Find the length of the edge of the cube, if an edge is increasrd by 6 dm, another edge has a 12 dm increase and the third one decreases by 4 dm, results to 100% increase of its original volume. (With complete solution)

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

A: Surface area of cube = 6x2Where x is the edge of the cube

Q: The edges of a cube increase at a rate of 2cm/s. How fast is the volume changing when the length of…

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Q: # 3) Each side of a square is increasing at a rate of 6cm/s. At what rate is the area of the square…

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

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Q: All edges of a cube are expanding at a rate of 2 centimeters per second. (a) How fast is the surface…

A: We have given change in edge with respect to time is 2cm/sec.  We have to find the changes in…

Q: A tank contains 1000L of brine with 16kg of dissolved salt. Pure water enters the tank at a rate of…

A: Given: A tank contains 1000L of brine with 16kg of dissolved salt. The pure water enters the tank at…

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

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Q: A gas in a container has an initial volume of 7L and an unknown temperature. The final temperature…

A: Given,Initial volume of a gas container, V1 = 7LFinal volume of a gas container, V2 = 12LFinal…

Q: The volume of a cube decreases at a rate of 10 m3/s. Find the rate at which the side of the cube…

A: We have to find rate  of change of side of cube .dV/dt  is negative beacuse it is…

Q: 2. All edges x of a cube are expanding at a rate of 8 centimeters surface area changing when each…

A: To solve the following problem, we use the given formula if S is equal to surface area then S = 6x2…

Q: If the length of the edge of a cube is increasing at a rate of 3cm/s, how fast is the volume of the…

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

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 rectangle is l cm and width is w cm area of rectangle is(A) =lxw differentiate…

Q: All edges of a cube are expanding at a rate of 5 centimeters per second. (a) How fast is the volume…

A: Rate of expansion of edges of a cube= 5 cm/sec

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

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Q: The base of a triangle is shrinking at a rate of 6cm/s and the height of the triangle is increasing…

A: The rate of change of the area with respect to time is the derivative of the area function with…

Q: 3. Each side of a square is increasing at a rate of 6 cm/s. At what rate is the area of the square…

A: Area of the square is increasing at a rate of  48cm2/sec.

Q: The volume of a cube is increasing at a rate of 10 cm/min. How fast is the surface area increasing…

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Q: The surface area of a spherical snowball is increasing at a rate of 9 mm2/min. Find how fast the…

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Q: Water in a canal, 30 dm wide and 12 dm deep is flowing with vel ocity of 10 km/ha How much area will…

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Q: The volume of a cube is increasing at a rate of 60 in3/sec. At what rate is the length of each edge…

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

A:

Q: 5. The volume of a cube is increasing at a rate of 10 cm³/min . How fast is the surface area…

A: Given:- The volume of a cube is increasing at a rate of 10 cm³/min. To find:- How fast is the…

Q: The radius of a spherical ball is increasing at a rate of 2 cm/min. At exactly what rate (in…

A: Rate of increase of radius of a spherical ball,drdt= 2 cm/min Radius of the ball = 9 cm

Q: The length of a rectangle is increasing at a rate of 9cm/s and its width is increasing at a rate of…

A: To Determine: How fast is the area of the rectangle increasing? Given: we have the length of a…

Q: The volume of a cube decreases at the rate of 74 m³/ sec. The rate at which the side of the cube…

A:

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

A: Rate of change of surface area is given by ds/dt = a . dA/dt Where a = edge length dA/dt =rate of…

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: shrinking

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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: An edge of a variable cube is increasing at the rate of 10cm/sec.How fast the volume of the cube is…

A:

Q: At 1800 hours an IV is infusing at a rate of 10 gtt/min. How much can you expect the patient to…

A: The drop factor is the term that defines the number of drops of an infusion that constitutes 1 mL.…

Q: The radius of a spherical ball is increasing at a rate of 2 cm/min. At exactly what rate (in…

A: Given :radius of spherical ball is increasing at a rate of 2cm/minso, drdt=2cm/min

Q: A swarm of bees is spreading from an original region of 1 square mile. The region the swarm occupies…

A: Given that the original region of 1 square mile.  After 1 year area will be 2(1)=2=21 square miles…

Q: 3. The volume of a cube is increasing at the rate of 6 cm³/min. How fast is the surface increasing…

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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…

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Q: how long will it take $800 to triple if it is invested at an annual intrest rate of 5.3%

A: P=$800 , R=5.3%

Q: The volume of a cube is increasing at a rate of 56 in3/sec. At what rate is the length of each edge…

A: It is given that volume of cube V=x3 rate of volume increasing at dVdt=56 in3/sec The edge of the…

Q: The volume of a cube is increasing at the rate of 4cm³/min. How fast is the surface area increasing…

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Q: Acar traveling 25 m/s begins to decelerate at a constant rate of 4 m/s2. After how many seconds does…

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

A:

Q: Sodium chlorate crystals are easy to grow in the shape of a cube by allowing a solution of water and…

A:

Q: A nurse gives 1,100 mL of an intravenous (IV) solution over a period of 9 h. It is given first at a…

A: Suppose, the time taken at a rate of 140 mL/h is x and the time taken at a rate of 100 mL/h is y.…

Q: All edges of a cube are expanding at a rate of 3 centimeters per second. (a) How fast is the volume…

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Q: 18 Show that the volume V of a regular tetrahedron, all of whose side lengths are s, is V = s°V2…

A: Given that the volume of a tetrahedron is: 1442cm3 So, V=112s32 So, 112s32=1442⇒s3=123⇒s=12

Q: The original 24 m edge length x of a cube decreases at the rate of 4 m/min. a. When x = 3 m, at what…

A: Given query is to find rate of change of surface are and volume when rate of chnage edge length is…

Q: The volume of a cube increases at the rate of 59m3/sec The rate at which the side of the cube…

A:

Q: A circular pool of water is expanding at the rate of 16pi in^2/sec. At what rate is the radius…

A: expanding at the rate of 16pi in^2/sec of circular loop rate is the radius expanding if radius…