A square is measured and each side is found to be 8 inches with a possible error of at most 0.01 inches. Use differentials to find the approximate error in computing the area of the square.

Q: An engineering instrument is able to measure the side of a square to within ±0.05 mm (dr). First,…

A: Assume the area to be A and the side length be a. Use the derivative to determine the error dA for a…

Q: The measurements of the base and altitude of a triangle are found to be 36 and 50 centimeters,…

A: Let base= B  Altitude= H Given that B= 36 , H=50 , dB=0.25 , dH=0.25

Q: A circular plate is measured to have a diameter of 3.5 feet if the measurement could be off by as…

A: Given, The diameter of the circular plate,d=3.5feet The radius of the circular…

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

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

Q: The measurement of the edge of a cube is found to be 15 inches, with a possible error of 0.03 inch.…

A: Let ‘x’ be the edge of cube. Then

Q: he measurements of the base and altitude of a triangle are found to be 38 and 42 centimeters,…

A: The solution is :

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 ball 6 inches in diameter is to be covered by a rubber material which is in-thick. Using…

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Q: The measurements of the base and altitude of a triangle are found to be 24 and 42 centimeters,…

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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°…

A: Given : θ = 26.75°

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: 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: 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: Hello! Can you help me with this calculus problem? I think I got something very wrong.

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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°,…

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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: A hollow cylinder has a radius R of the outer surface, radius r of the inner surface and height h.…

A: Given, a hollow cylinder has a radius (R) of the outer surface, radius(r) of the inner surface and…

Q: The measurements of the base and altitude of a triangle are found to be 20 and 60 centimeters,…

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

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Q: Use differentials to estimate the amount of metal in a closed cylindrical can that is 30 cm high and…

A: Given a closed cylindrical can has height 30 cm and 6 cm is diameter. the metal in the top  and…

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: Use differentials to approximate the value of: 26

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Q: Use differentials to approximate v410, and then compare your approximation with the actual answer…

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Q: The measurement of the side of a square floor tile is 16 inches, with a possible error of 86 nch Use…

A: we know the area of square is x^2.

Q: complete solution

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Q: Estimate V65 using Newton's method with an accuracy of ɛ < 0.001

A: Newton's method uses the formula, xn+1=xn-f(xn)f'(xn) to perform the iteration.

Q: V9.22

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Q: Find the approximate surface area of a sphere of radius 5.02 cm. (SOLVE BY USING DIFFERENTIAL…

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Q: The measurements of the base and altitude of a triangle are found to be 26 and 44 centimeters,…

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Q: The inside radius of a pipe is 4.50 cm. By using differentials, find the approximate volume of metal…

A: According the problem, we have

Q: 7. The raidus of a circle is equal to 4m and is measured with an error of ±0.5m. Use differentials…

A: Given: The radius of the circle is 4m and with an error ±0.5m To find the relative error ∆AA≈dAA "As…

Q: Use differentials to approximate the change in the area of a square if the length of its side…

A: Area of a square with a side length of x cm is, Ax=x2 Here, x=5 cm &amp; ∆x=5.32-5=0.32 cm Now…

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°…

A:

Q: Use a linear approximation (or differentials) to estimate the number V100.5

A: To find 100.5Let y=xLet x=100 and ∆x=0.5⇒y=100y=10Differentiate…

Q: The outside diameter of a thin spherical shell is 12 feet. If the shell is 0.3 inch thick, use…

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

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Q: Compute the approximate value using differentials. /272 √234 The final answer should be in fractions…

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Q: Use a linear approximation (or differentials) to estimate the given number. 99.6

A: Given query is to perform linear approximation on given redical.

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 measurements of the base and altitude of a triangle are found to be 38 and 56 centimeters,…

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Q: 6. The length of a rectangular yard is measured to be 84 feet and the width to be 36 feet. If the…

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Q: Match the graph with the first order differential

A: In this question we will use basic concepts of calculus i.e graphing of differential equation.…

Q: If a current I passes through a resistor with resistance R ,Ohm’s Law states that the voltage drop…

A: Given the ohm's law relationship that is V=IR , where V is the voltage , R is the resistance and  I…

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: a machinist is required to manufacture a square metal plate with the side length of 5cm.  if the…

A: The length of the metal plate is x=5cm. The machinist is allowed an error of 0.3 cm. The area of the…