A manufacturer produces a triangular lamina with a standard base and height of 30 cm and 12 cm, respectively. However, due to errors in measurements, the base and height measurements can be off by at most 0.1 cm. Use differentials to estimate the maximum error in the calculated area of the triangle

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

A: The volume of the cylindrical shell is given by V=2πrh∆r, where ∆r is the thickness of the shell.…

Q: The dimensions of a closed rectangular box are measured as 90 centimeters, 80 centimeters, and 60…

A: Given: The dimensions of a closed rectangular box are measured as 90 centimeters, 80 centimeters and…

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

A: The solution is :

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

A:

Q: The radius of a spherical balloon is measured to be 9 inches, with a possible error of 0.03 inch.…

A: we know that  surface area of sphere =4pi r^2 where r is the radius of sphere  Given radius of…

Q: (a) Use differentials to approximate the possible propagated error in computing the area of the…

A:

Q: The roots of Characteristic equetion of a thrrd oreler, lineor homapeneous-equation with constaut…

A: Consider homogenous differential equation with constant coefficient:…

Q: The possible error involved in measuring each dimension of a right circular cone is + inch. The…

A: The propagated error dV = V'(r)dr, here dr = +0.1 or -0.1 inch and r = 4 inches.

Q: The radius of a circular disk is given as 20 cm with a maximum error of 0.3 cm. (a) Use…

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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 radius of a circular disk is given as 20 cm with a maximum error of 0.3 cm. a) Use differentials…

A: GIVEN The radius of a circular disk is given as 20 cm with a maximum error of 0.3 cm we need to find…

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

A:

Q: The edge of a cube was found to be 30 cm with a possible error in measurement of 0.1 cm. Use…

A: Given: The edge of a cube, x=30 cm The error in measurement, ∆x=0.1 cm

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: Use differentials to determine the approximate area, dA, of a circular ring which has an inside…

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

A:

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

A: The measurement of the side length is accurate to within 0.1 cm. Therefore,  -0.1≤dx≤0.1  The volume…

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 dimensions of a closed rectangular box are measured as 80 centimeters, 60 centimeters, and 100…

A: Let the dimensions of a closed rectangular box are: Length=L=80 cmWidth=W=60 cmHeight=H=100 cm And…

Q: The diameter of a circular disk is measured as 30 cm with a maximum error in measurement of 0.2 cm.…

A: Given that :- Diameter = 30 cm , error = 0.2cm Area of circular disk = πr2 . Where ( r = d/2) So ,…

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

A: Solution.

Q: the length and with of the rectangets are measured at 29 am and 12 cm respectively, with a maximum…

A: It is provided that the length and width of a rectangle are l=29 cm, w=17 cm, respectively. The…

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

A:

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

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: 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: While measuring the side of a cube, the percentage error incurred was 3%. Using differentials,…

A:

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

A: Volume of a sphere with radius r is V=43πr3

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 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: 6. The radius of a sphere is measured to be 7 cm, with a possible error of + (1/10) cm. Estimate the…

A: Volume of sphere   V=3π​r3/4 Percentage error in volume    ΔV​×100/V=3×Δr​×100/r =3*1*100/10*7= 4.3…

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

A:

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

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: Use differentials to estimate the maximum error in the volume of a rectangular box with square base…

A: Here we find the error in volume by using differential.

Q: The radius of a circular disk is given as 27 cm with a maximum error in measurement of 0.2 cm. Use…

A:

Q: The radius of a circular disk is given as 28 cm with a maximum error in measurement of 0.2 cm. Use…

A: Write the expression for the area of the circle and take the derivative.