4. A street light is at the top of a 16 ft pole. A 6 ft tall woman walks along a straight path away from the pole with a speed of 3 ft/sec. At what rate is her shadow growing when the girl is 24 ft away from the pole?

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: The legs of an isosceles right triangle increase in length at a rate of 2 m/s. a. At what rate is…

A:

Q: A baseball diamond is a square 90 ft on a side. A player runs from first base to second base at 15…

A: 6)

Q: 4. A baseball diamond is a square 90 ft on a side. A player runs from first base to second base at…

A:

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

A:

Q: Water is poured into a conical paper cup at the rate of 3/2 in/sec (similar to Example 4 in Section…

A: I will use the formula V=13πr2h and differentiation method to solve this problem.

Q: 1. Water is flowing at the rate of 2 m3/min into a tank in the form of an inverted cone having an…

A: It is given that the cone has altitude 16 m and radius 4 m. That is, hcone=16,rcone=4. Let r and h…

Q: 2. A water tank is in the form of an inverted right circular cone h feet deep and d feet wide across…

A:

Q: The sides of a square increase in length at a rate of 3 m/sec. a. At what rate is the area of the…

A: lets the size of square is l so the rate of change of length = dl/dt = 3 m/sec area of square = l2…

Q: 2) Water is pouring into an inverted cone at the rate of 8 cubic me- ters per minute. If the height…

A: Given that Height of cone h=12 m radius of its base r=6 m rate of pouring water into cone dVdt=8 m3

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

A:

Q: 1. The sides of a square decrease in length at rate 2 m/sec. At what rate is the area of the square…

A:

Q: The legs of an isosceles right triangle increase in length at a rate of 6 m/s a. At what rate is the…

A: Let, l be the length of a legth of a leg of an isosceles right triangle, h be the length of the…

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 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: The sides of a square increase in length at a rate of 5 m/sec. a. At what rate is the area of the…

A: We apply chain rule of differentiation. Area of the square is: A= s2.  Where s is the side of a…

Q: The edge of an expanding cube is changing at the rate of 2.3 cm/s at the instant its edge is 18.3 cm…

A:

Q: 2. A water tank is in the form of an inverted right circular cone h feet deep and d feet wide across…

A: At any time t, let the height of the water be h ft and the radius of the cone formed by the volume…

Q: 10. At what rate is the vertex angle of a right circular cone changing when the radius is 3 ft and…

A:

Q: A baseball diamond is a square 90 ft on a side. A player runs from first base to second base at 15…

A:

Q: 1) A baseball diamond is a square whose sides are 90ft long. Suppose that a player running from…

A: Given : Side of Baseball diamond square =90 ft. Drawing the diagram of the whole situation,

Q: A man of height  1.9  meters walks away from a 5-meter lamppost at a speed of  2.1  m/s. Find the…

A: Let distance of the man from the pole=x   Let the length of the shadow =y…

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 trough whose cross section is an equilateral triangle is 6 m long and 2 m wide across the top. If…

A: Solve by diagram and using formulas of equilateral triangle

Q: A cone-shaped tank of water is leaking water at a constant rate of 3 m³/hour. If the base radius of…

A: Using volume  of cone and applications of derivative idea we solve this

Q: A man of height 1.8 m walks away from a 5-m lamppost at the speed of 1.2 m/s. Find the rate at which…

A:

Q: 2. a) A ladder 10 ft long leans against a vertical wall. If the top of the ladder slides down the…

A: Given:-  a) A ladder 10 ft long leans against a vertical wall. If the top of the ladder slides down…

Q: A man of height 1.7meters walks away from a 5-meter lamppost at a speed of 1.1 m/s. Find the rate at…

A: Given that a man of height 1.7m walks away from a 5 meters lamp post at a speed of 1.1 m/s. We need…

Q: 2. A street lamp is 5m tall and located 6m from a brick wall. A person who is 2m tall walks away…

A:

Q: How fast is the surface area of a circular oil spill in the ocean changing when the radius is 10ft…

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: 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: The legs of an isosceles right triangle increase in length at a rate of 6 m divided by s.a. At what…

A: Let x  be the length of leg and h be the length of hypotenuse of an isosceles right triangle. Then…

Q: The sides of a square increase in length at a rate of 3 m/sec. a. At what rate is the area of the…

A: let the side of the square is a meter, and the area is A given that da/dt=3m/sec a. a=15m area of…

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: Answer the following True or False: If an ice skater is skating directly away from a 3 meter tall…

A:

Q: 5. A baseball diamond has the shape of a square with sides 90 ft long. A player 60 ft from second…

A:

Q: Suppose that a tumor in a person’s body has a spherical shape and that treatment is causing the…

A: we know that the volume of the sphere                       V=43πr3                          (1)

Q: A man of height 1.9 meters walks away from a 5-meter lamppost at a speed of 1.1 m/s. Find the rate…

A: Given Data: The height of the man is: h=1.9 m The height of the lamppost is: H=5 m The increasing…

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: 11. At what rate is the volume of the cube changing if the edge is 8 cm and is changing at 4 cm/s?

A: As we know that; The expression for the volume of the cube with the edge length ''a'' is: v=a3…

Q: At what rate is the height of the water rising at the instant the tank is half full?

A: To find the rate at water rising

Q: A trough 21m long has ends shaped like isosceles triangles, with base 5m and height 14m. Water is…

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: 1. How fast is the water level rising in a rectangular fish tank whose base is 20 ft² if the tank is…

A: Give: Area of base is A=20 ft2 Rate with which tank is filling dVdt=0.5 ft3/min. Volume of a…

Q: 7. A vertical cylinder is leaking water at a rate of 1 ft'/sec. If the cylinder has a height of 10…

A: To find the rate of change of height of water changing

Q: 1. A man on a wharf, whose hand is 8.2 m above the level of the water surface is pulling a rope tied…

A:

Q: 2) A kite is flying at a fixed height of 30 ft. If 50 feet of string is out already from the spool,…

A: Given- A kite is flying at a height of 30 feet, if 50 feet of string is out already from the spool…

Q: A weather balloon is rising vertically at the rate of 10ft/s. An observer is standing on the ground…

A: Given: -

Q: How do you solve question 2?

A: Let x= horizontal distance y= vertical distance Given that dx/dt=1 ft/sec We have to find dy/dt at…