Pebbles are poured out of a tube at one cubic meter per second. It forms a pile which has the shape of a cone. The height of the cone is equal to the radius of circular base. How fast is the pile of pebbles rising when it is 2 meters high?

Q: At JCS Construction Plant, cement mixture is falling off a metal conveyor and onto an inverted…

A: Given: Cement mixture is falling off a metal conveyor and onto an inverted conical pile at a rate of…

Q: A Sphere of diameter 6 cm is dropped in a right cylindrical vessel party filled with water. The…

A: Let the level of the water rises in the cylindrical vessel is 'H'. So, The volume of the cylinder…

Q: A streetlight is mounted at the top of a 16 foot pole. An 8 foot tall Sasquatch walks away from the…

A:

Q: A cylindrical pool has a height of 8 feet and radius of 6 feet. How fast is the volume (in cubic…

A: Solved below

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: 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: 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 kite is 40 ft. high with 50 ft. of cord out. If the kite moves horizontally at 5 mi. per hr.…

A: Draw the position of kite as shown below.

Q: While John was on a hike, he filled his cylinder canteen, that was 10 in. tall and 6 in. in diameter…

A: Given that the canteen is 10 in. tall and 6 in. diameter. Since John filled the canteen, the initial…

Q: Grumpy, anti-social Professor Sosa loves standing on top of a 262 ft building and tossing water bal-…

A:

Q: A lont strip of sheet metal 12 inches wide is to be made into a small trough by turning up two sides…

A: Let x be the sides and B is the base. Perimeter is 12. The cross section of the area is given by…

Q: A girl flies a kite at a height of 300 ft, the wind carrying the kite horizontally away fromher at a…

A:

Q: On our moon, the acceleration of gravity is 1.6 m/sec2. If a rock is dropped into a crevasse, how…

A: It is given that the acceleration of the gravity is 1.6m/sec2.

Q: The radius of the wheel of a car is 15 inches. If the wheel is turning at the rate of 3 revolutions…

A: Given: The radius of the wheel of a car = 15 inches Rate of turning of wheel = 3 revolutions per…

Q: A baseball diamond is 90 feet square, and the pitcher's mound is at the center of the square (which…

A: You have asked multiple unrelated questions in the same post. I have addressed the first one. Please…

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: If a snowball melts so that its surface area decreases at a rate of 2 cm2/min, find the rate at…

A:

Q: If a snowball melts so that its surface area decreases at a rate of 9 cm2/min, find the rate at…

A:

Q: A train, starting at noon, travels north at 40 ml per hr. Another train, starting from the same…

A:

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

A:

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

A:

Q: The height of a right circular cylinder is 50 inches and decreases at the rate of 4 inches per…

A: Topic = Volume

Q: A 3-m long steel pipe has its upper end leaning against a vertical wall and the  lower end on a…

A: Given that: Length of steel pipe=3mLower end moves away from the wall at a speed = 2cm/s

Q: A ladder 10 feet long is leaning against a wall, with the foot of the ladder 8 feet away from the…

A: To determine the rate at which the ladder is sliding.

Q: a large gear with 42 rotates at 25 rpm. it turns a small gear with 14 teeth. how fast does the small…

A:

Q: An automobile with 0.310 m radius tires travels 95,000 km before wearing them out. How many…

A: An automobile with 0.310m radius tires travels 95,000km before wearing them out. We have to find how…

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 45-caliber bullet shot straight up from thesurface of the moon would reach a height of s = 832t -…

A: Given, A 45-caliber bullet shot straight up from the surface of the moon would reach a height of…

Q: The side of a cube decreases at a rate of 7 m/sec. Find the rate at which the volume changes, when…

A:

Q: A girl starting at 11 A.M., travels east at 4 km/hr while a boy, starting at noon from the same…

A:

Q: A limestone stalactite grew in length at a rate of – of a millimeter per year. At this rate, how…

A: Given the limestone is growing at a rate of 18mm per year i.e. 0.125 mm every year

Q: On the moon, the acceleration due to gravity is 1.6 m/sec2. If a rock is dropped into a crevasse,…

A: Consider the given value of acceleration due to gravity 1.6 m/sec2.

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: A square baseball diamond has sides that are 90 feet long. A player is running to third base at a…

A: Solution

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 boat moves at a rate of 13 mph in still water. If the river's current flows at a rate of 3mph, how…

A: given that: A boat moves at a rate of 13 mph in still water. the river's current flows at a rate of…

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: The Grain is falling from a chute onto the ground, forming a conical pile whose diameter is 3 times…

A: To determine the height of the pile.

Q: Let's say you're on a ferris wheel with a diameter of 20 m and 1 lap per minute. How fast do you…

A: Given: diameter =20m;  radius =10mAlso, a=horizontal distance = 6 feet;…

Q: A car braked with a constant deceleration of 16 fts 2 , producing skid marks measuring 200 ft…

A: Given, deceleration a(t) = 16 ft/sec2. s(0) = 0 ft and s(T) = 200 ft and v(T) = 0. Where T is the…

Q: If a snowball melts so that its surface area decreases at a rate of 3 cm2/min, find the rate at…

A: Given information:

Q: A man 6 feet tall walks at a rate of 2 feet per second away from a light pole that is 16 feet high.…

A: From the figure substitute value of BE, AE, AD and AC in equation (1)

Q: If a snowball melts so that its surface area decreases at a rate of 5 cm2/min, find the rate at…

A:

Q: The volume of a cube is increasing at a rate of 56 in/sec. At what rate is the length of each edge…

A: Given that the volume of a cube is increasing at a rate 56 in3/sec and the edges are 8 in. long. It…

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: A hot air balloon is tethered at an angle of elevation of a/6. The rope holding the balloon is being…

A: Given Data: The angle of elevation is: α=π6 The rate at which the rope is being brought is: dxdt=-4…

Q: A cone has a volume that is 350 cubic meters. What is the volume of a similar cone that is twice as…

A: Given, Volume of 1st cone = 350 cubic meters To find the volume of a similar cone that is twice as…

Q: The legnth of a rectangle decreases at 3cm/sec, while its width increases at 2cm/sec. At a certain…

A: Given:     Length of a rectangle decreases at a rate of 3 cm/sec               dldt=-3 cm/sec…

Q: Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the…

A: Given : 1) Oil spills from a ruptured tanker and spreads in a circular pattern.             2)…

Q: A jogger jogs around a circular track with a diameter of 375 m in 16 minutes. What was the jogger's…

A: Given:  Diameter of circular track =375 m So, radius of the track