Water is flowing into a leaky cistern at the rate of 31.4 cu ft./min. The cistern is a right circular cone 20 ft deep and 20 ft in diameter at the top. If water level is rising at the rate of % ft/min, how fast will the water be leaking out when the water level is 12 ft deep?

Q: 3. A light is hung 15 ft above a straight horizontal path. If a man 2 ft tall is walking away from…

A:

Q: If a snowball melts so that its surface area decreases at a rate of 1cm /min, find the rate at which…

A: Diameter= DRadius = r =D/2Surface area = A= 4pi*r^2Given dA/dt= -1 cm^2/min (negative because…

Q: The volume of an ice cube is decreasing at a rate of 1.5 cm³/ sec. At what rate is a side of the ice…

A: We know that volume of a cube is given by V=a3 here V=volume of cube ,a=edge of cube Rate of change…

Q: At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 8…

A:

Q: Find the rate at which the water level is rising when the water level is 2 cm.

A:

Q: Each side of a square is 6 ft and is increasing at a rate of 2 ft per second. How fast is the area…

A: By differentiating equation of area of square with respect to time and substituting the value of…

Q: At what rate is water pouring into a rectangular bathtub with base 65 fť if the water level rises at…

A: According to the given information it is required to calculate the rate at which water is pouring…

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

A:

Q: The volume of an ice cube is decreasing at a rate of 1.5 cm³/sec. At what rate is a side of the ice…

A: option A is correct detailed solution with explanations given below

Q: A l10-ft ladder is leaning against a vertical wall. If the bottom of the ladder is pulled away from…

A: If you like the solution then please give it a thumbs up.. The Answer is:        dy/dt = -3/2  or…

Q: The rate at which bacteria multiply is proportional to the instantaneous N numbers present. If the…

A: Let y(t) represents the number of bacteria present in the culture after t hours. Let the initial…

Q: A rope is attached to a boat at water level, and a man on the dock is pulling on the d) rope at the…

A: Draw a schematic diagram of given figure.

Q: A ladder 20 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A:

Q: A 6-ft man walks away from a 16-ft high lamp post at the rate of 4 ft/s. How fast does the tip of…

A:

Q: A water trough is 10m long and a cross-section has the shape of an isosceles trapezoid that is 30cm…

A:

Q: An ice cube that is 3 cm on each side is melting at a rate of 2 cm3 per min. How fast is the length…

A: Given: Length of cube L=3cm Rate of melting =-2cm3

Q: A light is hung 15ft above a straight horizontal path. If a man 2 ft tall is walking away from the…

A:

Q: The volume of. a cube decreases at a rate of 0.5 ft?/min. what is the rate of change of the side…

A: Application of derivative

Q: A swimming pool is 20 ft wide, 40 ft long, 3 ft deep at the shallow end, and 9 ft deep at its…

A:

Q: A ladder is 36 feet long and is leaning against the side of a house. The base is moved away at 2 ft…

A:

Q: A spherical balloon is inflated at a rate of 10 cm3>min. At what rate is the diameter of the…

A:

Q: A 100-ft long cable of diameter 4 in. is subsequently submerged in seawater. Due to corrosion, the…

A: Given that diameter is 4 inches and height is 100 feet. And rate of decrease in area is 750 in2yr.…

Q: At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 4…

A:

Q: A 50 feet ladder is leaning against a wall of a building. Suppose the base of the ladder slides away…

A:

Q: Each side of a square is increasing at a rate of 3 cm/s. At what rate is the area of the square…

A: Let the length of side of square be' a '

Q: The top of a ladder slides down a vertical wall at a rate of 1.5 m/s. At the moment when the bottom…

A:

Q: A ladder 15 feet long leans against a vertical wall. If the bottom of the ladder is pulled away from…

A: According to Pythagorean theorem , square of the hypotenuse side is equal to sum of the square of…

Q: The rate at which bacteria multiply is proportional to the instantaneous Number Present. If the…

A:

Q: 14. If a snowball melts so that its surface area decreases at a rate of 1 cm2/min, find the rate at…

A: To find the rate

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

A: Given: The drop evaporates to 18 of its volume in 5 minutes

Q: The top of a ladder slides down a vertical wall at a rate of 0.25 m/s. At the moment when the bottom…

A: Given:

Q: a. If a snowball melts so that its surface area decreases at a rate of 1 cm²/min, find the rate at…

A:

Q: A box has a length increasing at a rate of 2 in/s, a height decreasing at a rate of 3 in/s, and a…

A:

Q: A 5-foot ladder is leaning against a vertical wall. If the bottom of the ladder is being pulled away…

A: Given: Length of the ladder, l=5 ft. Distance between wall and the bottom of the ladder, x=4 ft…

Q: Initially filled with water, a conical reservoir is 24 ft deep and 12 ft across the top. Water goose…

A: Solution: Consider the given that conical reservoir 24ft (h) deep and 12ft across the top that is…

Q: A kite, at a height of 60ft.is moving horizontally at rate of 5ft./sec away from the boy who flies…

A: In right angle triangle ,According to the Pythagoras theorem , H2 = P2 + B2 Where H is horizontal ,…

Q: 1. How fast is the water level rising in a rectangular fish tank whose base is 20 ft² if the tank is…

A: Give: Area of base is A=20 ft2 Rate with which tank is filling dVdt=0.5 ft3/min. Volume of a…

Q: 2. A ladder 13 ft long rests against a vertical wall. If the bottom of the ladder slides away from…

A:

Q: A spherical balloon is deflated at a rate of 10 cm3 s-1. Find the rate change of the surface area…

A: given: A spherical balloon is deflated at a rate of 10 cm3s-1. we have to find the rate change of…

Q: The radius of a sphere, initially zero, increases at the rate of 6 ft per second. How fast the…

A: Given ,The radius of a sphere , initially zero , increases at the rate of 6 per second.The volume is…

Q: Each side of a square is increasing at a rate of 2 cm/s. At what rate (in cm2/s) is the area of the…

A:

Q: A 20-foot ladder is leaning against a vertical wall. Suppose the base of the ladder slides away from…

A:

Q: A ladder 5 m long rests against a vertical wall. If the top of the ladder slides down the wall at a…

A:

Q: A 15-ft ladder is leaning against a wall. If the bottom is pulled away from the wall at a rate of 3…

A:

Q: Each side of a square is increasing at a rate of 7 cm/s. At what rate is the area of the square…

A: If the area of a square, A, is x2 units , then the length of its side is x unit .

Q: A 6-ft man walks away from a 16-ft high lamp post at the rate of 4 ft/s.  How fast does the tip of…

A: Given that, A 6-ft man walks away from a 16-ft high lamp post at the rate of 4 ft/s.

Q: The height of a triangle is increasing at a rate of 2 [cm/min] and its area at a rate of 2 [cm²/…

A: It is given that height of triangle is increasing with a rate 2 cm/min and area with a rate 2…

Q: A process tank is being filled at a rate of 1200 GPM. If the tank is completely full, how much is…

A: In flow rate is 1200 GPM. Out flow rate is 320 GPM.

Q: A spherical iron ball 12 in. in diameter is coated with a layer of ice of uniform thickness. If the…

A: Given problem:- A spherical iron ball 12 in. in diameter is coated with a layer of ice of uniform…

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.