The volume of water in a hemispherical bowl of radius 30cm is given by V =36x2 – x³ ) where x - X cm is the depth of the water. If the water is poured in at a constant rate of 10cm/s, at what rate is the level rising when the depth is 8 cm?

Q: A car is traveling at 88 ft /s when the brakes are fully applied, producing a constant deceleration…

A: Solve for the distance

Q: The radius of a sphere decreases at a rate of 1 m/se decreases when the radius is 15 m

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: Let y be height of wall upto ladder and x be distance between bottom of wall and bottom of ladder…

Q: If a rock is thrown upward on the planet Mars with a velocity of 10m/s, its height (in meters) after…

A: This is application of derivative problem

Q: A trough of water is 8 meters in length and its ends are in the shape of isosceles triangles whose…

A: Given:- A trough of water is 8 meters in length and its ends are in the shape of isosceles triangles…

Q: A high-speed bullet train accelerates and decelerates at therate of 4 fts 2 . Its maximum cruising…

A:

Q: A spherical drop of liquid evaporates at a rate proportional to its surface area. If a given drop…

A:

Q: 3

A:

Q: The position from its starting point of a small plane preparing for takeoff is given by x(1) = 1.412…

A:

Q: The kinetic energy K of a movingobject varies jointly with its mass m and the square of itsvelocity…

A: Given, The kinetic energy K of a movingobject varies jointly with its mass m and the square of…

Q: The volume of a cube is increasing at a rate of 60 in/sec. At what rate is the length of each edge…

A: The objective is to find the rate at which the length of each edge of the cube is changing when the…

Q: The mass of a cube in grams is M=x^3+0.1x^4, where is the length of one side in centimeters. If the…

A:

Q: An auto A is moving at 20 ft/s and accelerating at 5 ft/s2 to overtake an auto B which is 384 ft…

A:

Q: The width of a rectangle is increasing at a rate of 2 cm/sec, while the length increases at 3…

A: The rate of increase of the width of a rectangle i.e. dwdt=2 cm/sec The rate of increase of the…

Q: A car traveling at 45 miles per hour is brought to a stop, at constant deceleration, 132 feet from…

A: Given: A car traveling at 45 miles per hour.

Q: The width of a rectangle is increasing at a rate of 5 cm/sec, while the length increases at 6…

A:

Q: The side of an equilateral triangle is increasing at the rate of 3 cm/s. What is the rate at which…

A: We can solve the given problem by using the following concept of differentiation. Let f(x) be the…

Q: The side of a cube is increasing at a rate 7m/s, then the rate at which the volume of the cube…

A: Let s be the side of the cube in meter and V be the volume of the cube and t be the time in…

Q: If the original 24 m edge length x of a cube decreases at the rate of 5 m/min, when x = 3 m at what…

A: (a)Given:

Q: A motorcycle traveling at a speed of 34.0 mi/h needs a minimum of 44.0 ft to stop. If the same…

A: Stopping distance is given by the formula d=kv2

Q: The lower base of a trapezoid is 8 m. If its height is increasing at the rate of 0.5m/sec while its…

A:

Q: The length of the rectangle is increasing at a rate of 5cm/s and its width is decreasing at a rate…

A:

Q: The side of a cube decreases at a rate of 9 m/sec Find the rate at which the volume changes, when…

A:

Q: The length of a rectangle is increasing at the rate of 2 feet per second, while the width is…

A: Let length = x feet and width = y feet  Given that dx/dt= 2 and dy/dt= 1

Q: The length l of a rectangle is increasing at a rate of 7 cm divided by sec while the width w is…

A: Given:-             The length l of a rectangle is increasing at a rate of 7 cm/ sec while the width…

Q: A van is 5km due north of a bus at 2:00PM. If the van is traveling northward at the rate of 60 kph…

A:

Q: If a hemisphere bowl of radius 6 cm contains water to a depth of x cm, the volume of the water is rx…

A: This question is related to application of derivatives.

Q: The width of a rectangle is increasing at a rate of 2cm/sec, while the length increases at 3cm/sec.…

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 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 length l of a rectangle is decreasing at a rate of 2 cm divided by sec while the width w is…

A: Given,           dldt=-2cm/s           dwdt=+2cm/s(a) Area, A=lw              dAdt=ddt(lw)…

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: The length of a rectangle is increasing at a rate of 7cm/s and its width is increasing at a rate of…

A:

Q: If the ocean is opening at a rate of 3 cm/year., how wide will the ocean be in 100 million years in…

A: If the ocean is opening at a rate of 3 cm/year, then we have to find how much wide will the ocean be…

Q: A hemispherical dome with a diameter of 60 meters has to receive a coat of 5 cm of paint. Use…

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:

Q: Water flows out of a hemispherical tank at a rate which is 4 times the square root of its depth. If…

A: GIVEN: Radius of the tank is 8 ft

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: 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: The side of a cube is increasing at a rate 9m/s, then the rate at which the volume of the cube…

A: The function f(t) is a rule that associates or fixes a number to the particular point t. The…

Q: The length { of a rectangle is increasing at a rate of 9 cm/sec while the width w is decreasing at a…

A:

Q: A cylindrical vessel whose diameter and altitude are 26 cm and 500 cm respectively, is filled with…

A: Given  The diameter of cylindrical vessel  dc=26 cm. The altitude of cylindrical vessel is H=500…

Q: How long (in hours) would it take to fill a city water tank that has an inside diameter of 120 feet…

A:

Q: The surface area of a balloon that is being filled with helium increases at a rate of 5 square feet…

A:

Q: The length of a rectangle is increasing at a rate of 2 ft/s, and its width is increasing at a rate…

A: Here we have, The length of a rectangle is increasing at a rate of 2 ft/s, and its width is…

Q: An express train reducing its velocity to 40 km./h. , has to apply the brakes for 50 sec.. If the…

A: Rate of change of velocity is called acceleration. When there will be retardation,the sign of…

Q: A spacecraft is launched from the surface of a 6.7 x 1024 kg planet. If the spacecraft is moving at…

A:

Q: The diameter of a sphere is 5(2x+ 5), the rate of change of its surface area with respect to x is

A:

Q: A stone weighing 1/2 lb is thrown upward from an initial height of 5 ft with an initial speed of 32…

A:

Q: The diameter of a steel ball is measured to be 16 cm, with a maximum error of 0.3 cm. Estimate the…

A: The relation between the radius, r, and the diameter, l, can be defined by the equation: r=l2. It is…