ft and 10 ft…

A:

Q: 8. If a snowball melts so that its surface area decreases at a rate of 4 cm2 /min , find the rate at…

A:

Q: A water tank has a shape of an cylinder with a base radius of 4 m and a height of 24 m. If water is…

A: Given

Q: A Conical Cup is 4cm across and 6cm deel. Water leaks cut of the bottom of the cup cit a rate of…

A: Consider the given information. The diameter of the cup is 4 cm. r=d2=42=2 cm The height is 6 cm.…

Q: A conical tank with an upper radius of 4 m and a height of 5 m drains into a cylindrical tank with a…

A:

Q: If a snowball melts so that its surface area decreases at a rate of 7 cm2/min, find the rate at…

A: Solve using increasing & decreasing function.

Q: A boat is being pulled with a rope towards a dock that is 10 ft above the water, as shown in the…

A: Let the distance of the boat= x ft y=length of the rope.  So,  given that dy/dt= 1.5 ft/min We have…

Q: If a snowball melts so that its surface area decreases at a rate of 6 cm2/min, find the rate (in…

A:

Q: The lengths of the edges of a cube are increasing at a rate of 9 ft/min. At what rate is the surface…

A: Total surface area of cube S = 6x2 Where x is length of the side of cube. we have given x = 19 ft.…

Q: If a snowball melts so that its surface area decreases at a rate of 6 cm2/min, find the rate (in…

A: we have to find the rate change in diameter

Q: 21. For the camera and rocket shown in Figure 3.4.5, at what rate is the camera-to-rocket distance…

A: Given that the distance between camera and launching pad is 3000 ft., the distance between launching…

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

A:

Q: 1.The speed of a stey diver t seconds afer jumping is given by VCt) = 80(1-e) ft.lsec. After how…

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: find the rate of change of the circumference of a circle when the area is increasing at the rate of…

A:

Q: 8. A street light hangs 24 ft. above the sidewalk. If a man 6 ft. tall walks away from the light at…

A: We can find the required as answer as below.

Q: 12) A vertical cylinder is leaking wader at a rate I ft3% If the cylinder har a height of 10t Sec.…

A: Volume of cylinder = πr2h  r= radius of cylinder  h= height of cylinder

Q: A ladder is 36 feet long and is leaning against the side of a house. The base is moved away at 2 ft…

A:

Q: A boat is pulled into a dock by means of a rope attached to a pulley on the dock. The rope is…

A: Given

Q: A rope is attached to a boat at water level, and a personon a dock is pulling the rope at the rate…

A: Let's find speed of boat.

Q: A light is on the top of a 12 ft tall pole and a 5 ft 6 in tall person is waking away from the pole…

A: Given that:Height of the poll is 12 ft and height of the person is 5 ft 6 in or 5.5 ft.Let x and y…

Q: Between 1 seconds and 9 seconds the ball's average velocity is If necessary, round the answer to two…

A:

Q: A baseball diamond is a square with sides of length 90 ft. A batter hits the ball and runs toward…

A:

Q: Each side of a square is increasing at the rate of 8 cm/sec. At what rate is the area of the square…

A: We have to find the increase of area

Q: . A 13-ft ladder is leaning against a house when its base is 12 ft from the house, the base is…

A:

Q: The radius of a circle is increasing at a rate of 5 ft/min. At what rate is its area changing when…

A:

Q: Cuntainr GOULA sulatunr tun cuntaining 597L of the into the fank at a rate cf he well-s7imed mixtuie…

A:

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 boat that arrives at a dock 20 ft above water level is being pulled in by a fisherman using a rope…

A: To find: The speed of the boat approaching the dock when the total length of rope out is 50 feet.…

Q: A 13 ft. ladder is leaning against a house while the base is pulled away at a constant rate of 1…

A: We need to find the rate at which top of ladder sliding down

Q: The radius of a circle is increasing at a rate of 5 ft/min. At what rate is its area changing when…

A: We can find the rate of change of area as below.

Q: The volume of a cube is increasing at a rate of 68 in3/sec. At what rate is the length of each edge…

A: Given Volume of cube increasing at a rate of 68 in3/ secTo the rate of change of length of each edge…

Q: If a snowball melts so that its surface area decreases at a rate of lcm²/min, find the rate at which…

A: Snowball represents a sphere So , Surface Area of sphere is 4πr2.  And , d=2r.  Using this we solve…

Q: The volume V=r° of a spherical balloon changes with the radius. a. At what rate (ft°/ft) does the…

A: Consider the given equation: V=43πr3 Where V is the volume and r is the radius. Differentiating the…

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: c) Ship A is 15 miles east of P and moving west at 20 mi/hr; ship B is 60 miles south of P and…

A: (In this figure, P is the point mentioned in the question, which is at some distance from ship A and…

Q: 1. The width of a rectangle is increasing at a rate of 2 cm/sec, while the length increases at 3…

A: I have stated the used formulas in the solution

Q: 3rd 2nd Home 0 90 ft 1st

A:

Q: An arrow is shot vertically up word from a platform 20 feet high at a rate of 179 ft./s, when will…

A: We will use the quadratic equation approach to solve the problem given: Height , h = 2ft speed = 179…

Q: Ship A is 15 miles east of P and moving west at 20 mi/hr; ship B is 60 miles south of P and moving…

A: Given data: The speed of  A is dxdt=-20 mph. The speed of  B is dydt=15 mph. Position of A is xA=15…

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.