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 of the side decreasing?

Q: The length of a rectange is increasing at a rate of 8 cm/s and its width is increasing at a rate of…

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: The radius of a sphere is increasing at a rate of 2 mm/s. How fast is the volume increasing (in…

A:

Q: 10. A large ice cube that is 4cm on each side is melting in a jug of lemonade at the rate of 3cm per…

A: Here we want to find how fast is the length of the side is decreasing under a volume change of 3…

Q: A large icecube that is 4cm on each sode is melting in a jug of lemonade at the rate of 3cm3 per…

A:

Q: If the diagonal of a cube is increasing at a rate of 3 cubic inches per minute, how fast (in…

A: We will find the rate of increase of side of cube.

Q: The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of…

A: We have to find the area of rectangle increasing

Q: Water is pouring from a hole at the rate of 25 cu. m per minute and is forming a conical pile on the…

A: This question can be solved by applying the concept of rate of change of physical quantities.

Q: The length of a rectangle is increasing at a rate of 4 cm/s and its width is increasing at a rate of…

A:

Q: An inverted conical tank with a height of 6 feet and a diameter of 4 feet that was filled with water…

A: It is given that, the height and diameter of the conical tank is 6 feet and 4 feet, respectively.Let…

Q: The radius of a sphere is increasing at a rate of 5 mm/s. How fast is the volume increasing when the…

A: Let be the volume and r be the radius of the sphere respectively.

Q: The length of a rectangle is increasing at a rate of 3 cm/s and its width is increasing at a rate of…

A:

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

A: We need to find reat of change of area.

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: How fast is the circumference of a circle changing if the radius is changing at the rate of 3 mm/s?

A: Solution

Q: All edges of a cube are expanding at a rate of 8 centimeters per second. (a) How fast is the surface…

A: All edges of a cube are expanding at a rate of 8 centimeters per second.a To determine how fast is…

Q: The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of…

A: The derivative represents the rate of change. Since given that, the length of a rectangle is…

Q: The length of a rectangle is increasing at a rate of 4cm/s and its width is increasing at a rate of…

A: The length of a rectangle is increasing at a rate, dldt = 4 cm/s The width of a rectangle is…

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

A:

Q: The length of a rectangle is increasing at a rate of 3 cm/s and its width is increasing at a rate of…

A: Consider the given situation, Let the length of the rectangle be ‘l’ and breadth be ‘b’.Area of…

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

A: It is the application of Derivative.

Q: Gravel is being dumped from a conveyor belt at a rate of 25 ft3/min, and its coarseness is such that…

A:

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

A:

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

A:

Q: The volume of a cube decreases at a rate of 0.75 ft3/min. What is the rate of change of the side…

A: Consider a cube with side 'a' The rate at which the volume of cube is decreasing is 0.75 cubic feet…

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

A:

Q: The length of a rectangle is increasing at a rate of 3 cm/s and its width is increasing at a rate of…

A: We know for rectangle, Area (A) = Length (l) × width (w) So, rate of change of area, (dA/dt) =…

Q: The radius of a sphere is increasing at a rate of 4 mm/s. How fast is the volume increasing when the…

A:

Q: Gravel is being dumped from a conveyor belt at a rate of 20 ft3/min, and its coarseness is such that…

A:

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

A:

Q: The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of…

A:

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

A:

Q: The side of a cube is increasing at a rate of 2 mm/s. How fast is the volume Q4. - increasıng when…

A: To find  How fast is the volume of a cube increasing.

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

A: Given oil is spilled from tank and it flowing  in a circular path with increasing radius of 2m/s .…

Q: A searchlight, 1/2 mi from a straight shore, rotates at the rate of 2 rev/min. How fast is the spot…

A: Let the angle formed by line AB with the line AC is x  in the triangle ABC,   So, from the tangent…

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: The volume of a cube is increasing at the rate of 6 cm/min. How fast is the surface area increasing…

A: It is given that, the volume of a cube is increasing at the rate of 6 cm3/min.   The objective is to…

Q: A kite flying 80m high is blown horizontally by the wind at a velocity of 5m/s. If the string is…

A: We are given that a kite flying at 80m height is blown horizontally by the wind at a velocity of…

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: A spherical iron ball 8cm in diameter is coated with a layer of ice of uniform  thickness. If the…

A: Given data:- The diameter of the iron ball is, 8 cm The thickness of the coating is, 2 cm The rate…

Q: Two cars start moving from the same point. One travels south at 64 mi/h and the other travels west…

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Q: how

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Q: The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of…

A: Let the length of the rectangle be:  l  cm Let the width of the rectangle be:  w  cm

Q: Gravel is being dumped from a conveyor belt at a rate of 35 ft3/min, and its coarseness is such that…

A: Now given that

Q: A spherical iron ball 8 in. in diameter is coated with a layer of ice of uniform thickness. If the…

A:

Q: A man on a wharf, 4.2 m above the water surface, is pulling a rope tied to a boat at the rate of…

A:

Q: How fast is the surface area of a cu

A: Given that : Edge of a cube = 30 cm Th edge changing at the rate of 3 mm per second.

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…

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

A: We have to find

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.