Consider a tank in the form of an inverted cone (i.e. the vertex looks down), of radius 20 feet and height 30 feet. If you pour water in it, at the rate of 10 cubic feet per minute, determine the speed at which the height of water in the tank is increasing, when that height is 20 feet.

Q: An airplane is flying west at 500 ft/sec at a constant altitude of 4000 ft and a searchlight on the…

A:

Q: An airplane heading due east has a velocity of 200 miles per hour. A wind is blowing from the north…

A: The velocity of the plane=200 mph  The wind hits the plane in the direction of south. so, the…

Q: At noon, ship A is 160 km north of ship B. Ship A is sailing south at 40km/h and ship B is sailing…

A:

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: Suppose you drive for 60 miles at 60 miles per hour, then for 60 miles at 30miles per hour. In miles…

A: Recall the equation connecting the three variables of speed, distance and time as: time = distance /…

Q: An airliner passes over an airport at noon traveling 520 mi/hr due east. At 1:00 p.m., another…

A: Given: An airliner passes over an airport at noon traveling 520 mi/hr due east. At 1:00 p.m.,…

Q: A neighborhood carnival has a merrygo-round whose radius is 25 feet.If the time for one revolution…

A: Since,it is known that the speed can be calculated by using the formula speed=Radius×Angular…

Q: At noon, ship A is 150 km west of ship B. Ship A is sailing east at 30 km/h and ship B is sailing…

A:

Q: The restaurant in the Space Needle in Seattle rotates at the rate of one revolution per hour (or one…

A: The restaurant in the Space Needle in Seattle rotates at the rate of one revolution per hour. And…

Q: A goat is tethered to a stake In the ground by a rope that is 10 feet long in terms of pi, what is…

A:

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: An airliner passes over an airport at noon traveling 510 mi / hr due east. At 1:00 p.m., another…

A:

Q: A softball diamond has the shape of a square wide sides 60 ft long. If a player is running from…

A: A softball diamond has the shape of a square with sides 60 ft long. A player is running from second…

Q: At noon, ship A is 150 km west of ship B. Ship A is sailing east at 35 km/h and ship B is sailing…

A: distance between the ship A and B is 150 km speed of ship A is 35km/h so at time t, the distance…

Q: An arc light is hung 12 ft. directly above a straight horizontal wall on which a boy 5 ft. tall is…

A: Given an arc light is hung 12 ft. directly above a straight horizontal wall on which a boy 5 ft.…

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

A:

Q: At noon, ship A is 100 km west of ship B. Ship A is sailing south at 25 km/h and ship B is sailing…

A: The below diagram represents the pictorial representation of the given problem.The position of the…

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

A: In the figure, x is the distance of pole from the man at the ground level. s is the length of the…

Q: When a rocket is 2 kilometers high, it is moving vertically upward at a speed of 300 kilometers per…

A:

Q: At noon, ship A is sailing north at a speed of 7mph, at the same time ship B, 5 miles west of ship…

A: Given, at noon, Ship A is sailing north at a speed of 7mph. At the same time, Ship B, which is 5…

Q: If the volume of a different sphere is increasing at a rate of 24 cubic inches per minutes and the…

A:

Q: A jet ascends at a 10° angle from the horizontalwith an airspeed of 550 mi>hr (its speed along…

A: Given: A jet ascends at a 10° angle from the horizontal with an airspeed of 550 mi>hr. Let x be…

Q: A man 6 ft tall walks along a level sidewalk away from a lamppost. On the post is a street light 18…

A:

Q: A conical water tank with vertex down has a radius of 10 ft at the top and is 24 ft high. If water…

A:

Q: An automobile uses gasoline at a rate of 12 kilometres per litre and has a 65 litre tank. How far…

A:

Q: A 75 kg box is pushed off of a 120 m tall building with an initial horizontal speed of 15 m/s. How…

A: We have to first sketch the given situation.

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:

Q: A trough is 12 ft long and its ends have the shape of isosceles triangles that are 3 ft across at…

A:

Q: A street light is at the top of a 13 foot tall pole. A 6 foot tall woman walks away from the pole…

A: The given data is: A street light is at the top of a 13-foot tall pole A 6-foot tall woman walks…

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

A:

Q: a of 3 inche tall and has a radius of 2 inches How fast does the water level rise when the water is…

A:

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

A:

Q: A trapezoidal trough is 10 ft long, 4 ft wide at the top, 2 ft wide at the bottom and 2 ft deep. If…

A:

Q: The ends of a trough, 8 ft in length, are isosceles triangles with height 2ft and base 4ft. Water is…

A: Rate of change

Q: The fixed sides of an isosceles triangle are of length 6 cm. (See the figure.) If the sides slide…

A: Given: The fixed sides of an isosceles triangle are of length 6 cm and the sides slide outward at a…

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

A: Diagram of the given question will be as following x is the distance of the man from pole y is the…

Q: At noon,ship a is 130 km west of ship b.Ship a is sailing east at 25 km/h and ship b is sailing…

A:

Q: When a rocket is 3 kilometers high, it is moving vertically upward at a speed of 400 kilometers per…

A:

Q: An aircraft is climbing at a 300 angle to the horizontal. How fast is the aircraft gaining altitude…

A: An aircraft is climbing at a constant 30 degree angle to the horizontal and the speed is 500 mph…

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

A: This question is based on application of  differentiation and Pythagoras theorem, We will solve it…

Q: a 5-ft tall person walks away from a 20-ft tall streetlamp at a constant rate of 3 ft/s . at which…

A: Let us denote: x= distance of the person from the post y=length of the shadow Given that, dx/dt=3 ,…

Q: An aircraft is climbing at a constant 32 degree angle to the horizontal. If the speed is 550 mph,…

A: Refer to the question . An aircraft is climbing at a constant 32 degree angle to the horizontal and…

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

A: Given,  Consider the height of the lite from the ground is 100 ft. The speed is dxdt=8 ft/s. To find…

Q: The radius of the tires of a car is 18 inches, and they are revolving at the rate of 673 revolutions…

A: To find the circumference of the tyre.

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 4 ft across at…

A: Given that: A trough is 14 feet long and its ends have the shape of isosceles triangles that are 4…

Q: A conical water tank with vertex down has a radius of 13 feet at the top and is 28 feet high. If…

A: Let V be the volume of the water and d be the depth of the water. Then, the volume is given by,…

Q: A stone is dropped into a quiet lake and waves move in the form of circles at a speed of 4 cm/ sec.…

A: Please see the answer in Step 2.

Q: An airplane with an airspeed of 80 meters per second is due east, gaining altitude, and has a line…

A: Let us sketch the situation roughly using these following information: N = North, S = South, E =…

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.