4. A basketball player is 7 feet tall walking away from a light that is 28 feet above the ground at the rate of 6 ft/sec. How fast is the shadow of the basketball player moving?

Q: 3. A man 6 ft tall walks along a straight path away from a lamp post 15 ft high at the rate of 2…

A:

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: A lamp post 3 m high is 6m from the wall. A man 2 m tall is walking directly from the post toward…

A:

Q: Two cars start moving from the same point. One travels south at 48 mi/h and the other travels west…

A: Given  Speed of first car =48 mi/h towards south Speed of second car =20 mi/h towards west

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: The volume of an ice cube is decreasing at a rate of 1.5 cm³/ sec. At what rate is a side of the ice…

A: We know that volume of a cube is given by V=a3 here V=volume of cube ,a=edge of cube Rate of change…

Q: Two cars start moving from the same point. One travels south at 24 mi/h and the other travels west…

A:

Q: A 10​-foot ladder is leaning against a vertical wall​ when Jack begins pulling the foot of the…

A: The given data can be expressed in a right triangle as shown below.

Q: A kite 160 feet above the ground moves in a direction parallel to the ground at the rate of 5 feet…

A: Let, x= the horizontal distance of the kite y=the length of the string Given that dx/dt=5 ft/sec  We…

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: Two cars start moving from the same point. One travels south at 60 km/h and the other travels west…

A: follow next step

Q: A picture 40cm high is placed on a wall with its base 30cm above the level of the eye of an…

A: Shown below

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

A:

Q: 2. A rope is attached to a boat at water level, and a man on the dock is pulling on the rope at the…

A: Draw the given situation at any time t then using Pythagoras theorem and application of derivative.…

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 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: 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: A lamp post 3 m high is 6 m from a wall. A man 2 m tall is walking directly from the post toward the…

A:

Q: What is the velocity (in ft/s) of a sandbag 2.5 s after it is released from a hot-air balloon that…

A: Given that a sandbag is released from a hot-air balloon that is stationary in the air. Then we have…

Q: A sphere is filled with air. If the volume of the sphere is decreasing at a rate of 534 cubic cm per…

A: Given

Q: A 6-ft man walks away from a 16-ft high lamp post at the rate of 4 ft/s. How fast does the tip of…

A:

Q: Two cars start moving from the same point. One travels south at 48 mi/h and the other travels west…

A: Given the data :

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

A:

Q: Two cars start moving from the same point. One travels south at 60 mi /h and the other travels west…

A:

Q: Two cars start moving from the same point. One travels south at 48 mi/h and the other travels west…

A: Consider the provided information, Let x and y be the traveled by the cars after time t. We can…

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

A: This problem is based on the application of differentiation.  First we have to write an equation in…

Q: A 50 ft ladder is placed against a wall, as shown below. The base of the ladder is slipping away…

A: Let the horizontal distance of the ladder is = x ft Vertical distance = y ft So, Given that:…

Q: c. A man 5 ft tall is walking along a straight line at a rate of 3 ft/sec towards a lamp post that…

A: Definition uses-       Similar triangles -        If two triangles are similar then their…

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

A: From the given information, draw a picture.

Q: 4. A street light is at the top of a 16 ft pole. A 6 ft tall woman walks along a straight path away…

A:

Q: The rate at which bacteria multiply is proportional to the instantaneous Number Present. If the…

A:

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: Two cars start moving from the same point. One travels south at 84 mi/h and the other travels west…

A:

Q: A baseball diamond is a square with with side 90 feet (between the bases). A batter hits the ball…

A: Roughly draw the situation first Where x= Distance covered by batter at time t D= Distance of the…

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

A: Let boy is at the point A, and when 100 ft cord is released the kite is at the point C, which is…

Q: 2. A ladder 13 ft long rests against a vertical wall. If the bottom of the ladder slides away from…

A:

Q: Two cars start moving from the same point. One travels south at 64 mi/h and the other travels west…

A:

Q: 6. Shan, who is 2 meters tall, is approaching a post that holds a lamp 6 meters above the ground. If…

A:

Q: light is 25 ft above a sidewalk and a man 6 ft tall is walking away from the point under the light.…

A:

Q: 6) A light is 20 meters above a straight horizontal path. If a man 1.65 meters tall is walking away…

A: Given: Height of light is 20 meter. Height of man is 1.65 meters. Rate with which man is walking is…

Q: a 10-foot ladder is leaning against a vertical wall when Jack begins pulling the foot of the ladder…

A:

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 man 7.00 ft tall approaches a street light 16.0 ft above the ground at the rate of 6.00 ​ft/s. How…

A: Given data: The height of the man is CD=7 ft. The height of the street light is AB=16 ft. The rate…

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.