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

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 radius of a right circular cylinder is increasing at a rate of 4 inches per minute, and the…

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Q: find by use of differentials the approximate total area of a right circular cone whose base radius…

A: Given : Right circular cone whose base radius and height are 5.03 inches and 11.89 inches. We know…

Q: Use differentials to estimate the amount of paint needed (in m3) to apply a coat of paint 0.06 cm…

A: Given information: The diameter of the hemisphere is 52 m that means the radius is 26 m. Formula…

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: A cube is heated in such a way that the volume increases at a rate of 1 mm/s. The rate of change of…

A: A cube is heated in way that volume increases at the rate of 1mm/s. the side of the cube is 7mm…

Q: the circumference of a sphere was measured to be 100 mm with a possible error of 0.4 cm. use the…

A: The circumference of a sphere with radius r is  given as C = 2 π r  and the surface area is given by…

Q: the radius of a circle is increasing at a constant rate of 100 meters per second. at what rate is…

A: First of all, consider the area for the circle.Then differentiate on both sides of equation w.r.t…

Q: The side of an equilateral triangle was measured to be 233 cm with at most possible error of 0.5 cm.…

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Q: The area of an equilateral triangle is decreasing at a rate of 4 sq. cm. per minute. Find the rate…

A: Given,dAdt=-4 cm2/minA=100cm2Let,x=side of the equilateral triangle find dxdt when dAdtis decreased…

Q: A potter forms a piece of clay into a cylinder. As he rolls it, the length, L, of the cylinder…

A: Differentiate volume wrt t

Q: A woman 1.5 m tall walks directly away from a street light which is 6 m above the ground at a rate…

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Q: Use differentials to estimate the amount of tin in a closed tin can with diameter 8 cmand height 12…

A: Given : Diameter of tin = 8 cm. Height of tin = 12 cm. Thickness of tin = 0.04 cm.   To estimate…

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

A: Answer: 40π cm³ or 125.66 cm³

Q: Use differentials to estimate the amount of paint needed to apply a coat of paint .05 cm thick to a…

A: Using differential to estimate the amount of paint needed to apply a coat of paint of 0.05cm thick

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: If we know the rate of growth of a patch of moss, how can we calculate the area the moss covers?

A: The rate of growth of a patch of moss is modeled by a complex function A't, where t is measured in…

Q: A man 2 mts high walks at a uniform speed of 6 km / h away from a lamp post 6 mts high. Find the…

A: According to the question,   To sketch the figure of the given condition,

Q: A right circular cone has a base radius of 6 feet and slant height of 10 feet. If the approximate…

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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: One airplane is approaching an airport from the north at 203 km/hr. a second airplane approaches…

A: Let in the below figure P represents the airport, Q represents the southbound plane and R represents…

Q: A patient's blood is traveling at a rate of 16 mL/sec while conveying a medicine into the liver and…

A: so, initially, liver is full at t = 0, but has no medicine,  medicine rich blood comes in, mixes…

Q: The pressure difference of the two ends of a small pipe of cross-sectional radius x is given by P =…

A: Here in this question we have to find change in pressure across pipe given change in radius.

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: A potter forms a piece of clay into a cylinder. As he rolls it, the length, L, of the cylinder…

A: Here, the amount of the clay is fixed. dVdt=0...(1) Now, the volume of the cylinder is given by:…

Q: Use differentials to estimate the amount of paint needed to apply a cost of paint 0.06 cm thick to a…

A: It is given that a paint cost 0.06 cm is applied to a hemispherical dome whose diameter is 54 m.…

Q: A rectangle's length is increasing at the rate of 5 inches/sec, its width at 2 inches/sec. At what…

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Q: a hemischperical dome has a diameter of 50 m. use differentials to estimate the amount of paint…

A: the problem concerns an application of differentials

Q: A 25,000 machiene depreciates linearly to 0 over a ten year period.What is the value of the machiene…

A: The Initial value of machine is 25000 and its depreciates linearly to 0 over a ten year period. We…

Q: A bacteria culture is known to grow at a rate proportional to the amount present. If the population…

A: This is a problem of the application of differential equations.

Q: A right triangle has legs of 18 inches and 24 inches whose sides are changing. The short leg is…

A: A right triangle has legs of 18 inches and 24 inches. The short leg is decreasing by 3 in/sec. The…

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: 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 & ∆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: Use differentials to estimate the amount of paint needed to apply a coat of paint 0.05 cm thick to a…

A:

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

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Q: Use differentials to approximate the quantity   √99.7

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Q: The radius of a circle is increasing at a constant rate of 0.2 meter per second. What is the rate of…

A: Given Where r is radius. and

Q: Use differentials to estimate the amount of paint needed (in m³) to apply a coat of paint 0.07 cm…

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Q: Use differentials to estimate the amount of paint needed toapply a coat of paint 0.05 cm thick to a…

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Q: The length { of a rectangle is increasing at a rate of 9 cm/sec while the width w is decreasing at a…

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Q: Use differentials to approximate the change in the BMI when weight increases from 55 to 56.5 kg and…

A: Let's find.

Q: In your own words, explain what a differential is, and what it's used for.

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Q: After an hour, the population of bacteria with a number of P0 found that their number became 3 /…

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Q: Use differentials to estimate the amount of tin in a closed tin can with diameter 12 cm and height…

A: The volume of a cylinder is given by the expression . Thus the volume of a thin cylinder is obtained…

Q: When a metal plate is heated, it expands. If the shape of the plate is circular and its radius is…

A: When a metal plate is heated, it expands. If the shape of the plate is circular and its radius is…

Q: Use differentials to estimate the amount of tin in a closed tin can with diameter 6 cm and height 20…

A: Since volume is a function of both radius and height, therefore we will use method of partial…