Four positive numbers, each less than 130, are rounded to the first decimal place and then multiplied together. Use differentials to estimate the maximum possible error in the computed product that might result from the rounding.

Q: The length, width, and height of a rectangular box are measured with an error of at most 5%. Use a…

A: Differentiate diagonal and use error

Q: Use differentials to approximate the value of 52.1. 100+ 5ln5 50+ 6ln5 50+ 5ln5 2 100+ 6ln5 4

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Q: Each side of an equilateral triangle measures 3 cm, with a possible error of 0.1 cm. Using…

A: This question is taken from the differentiation in which we have to find the relative error in the…

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

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Q: coat of paint of thickness 0.07 cm is to be applied uniformly to the faces of a cube of edge 40 cm.

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Q: One side of a right triangle is known to be 20 cm long and the opposite angle is measured as 17°,…

A: We have to estimate the error in computing the length of the hypotenuse.

Q: A wooden rectangular box is to be made having dimensions 3 ft, 4 ft, 5 ft. The cost of the wood to…

A: From the given information, the length, width and height is 3 ft, 4ft, 5ft respectively. The given…

Q: The height and base radius of a circular cylinder are measured as 15 cm and 4 cm, respectively, with…

A: Note the formula and result . Volume of cylinder is . Suppose f and g is a differentiable function…

Q: Jse differentials to approximate 47. (Express as a rational number.)

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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: The side of a square floor tile is measured to be 20 inches, with a possible error of 1/32 inch. Use…

A: The given question is of the application of derivative where x=20 inches, and dx= 1/32 inches given.…

Q: 5. Gordon is making a chocolate dome by coating a plastic dome with a layer of chocolate 2 mm thick.…

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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: 3. Use differentials to estimate the value of 10 - (0.98) correct to two decimal places.

A: Please see the below picture for detailed solution.

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

A: Given that the side length of a cube is 5 cm with an accuracy of 0.1 cm Volume of a cube=side…

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: The length and width of a rectangle are measured as 35 cm and 28 cm, respectively, with an error in…

A: To determine the maximum error in the area.

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: The base radius r and height h of a right circular cone is measured as 5 inches and 10 inches,…

A: The volume of a right circular cone is given as, V=13πr2h The volume of the cone is a function of…

Q: One side of a right triangle is known to be 20 cm long and the opposite angle is measured as 30°,…

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Q: An open cylindrical tank is to have an outside coating of thickness 2cm. If the inner radius is 6cm…

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Q: he measurement of the radius of the end of a log is found to be 20 inches, with a possible error…

A: Given that: Radius of log, r=20 inError in measuring radius, dr=18 in

Q: 5. Use differentials to approximate V4 + In(1.2) correct to two (2) decimal places.

A: Let us take the function f(x)= √x f'(x)=1/(2√x) f(x+Δx)=f(x) + f'(x) . Δx   ___i) Here let us…

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

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Q: Use differentials to approximate the value of: 26

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Q: The length and width of a rectangle are measured as 89 cm and 22 cm, respectively. The error in…

A: According to the given information:Length of rectangle (l) = 89cmWidth of rectangle (b) = 22cmError…

Q: A coat of paint of thickness 0.04 cm is to be applied uniformly to the faces of a cube of edge 30…

A: Given that a coat of paint of thickness 0.04 cm is to be applied uniformly to the faces of a cube of…

Q: complete solution

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Q: Jesaki Inc will sell N units of product after spending $x thousand in advertising, as given by  N=…

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Q: A square is measured and each side is found to be 8 inches with a possible error of at most 0.01…

A: We are given that each side of a square is 8±0.1. Let x be the side of square and then the side of…

Q: A certain cube with side equal to 5 inches is said to have an incremental error of 0.1 inch in its…

A: Topic :- Application of Derivative  Volume of cube = (side)3

Q: Suppose the measurement of the side of a square is to be 30 cm with an error of 0.03 cm. Use…

A: Definition used -      Error in area of the square -                 ∆A=2x∆x          Here x is…

Q: The base radius and height of a right circular cone are measured as 10cm and 25cm, respectively,…

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Q: Give 1 problem application of differential

A: We have to explain a real life example of differential equation.

Q: Use differentials to approximate √16.5.

A: Given:

Q: 5. Use differentials to estimate 3.99 + (3.99)3 correct to two decimal places.

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

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

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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 two legs of a right triangle are measured as 5 m and 12 m with a possible error in measurement…

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

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Q: Use a linear approximation (or differentials) to  estimate the given number.    cube root of 1001

A: Given: 10013 or 100113

Q: Four positive numbers, each less than 80, are rounded to the first decimal place and then multiplied…

A: Solve the given problem.

Q: Estimate the value of V83251.69 in three decimal places by linear approximation.

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

Q: A conical glass, 10cm high and 8cm in diameter at the top is filled with an exquisite wine to a…

A: Find the sum of volume of the wine and ice cube and compare with the total volume of the conical…

Q: Use linear approximation or differentials to estimate v80. Show your work.

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Q: One side of a right triangle is known to be 20 cm long and the opposite angle is measured as 30 °,…

A: Given,  The one side of a right triangle is 20 cm long and the opposite angle is measured as 30°,…

Q: The length and width of a rectangle are measured as 38 cm and 34 cm, respectively, with an error in…

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Q: the width and length of rectangle are measure in cm as 6 and 18 respectively with an error of at…

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