Suppose the side length of a cube is measured to be 5 cm with an accuracy of 0.1 cm. a. Use differentials to estimate the error in the computed volume of the cube. b. Compute the volume of the cube if the side length is (i) 4.9 cm and (ii) 5.1 cm to compare the estimated error with the actual potential error.

Q: The edge of a cube was found to be 20 cm with a possible error in measurement of 0.2 cm. Use…

A: As we know that; The expression for the volume of the cube is: V=a3    ....(1) Where a is the edge…

Q: One side of a right triangle is measured as 9.5 inches and opposite angle equal to 26.75° with 0.25°…

A:

Q: The edge of a cube was found to be 107 cm with a possible error in measurement of 0.03 cm. Use…

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Q: A cylinder object has radius 2 cm and height 3 cm. Use differentials to approximate the error…

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Q: The length and width of a rectangle are measured with errors of at most 3% and 5%, respectively. Use…

A: Let the length and width of a rectangle are L and W respectively. Now, The length and width of a…

Q: One side of a right triangle is measured as 9.5 inches and opposite angle equal to 26.75° with 0.25°…

A: Given : θ = 26.75°

Q: The dimensions of a closed rectangular box are measured as 93 cm, 66 cm, and 50 cm, respectively,…

A: Given,           The dimensions of a closed rectangular box are measured as 93 cm, 66 cm…

Q: Use differentials to estimate the amount of metal in a closed cylindrical can that is 14 cm high and…

A: *given:- radius of the cylindrical can, R = 6/2 = 3 cm height of the cylindrical can, h = 14 cm

Q: A person measures the side of a cube as being 10 inches and thus calculates the volume of the cube…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Find the generol solution of the differential eguotion given below,

A:

Q: Write the differential formula that estimates the given change in volume or surface. Then, use the…

A: Let y=f(x) be a differential function.  differential dx  is an independent variable.  the…

Q: Use differentials to approximate the increase in the area of a soap bubble when its volume increases…

A: Let the radius of the soap bubble be a cm, then the volume of the soap bubble is: V=43πr3        And…

Q: A cylindrical shell has a thickness of 0.2 cm. Using differentials, approximate the volume of the…

A: The solution are next step

Q: For a given triangle, side y is measured as 10 cm, the horizontal side x as 20 cm and the included…

A: Concept: Estimating error using differentials: ∂A=∂A∂a∂a+∂A∂b∂b+∂A∂θ∂θ Here A is the area of the…

Q: Recall that the volume of a right circular cylinder of radius r and height h is V = r’h. Suppose…

A:

Q: Use differentials to estimate the relative error in the lateral surface area of a right circular…

A: Relative error

Q: A spherical ball is measured to have a radius of 6 cm with a possible measurement error of ±0.1rmcm.…

A:

Q: 3. A certaincubewithsideequalto5 inches issaidtohavean incremental error of 0.1 inch in its side.…

A:

Q: The altitude of a certain circular cone is the same as the radius of the base, and is measured as 5…

A:

Q: Suppose the side length of a cube is measured to be 5 cm with an accuracy of 0.1 cm. Use…

A:

Q: The radius of a star(spherical) was r=a and was observed to increase by 0.01%. Use a linear…

A: Given data is : Radius(r) of a star (spherical) is increase by 0.01% To find the percentage of…

Q: The radius of a sphere is given as 27 cm with a maximum error in measurement of .05 cm. Use…

A: From the given data:Radius of the sphere r=25cmMaximum error in radius of the sphere Δrr=0.05…

Q: The dimensions of a closed rectangular box are measured as 97 cm, 60 cm, and 30 cm, respectively,…

A: Let the dimensions of the box be l, w and h (for length, width and height).Surface area of the box…

Q: The radius of a circular disk is measured as 24 cm with a maximum error of 0.2 cm. By the…

A: The radius of a circular disk is measured as 24cm with a maximum error of 0.2 cm.

Q: The radius of a circular disk is given as  28cm with a maximum error in measurement of 0.3 cm. Use…

A:

Q: Use differentials to estimate the relative error in the lateral surface area of a right circular…

A: To find out the relative error in the lateral surface area of the cylinder.

Q: An astronaut using a camera measures the radius of Earth as 4000 mi with an error of ±80 mi. Use…

A: Please see the explanation below

Q: The edge of a cube was found to be 30 cm with a possible error in measurement of.1 cm. Use…

A: Consider the edge length of the cube is a , so the volume of the cube is: V=a3 The surface area of…

Q: The edge of a cube was found to be 20 cm with a possible error in measurement of 0.2 cm. Use…

A:

Q: write a differential formula that estimates the given change in volume or surface area. The change…

A: To write the differential formula that estimates the given change in volume or surface area.

Q: The dimensions of a closed rectangular box are measured as 88 cm, 53 cm, and 32 cm, respectively,…

A: Given: The dimensions of closed rectangular box is : =88cm×53cm×32cm

Q: The measurement of the radius of the end of a log is found to be 13 inches, with a possible error of…

A:

Q: One side of a right triangle is measured as 9.5 inches and opposite angle equal to 26.75° with 0.25°…

A:

Q: The measurement of the radius of the end of a log is found to be 17 inches, with a possible error of…

A:

Q: For small, slowly falling objects, the assumption made in the text that the drag force is…

A:

Q: The radius of a circular manhole cover is estimated to be 16 in. with a maximum error in measurement…

A: Due to our guidelines I am solving only first problem  The radius of circular manhole r = 16 in

Q: The measurement of the radius of the end of a log is found to be 5 inches, with a possible error of…

A: Given : Radius of end of log is 5 inches. Possible error ½ inches The end of log is in the shape of…

Q: The dimensions of a closed rectangular box are measured as 74 cm, 51 cm, and 50 cm, respectively,…

A: For a function y=fx, ∂y,∂x,dy and dx represents partial derivative of y and x and then differential…

Q: The length of the side of a square floor tile is 15 cm, with a possible error of 0.05 cm. Using…

A:

Q: Suppose a metal rod has length 20 cm and diameter 6 cm. If it is to be insulated, except for the…

A: Given: length,h=20 cmd=6 cmdr=0.001dV=?

Q: According to the Ideal Gas Law, the pressure P, temperature T, and volume V of a confined gas are…

A: We have to use differentials to approximate the percentage change in pressure if the temperature of…

Q: A goldsmith is tasked to coat a closed rectangular box with gold 0.1 cm thick. The height of the box…

A:

Q: The radius of a circular disk is measured as 24 cm with a maximum error of 0.2 cm of the disk.

A:

Q: One side of a right triangle is measured as 9.5 inches and opposite angle equal to 26.75° with 0.25°…

A:

Q: Suppose the side length of a cube is measured to be 5cm with an accuracy of 0.1cm. a) use…

A:

Q: The edge of a cube was found to be 30 cm with a possible error in measurement of .1 cm. Use…

A: Topic = Derivative

Q: Use differentials to estimate the relative error in the lateral surface area of a right circular…

A:

Q: A sphere is measured and the radius is 5 inches with a possible error of at most 0.02 inches.…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: One side of a right triangle is measured as 9.5 inches and opposite angle equal to 26.75° with 0.25°…

A: We need to choose correct option.