13. A light is hung 15 ft. above a straight horizontal path. If a man 6 ft. tall is walking away from the light at the rate of 5 ft. per sec., how fast is his shadow lengthening? 15ft 6 ft

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: A trough is 10 ft long and its ends have the shape of isosceles triangles that are 3 ft across at…

A:

Q: Assuming your car can slow at a constant rate of 15 ft/sec2, how much distance will your car cover…

A:

Q: A man starts walking north at 2 feet per second from a point P. A minute later a woman starts…

A:

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: How do you solve question 5?

A:

Q: A street light is fastened to the top of a 15-ft-high pole. If a 5-ft-tall women walks away from the…

A: In the figure,  AB=15 ft DE=5 ft BD=yDC=xdydt=3 ft/sec

Q: 1. A ladder 8 m long is leaning against a wall. If the bottom of the ladder is pulled horizontally…

A: We will draw figure and use differentiation  to find rate of change . Note . Only one question…

Q: A 5-ft-tall person walks toward a wall at a rate of 2 ft/sec. A spotlight is located on the ground…

A: 12. Let h be the height of shadow on wall using the similarity bof thr triangle,∆OAB, △OPQ,h40=540-x…

Q: At what rate is water pouring into a rectangular bathtub with base 65 fť if the water level rises at…

A: According to the given information it is required to calculate the rate at which water is pouring…

Q: 18. A kite string is paid out at a constant rate of 3 ft/s. If the wind carries the kite…

A:

Q: 7. A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base…

A:

Q: A light is at the top of a 16 ft pole. A man 6 ft tall walks away from the pole at a rate of 5ftsec…

A:

Q: . A man starts walking north at 4 ft/s from a point P. Five minutes later a woman starts walking…

A: We make diagram of the situation .

Q: A man starts walking north at 4 fts from a point . Fiveminutes later a woman starts walking south…

A:

Q: A trough is 10 ft long and its ends have the shape of isoscelestriangles that are 3 ft across at the…

A:

Q: A light is hung 15 ft above a straight horizontal path. if a man 6 ft tall is walking away from the…

A: Solution :x=distance from lights=length of shadowlet,height of light,D=15 ftheight of…

Q: 2. A boat is being pulled into a dock by a rope attached to it and passing through a pulley on the…

A:

Q: a fisherman on a wharf 1.2 meters above the level of still water is pulling a rope tied to a boat at…

A: topic - application of derivatives

Q: a) Water is flowing into a leaky cistern at the rate of 31.4 cu ft./min. The cistern is a right…

A: Given that  The water is flowing into a leaky cistern at the rate of 31.4 cu ft./min ⇒dVdt=31.4…

Q: 5. A rectangular trough is 10 ft long and 3 ft wide. Find how fast the surface rises, if water flows…

A:

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

A:

Q: 9. A man 6 ft tall walks away from a lamp post 16 ft high at the rate of 5 mi/hr. How fast does the…

A:

Q: 3. A man 6 feet tall walks at a rate of 5 feet per second away from a light that is 15 feet above…

A:

Q: A person stands at the end of a pier 8 ft above the water and pulls in a rope attached to a buoy. If…

A:

Q: A softball diamond is a square whose sides are 60 ft long. Suppose that a player running from first…

A: Suppose , y is the distance from the home and x is the distance from first base. Given that ,…

Q: A rectangular trough is 8 ft long. 2 ft across the top, and 4 ft deep. If water lows in at rate 2…

A: It is given that rectangular trough is 8 ft long. 2 ft across the top, and 4 ft deep. Suppose that x…

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 data:   The given height of the pulley is y=7 ft. The given rate at which rope pulled is…

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

A:

Q: 16. If the radius of a circle is increasing at the rate of 4 cm/s, find the rate of the increase in…

A: Given radius of a circle is increasing at the rate of 4 cm/sec.

Q: A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley…

A:

Q: 1. A conical paper cup 4 inches across the top and 4 inches deep is full of water. Since there is a…

A: We have been given the cone as in the figure  By the given figure we get r = 2 in. and h = 4 in. We…

Q: 4. A basketball player is 7 feet tall walking away from a light that is 28 feet above the ground at…

A:

Q: A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley…

A: Given : The pulley is 1 m higher than the bow The rate at which rope is pulled dydt=-1m/s and x=8.…

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 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: 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: The length of the horizontal leg of a right triangle is increasing at a rate of 3 ft/sec, and the…

A: Given A right triangle  horizontal leg = 7ft vertical leg = 1ft

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: The top of a ladder slides down a vertical wall at a rate of 0.25 m/s. At the moment when the bottom…

A: Given:

Q: A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley…

A: Let A= Pulley , B= Boat Given that AC=1  Let, x= distance of the boat from the dock. y=length of the…

Q: 4. A man 6 ft tall walks away from a lamp post 16 ft high at the rate of 5 miles per hour. How fast…

A:

Q: A kite, at a height of 60ft.is moving horizontally at rate of 5ft./sec away from the boy who flies…

A: In right angle triangle ,According to the Pythagoras theorem , H2 = P2 + B2 Where H is horizontal ,…

Q: a. How fast is the top of the ladder sliding down the wall when the base of the ladder is 12 feet…

A: It is given that the length of ladder is 13 foot which acts as the hypotenuse of the right angled…

Q: A trough is 14 ft long and its ends have the shape of isosceles triangles that are 2 ft across at…

A: It is required to find the rate at which water level is rising in the given trough whose sides are…

Q: A boat is pulled toward a pier by means of a taut cable. If the boat is 20 ft below the level of the…

A:

Q: Consider the given isosceles triangle of base 10 inches and side lengths x inches. If is increasing…

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…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.