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 at a rate if 2 ft/sec. a) What rate is the tip of the shadow moving away from the pole when the person is 25 ft from the pole?  b) What rate is the tip of the shadow moving away from the person when the person is 25 ft from the pole?

Q: A reservoir shaped like a right-circular cone, point down, 20 ft across the top and 8 ft deep, is…

A:

Q: The ends of a water trough 8 ft long are equilateral triangles whose sides are 2 ft long. If water…

A: Length = 8 feet         Side     = 2         dvdt = 5 ft3/min          h   = 8 inch  = 23…

Q: (b) If its' owner uses 3 pipes of radius 4cm, with water flowing at a rate of 30cm/s, how long will…

A: (a) Area of circuler face= pi*r2  =pi*102 = 314 cm2.                    (pi=3.14)

Q: a ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A: Given, A ladder 10 ft long rests against a vertical wall. Let x be the distance between the bottom…

Q: A pulley having a diameter of 36 cm is turned by a belt that moves at the rate of 5 m/sec. How many…

A: In one revolution the pulley will rotate by an angle of 360°. Hence, the belt will cover a distance…

Q: At what rate is water pouring into a rectangular bathtub with base 29 ft squared  if the water level…

A: Given a rectangular bathtub with base 29 ft squared.

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

A: Since you have asked multiple questions in a single request we will be answering only the first…

Q: A baseball is thrown straight downward with an initial speed of 40 ft/s from the top of the…

A: Let t be the time taken by the ball to reach the ground and the velocity of the ball is v. Now, the…

Q: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A: Given: Length of a ladder which rests against a vertical wall is 10 ft. Let the distance between…

Q: If the work required to stretch a spring 1 ft beyond its natural length is 12 ft-lb, how much work…

A: Given work required to stretch by 1ft is 12ft -lb

Q: A spherical balloon is inflated with air at a rate of 32 cm3/ min. At what rate does the radius…

A: Find dr/dr.

Q: 2. A water heater that has the shape of a right cylindrical tank with a radius of 2 ft and a height…

A:

Q: A round table has six equal designs as shown in the figure ,If the radius of the table top is 14 cm…

A:

Q: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A: To find: The rate at which the angle between the ladder and the ground  is changing

Q: A conical vessel is 12 m across the top and 15 m deep. If it contains water to a depth of 10 m, find…

A: We need to consider a section and then integrate accordingly.

Q: A hemisphere bowl with radius 13 ft is filled with water to a level of 6 ft. Find the work done to…

A:

Q: If the work required to stretch a spring 1 ft beyond its natural length is 15 ft-lb, how much work…

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 ladder 25 ft long is leaning against a wall. If the bottom of the ladder is pulled 10.…

A: We need to find change in angle.

Q: Question 4

A: Let a be the acceleration, v be the velocity, s be the position and t be the time of braking.

Q: A water tank has the shape of an inverted circular cone with base radius 2 m and height 4 m. If…

A:

Q: A cylindrical water tank has a height of 6 m and a radius of 4 m. How much work is required to empty…

A: To Determine: A cylindrical water tank has a height of 6 m and a radius of 4 m. How much work is…

Q: A trough is 14 ft long and its ends have the shape of isosceles triangles that are 5 ft across at…

A: Similar triangles property is used as the height and width of the water level is proportional to the…

Q: An 8 ft ladder rests against a vertical wall. If the bottom of the ladder slides away from the wall…

A:

Q: A water heater that has the shape of a right cylindrical tank with a radius of 1 ft and a height of…

A: The right cylindrical tank has radius 1ft and height 4 ft. The water in it is draining at the rate…

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: the tires of a bicycle have a radius of 14inches and are turning at the rate of 230 revolutions per…

A: Given that the tires of a bicycle have a radius of 14inches and are turning at the rate of 230…

Q: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A: A ladder with 10 ft resting on a wall is shown in below figure.

Q: a water tank has the shape of an inverted circular cone with a base radius of 2m and a height of 4m.…

A:

Q: If the work required to stretch a spring 3 ft beyond its natural length is 15 ft-lb, how much work…

A: Given that the work required to stretch a spring 3 ft beyond its natural length is 15 ft-lb.

Q: A 20-m-long, 50-kg chain hangs vertically from a cylinder attached to a winch. How much work is…

A: Consider the provided information, To compute the work by using the formula, w=∫0LρgL-ydy Let y=0 be…

Q: An 8 ft. ladder rests against a vertical wall. If the bottom of the ladder slides away from the wall…

A:

Q: A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole…

A: A streetlight is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole…

Q: A water trough is 9 m long and has a cros height 50 cm. If the trough is being filled m/min

A: Given a water trough which is 9 m long and has a cross section in shape of an isosceles trapezoid

Q: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A: To determine the rate of change of angle between the ladder and the ground.

Q: A (square) baseball diamond has sides that are 90 feet long . A player running from second base to…

A: Let X(t) be the distance from player’s to home plate at time t (in seconds).Given that the length of…

Q: A paper cup has the shape of a cone with height 10 cm and radius 3 cm (at the top). If water is…

A: From the given problem the representative diagram is shown as below: Let the radius of the cone be…

Q: A triangle has two constant sides of length 6 ft and 2 ft. The angle between these two sides is…

A:

Q: A kite 100ft above the ground moves horizontally at a speed of 8 ft/s. At what rate is the angle…

A: Using triangle find angle then find the rate of change of angle

Q: A trough, 10 ft long, has semi-elliptical ends which are 3 feet deep and 4 feet wide. If the trough…

A:

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

A:

Q: A trough is 14 ft long and its ends have the shape of isosceles triangles that are 4 ft across at…

A:

Q: At what rate is water pouring into a rectangular bathtub with base 73 ft² if the water level rises…

A: Given : The base of rectangular bathtub = 73ft2 The rate at which water level is rising = 1.2…

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 lawn sprinkler located at the corner of a yard is set to rotate through 600 and project water out…

A: A lawn sprinkler located at the corner of a yard is set to rotate through 60 degrees  and project…

Q: A 5 meter high conical tank has a radius of 2 meters, and is filled with a liquid (800 kgf/cu.m).…

A:

Q: Suppose that a copper sphere of radius 3 cm is beaten and drawn into a wire of diameter 0.2 cm. What…

A: This question is based on mensuration problem.

Q: An inverted conical tank is 10 feet high and 7 feet in radius. Water, which weighs 9800 Newtons per…

A: An inverted conical tank is 10 feet high and 7 feet in radius. Water, which weighs 9800 Newtons per…

Q: find the rate at which the area is increasing

A: Given an isoscles triangle has a constant length of 4 ft. Angle Ø between these sides increases at…

Q: A ladder 9 ft long rests agains a vertical wall. If the bottom of the ladder slides away from the…

A: Let the distance between base B of the wall and bottom of the ladder C, BC= x feet  And the angle…

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.