What are the dimensions of the rectangular field of maximum area that can be fenced with exactly 500 feet of fencing materials?

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A: We need to find the rate of change of volume of cube when side is 20 inches. Volume of cube=(side)3…

Q: The sides of a square are increasing at the rate of 2 inches per minute. How fast is the Area…

A: Given The side of square is increasing at rate of 2inches per minute.  The area of a square with…

Q: A cylindrical rod made of ice is melting at a rate of 8 cm3 per minute. When the length of the rod…

A: The formula for the volume of the cylindrical rod is, V=πr2h where r is the radius of the…

Q: The volume of a right circular cylinder is 60 cm3 and is increasing at 2 cm3/min at a time when the…

A: First we have to differentiate expression of volume with respect to time.

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Q: A plane is flying at a constant altitude of 1 mile and a speed of 400 mph toward an observer on the…

A: The plane is flying at a constant altitude of 1 mile. Let x be the horizontal distance and y be the…

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Q: A water trough is 8 feet long, and its cross section is an equilateral triangle with sides 2 feet…

A: Given thatLength of water trough is 8 feet and cross section is equilateral triangle with side 2…

Q: Suppose that the sides of a cube are expanding at a rate of 2 inches per minute. How fast is the…

A: all details are given in below. please check it

Q: Suppose an elastic rubber band is used to make a square, and is being stretched (while keeping the…

A: An elastic rubber band is being stretched (while keeping the square shape) at the rate of 2 inches…

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Q: A rectangular tank with a square bottom has base side lengths of 3 feet and a height of 10 feet is…

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Q: A water tank is in the shape of a right circular cylinder with height of 4 meters and radius of 2…

A: This question is related to application of derivative, we will solve it using given information.

Q: A block of ice, in the shape of a right circular cone, is melting in such a way that both its height…

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Q: A light is hung 6 meters above a straight horizontal path. If a man 2 meters tall is walking toward…

A: Decreasing:- We know that if something is decreasing then it is going down.

Q: A trough is 10 feet long and its ends have the shape of isosceles triangles that are 3 feeta cross…

A: To find: The rate of incresing level of the water. Given information: The trough is 10 feet long…

Q: hypothetical cube shrinks so that the length of its sides are decreasing at a rate of 3 ft/min. At…

A: we have to find

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Q: A plane that is flying horizontally at an altitude of 7 kilometers and a speed of 680 kilometers per…

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Q: rectangular parallelepiped with an altitude of 10 cm have its width decreasing by 2 cm/min and…

A: Topic:- application of derivatives

Q: A tank shaped like a right circular cone with radius 5 meters and height 15 meters is filled with…

A: What is Derivative: Physically, the derivative of a function represents in which rate a function…

Q: The radius of the circle is increasing at a rate of 3 meters per minute and the sides of the square…

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Q: All edges of a cube are expanding at a rate of 7 cm per second. How fast is the surface area…

A: All edges of a cube are expanding at a rate of 7 cm per second. How fast is the surface area…

Q: Two people on bikes are at the same place and start riding in different directions. One of the…

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Q: A conical water tank with vertex down has a radius of 10 ft at the top and is 24 ft high. If water…

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Q: A plane is flying at a constant altitude of 1 mile and a speed of 400 mph toward an observer on the…

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Q: The original 24 m edge length x of a cube decreases at the rate of 2m/min.   When x=2 m, the…

A: Given,           The original 24 m edge length x of a cube decreases at the rate of 2 m/min.We know…

Q: Two cars A and B, started moving from the same point. Car A traveled 60kph northward, while Car B…

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Q: A man 2 m tall walks toward a lamppost on level ground at a rate of 0.5 m/s. If the lamp is 5 m high…

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Q: A 10-meter ladder is leaning against the wall of a building. It begins to slide down the wall. When…

A: Let l denote the length of the ladder leaning against the wall of a building Let x denote the…

Q: All the edges of a cube are expanding at a rate of 6 centimeters per second. How fast is the volume…

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Q: Sand is accumulating in a conical pile with a radius that is always 3 times its height. If the sand…

A: Given: A conical pile with radius 3 times its height. r=3h Rate of change of velocity of sand…

Q: An artist paints a portrait on a circular canvas and encloses it in a circular metal frame. At a…

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Q: A straight 15 meter ladder is left leaning against a wall (which forms a right angle with the…

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Q: A girl is using a straw to drink coke from a right cylindrical glass at a rate of 6 cubic…

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Q: If the area A = s of an expanding square is increasing at the constant rate of 8 square inches per…

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

A: Since, we have been given that all edges of a cube are expandingat a rate of 8 centimeters per…

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

A: Volume of cylindrical shape V=πr2h ------------------(1)

Q: All edges of a cube are expanding at a rate of 9 centimeters per second. How fast is the volume…

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Q: Started at the same time from a very flat surface and 8 mm apart, two snails are vertically climbing…

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Q: As a balloon in the shape of a sphere is being blown up. the volume is increasing at the rate of 4…

A: Given that, Rate of increase of volume, dV/dt = 4 cu.in per sec Value of radius, r = 1 inch

Q: A ladder 13 meters long rests on horizontal ground and leans against a vertical wall. The top of the…

A: Given: A ladder of length 13 m; dadt=0.1 m/s, dbdtb=5m=?

Q: Find the dimensions of the largest rectangle that can be inscribed in an isosceles triangle if one…

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: A 7 foot long snake is crawling along the corner of a room. It is moving at a constant 2/3 foot per…

A: Given Length of snake = 7 feet Speed of snake = 23feet per second We need to calculate the rate at…

Q: All edges of a cube are expanding at a raete of 6 centimeters per second. How fast is the surface…

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Q: The radius of a right circular cone is increasing at a rate of 3 inches per second and its height is…

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Q: Suppose an elastic rubber band is used to make a square, and is being streched (while keeping the…

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Q: The length of the rectangle is increasing at a rate of 5 centimeters per second, and its width is…

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

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Q: The volume of a cube is increasing at the rate of 2 cubic inches per minute. How fast is the surface…

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