Vater is being poured at the rate of 2x m' /min into an invertedi with a radius of 6 meters at the top. If the water level is rising at

Q: A spherical snowball melts at a rate of 36π^2in³/sec. At what rate is the radius of the snowball…

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: find the rate at which the volume of a right circular cylinder of constant altitude 10 feet changes…

A: Given  Altitude=10feet We need to find the rate at which the volume of a right circular cylinder…

Q: A spherical balloon is to be deflated so that its radius decreases at a constant rate of 5 cm/min.…

A:

Q: A water tank in the shape of an inverted cone is being filled up with water at a uniform rate of…

A:

Q: Water is injected into a ball-shaped container of radius RR at a rate of 2 cm^3 per second. How fast…

A: Radius of spherical ball is R. Rate change in volume is 2 cubic centimeters. Mathematically, dVdt=2…

Q: A spherical balloon is being filled with air at a constant rate of 3 cm3/s. How fast is the radius…

A: Let,Volume of sphere = VRadius of sphere = rRate at which the volume of sphere is increasing = dVdt…

Q: A vertical cylinder is leaking water at a rate of 3 m/sec. If the cylinder has a height of 10 m and…

A: The volume of the cylinder is given by V=πr2h, where V=volume of the cylinder r=radius of the…

Q: A stone dropped into a still pond sends out a circular ripple whose radius increases at a constant…

A:

Q: The radius of a spherical balloon is decreasing at a rate of in/sec.

A: Radius of balloon = r = 4 inchesDecreasing rate of balloon = drdt = -2πinches/secondVolume of…

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: There is a constant outflow of a liquid into a inverted conical vessel 15 m deep and 7.5 m in…

A: Find the rate of change of volume of water in the cone, with respect to time:…

Q: Air is being pumped into a spherical balloon at a rate of 5 cubic centimeters per minute. Determine…

A: Given : The air is pumped into a balloon at a rate of 5 cm3/min The diameter of the balloon is 20 cm

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: Two concentric circles are expanding, the outer radius at the rate of 5 ft/sec and the inner one at…

A: Let A1 and A2 be the areas of the inner and outer circles at any instant and 'A' be the area between…

Q: Water is flowing at the rate of 9 ft3/min into a tank that is in the shape of a right circular…

A: Let r be the radius of base of cylinder, then r=2 ft .Let h be the height of water level at any time…

Q: The depth of water in a 4m diameter cylindrical tank is increasing at the rate 0.7m/min. Find the…

A:

Q: A cube’s surface area increases at the rate of 72 in2/sec. At what rate is the cube’s volume…

A: Given:

Q: Water is being poured at the rate of 2z m' /min into an inverted conical tank that is 12-meter deep…

A: We need to find rate of water leaking.

Q: The surface area of a sphere increases at a rate of 90 m/sec. Then the rate at which the radius…

A:

Q: A spherical balloon is being deflated at a rate of 80 cm³/min. At what rate is the radius decreasir…

A:

Q: You are blowing air into a spherical balloon at a rate of cubic inches per second. (The reason for…

A: You are given V'(t), which is    V'(t) = 4pi/3   From there you know   V(t) = (4pi/3) * t   You also…

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: A spherical snow ball is being made so that its volume is increasing at the rate of 8 ft /min. What…

A: given: dVdt=8 ft3 /min We have to find drdtwhen diameter of snowball is 4 ft i.e, radius= 2ft we…

Q: A spherical balloon is being deflated at a rate of 80 cm3/min. At what rate is the radius decreasing…

A:

Q: As a circular metal griddle is being heated, its diameter changes at a rate of 0.01 cm/min. Find the…

A:

Q: Water runs into a sunken concrete hemi- spherical bowl of radius 5 m at the rate of 0.2 m3/sec. How…

A: The derivative gives the rate of change of some variable with respect to other quantity. If a…

Q: Water is flowing at the rate of 6 ft/min into a tank that is in the shape of a right circular…

A: Given data:   The rate at which water is flowing in the cylindrical tank is dV/dt =6 ft3/min. The…

Q: When a circular plate of metal is heated in a oven, its radius increases at a rate of 0.05 cm/min.…

A: drdt=0.05cm/minradius, r=52cmArea=πr2Derivative formuladdxxn=n xn-1

Q: Water is flowing into a vertical cylindrical tank at the rate of 5cu.ft/min. if the radius of the…

A: The volume of a cylinder:,V = πr2hWhere, V = Volume of the cylinder  r = Radius of the base  h =…

Q: When a circular plate is heated on an oven its radius increases at a rate of 0.03 cm/ min at what…

A:

Q: A spherical balloon is increasing in volume at 24t Cm . How fast is the radius ст S. of the balloon…

A:

Q: A Ferris wheel with a radius of 13m is rotating at a rate of one revolution every 2 minutes. How…

A: Given thatRadius of the Ferris wheel is 13 mThe time period of the Ferries wheel is 2 min To find…

Q: A yellow balloon, spherical in shape is inflated with a rate of 100 cm3 /sec. Calculate the rate at…

A: Given

Q: The radius of the sphere is decreasing at a rate of 2in/min. What is the rate of change of its…

A:

Q: . Suppose that an air-filled cone-shaped balloon has a leak causing air to escape at a rate of 24…

A:

Q: A conical cistern of height 5 ft and 7 ft across the top is being filled at a rate of 5 ft3/s while…

A: A conical cistern is given whose height is 5 ft and diameter at the top is 7 ft. A conical cistern…

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

A: Let x= horizontal distance L= length of string,  Then a rough sketch of the problem is as follows:

Q: an oil spill is spreading in a circle at a rate of 316.7in/sec2. at what rate is the radius changing…

A:

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

A:

Q: A comet loses material when it gets close to the Sun at a rate of 100 cubic meters per minute.…

A: Given Comet is a sphere Its radius is 200 meters Let V be the volume of the comet then r be the…

Q: If the radius of a sphere increases at a rate of 0.5 m/sec, then the rate at which the volume of the…

A: Let the radius of the sphere be r. Then the volume of the sphere is: V=43πr3…

Q: Water is pouring into a conical vessel 15 cm deep and having a radius of 3.5 cm across the top. If…

A: Given the water is pouring into a conical vessel of 15 cm deep and the radius of 3.5 cm across the…

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

A:

Q: A spherical balloon is being filled with air at the constant rate of 2 cm³ How fast is the radius…

A: Given that The spherical balloon is being filled with air at constant rate of 2cm3/sec. Since the…

Q: A cylindrical tank with radius 5 m is being filled with water at a rate of 3 cu. m / min How fast is…

A: Given, Radius of the cylindrical tank = 5 m Water rate = 3 m3/min

Q: A bacterial cell is spherical in shape. If the radius of the cell is increasing at the rate of 0.01…

A: Given , Bacterial cell is in spherical shape.Let radius be 'r' μm . ∴ Volume of cell, v v = 43π…

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.