Four positive numbers, each less than 80, 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: 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: Suppose a metal rod has length 20 cm and diameter 6 cm. If it is to be insulated, except for the…

A: Let the volume of the rod be V Radius of the rod be R and length be L Given: L=20cm; R=3 cm…

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

A:

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 width and length of a rectangle are measured to be 3 m and 5 m, respectively. These come with an…

A:

Q: 3. The edge of a cube is measured to be 6 inches with a possible error of ±0.1 inch. Estimate the…

A: The error in measuring the edge of the cube is 0.1 inches. to find the error in the surface area and…

Q: A 20 kg wagon moving at a speed of 0.5 m/s towards right collides with a 35 kg wagon which is at…

A: Solution:

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: The radius of a circular disk is measured and found to be 20cm, with a max error in measurement 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: 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: Use an appropiate linear approximation to estimate the value of In(1.01). Compare your approximation…

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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: 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: 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: If the radius of a circle increases by 3%, use differentials to approximate the increase in the area…

A: radius of a circle increases by 3%,

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: 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

A:

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: Under certain conditions, cane sugar in water is converted into dextrose at a rate proportional to…

A: Given: when the initial time t=0 amount of the cane sugar is 75 kg, and the time t=30 minutes amount…

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,…

A:

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: 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°…

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

A: a. let the hypotenuse of the triangle is h. so using the trigonometric ratio formula,…

Q: A painting contractor charges Php 120 per sq.m. for painting the four walls and ceiling of a room.…

A:

Q: Four positive numbers, each less than 130, are rounded to the first decimal place and then…

A: Let p,q,r,s be the four positive numbers and their product be w

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: Use differentials to estimate the amount of metal in a closed cylindrical can that is 18 cm high and…

A:

Q: The measurement of the radius of the end of a log is found to be 28 inches, with a possible error of…

A: Solution:- It is given that the radius of the end of a log=28 inches. ⇒r=28 inches possible…

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

A:

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

A: Given: 10013 or 100113

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: Use a linear approximation to estimate V8.05.² Show relevant work to explain your reasoning.

A: Linearization: If y = f(x) is differentiable function at x = a, then linear approximation at the…