The length and width of a rectangle are measured with errors of at most 3% and 5%, respectively. Use differentials to approximate the maximum percentage error in the calculated area.

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: 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: 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: A vehicle purchased for $32,500 depreciates at a constant rate of 5% per year. Determine the…

A: purchased cost of vehicle=$32,500Rate of depreciation=55 per yearNumber of years after purchased =10…

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: Explain the method of fitting of an exponential curves of the form (i)Y = abX and (ii) Y = aebx to…

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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: Write expressions for the average rate of change of y with respect to x between a and x and for the…

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Q: Can instantaneous velocity be defined as a ratio? If not, how is instantaneous velocity computed?

A: We know that instantaneous velocity is the average velocity between two points on the path in the…

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: Compute the average rate of change of h(x)=Sqrt(x) over the interval [3, 3+x]. Simplify the…

A: To  Compute the average rate of change of h(x)=Sqrt(x) over the interval [3, 3+x].

Q: 4. Use differential to estimate v15. (3 points total)

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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: Use differentials to estimate the value of V1.3. Compare the answer to the exact value of V1.3.

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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: 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: Find the average rate change of the function between the given values of X.  y= 6+3x+0.5x^2 between…

A: The given function is  f(x) = 6 + 3x + 0.5x2 x = 4, x = 6

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: 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: 1- Find the average rate of change for y == x, = 1 X = 2

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Q: 14. Find the average rate of change of y=x' over the interval [1, 3].

A: According to our terms and conditions I have solved first question for next question repost

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: The radius of a star(spherical) was r=a and was observed to increase by 0.01%. Use a linear…

A: Given data is : Radius(r) of a star (spherical) is increase by 0.01% To find the percentage of…

Q: At a certain moment, an object in linear motion has velocity 100 m/s. Estimate the distance traveled…

A: Given that: At a certain moment, an object in linear motion has velocity 100 m/s To estimate the…

Q: Over which interval does f(x) have a positive average rate of change?

A: Given that: Graph of f(x)

Q: The radius of a sphere is given as 27 cm with a maximum error in measurement of .05 cm. Use…

A: From the given data:Radius of the sphere r=25cmMaximum error in radius of the sphere Δrr=0.05…

Q: A circle has a radius of 5 cm, if the radius is increased by 0.1 mm., what is the estimated increase…

A: Let's find.

Q: use differentials to estimate the amount of metal in a cylindrical can that is 12cm high and 8cm in…

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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 a model for the surface area of a human body is given by S = 0.1094w0.425,0.725, where w is…

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Q: Suppose that the value of a yacht in dollars after t years of use is -0,24t What is the average…

A: Given:- Suppose that the value of a yacht in dollars after t years of use is  V(t) = 150000e-0.24t…

Q: A mothball loses volume by evaporation at a rate proportional to its instantaneous area. If the…

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Q: write a differential formula that estimates the given change in volume or surface area. The change…

A: To write the differential formula that estimates the given change in volume or surface area.

Q: The relationship between stress (o), force (F) and area (A) acting on an object is given as F A Find…

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Q: The heat transfer rate of the rocket engine is given by:

A: Part (a) - Given equation - Q = -kAdTdx        ..........(1)Given that - T(x) = tanxsecx + sinx2k =…

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 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.…

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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 18 cm high and…

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Q: A radioactive element decomposes at a rate proportional to the amount present. The amount remaining…

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Q: QUESTION 2 Estimate the value of V80.9 + V80.9 using differentials.

A: To evaluate : 80.94 +180.94 Let f(x) = x14 Now, we can write 80.9 = 81- 0.1 Take x=81, ∆x=-0.1

Q: Use differential to approximate the value e1.01.

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Q: A body weighing 64 Ib is dropped from a height of 100 ft with an initial velocity of 10 ft/sec.…

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Q: Let ​h(x)=x^2−8x.   ​(a) Find the average rate of change from 4 to 7. ​(b) Find an equation of the…

A: Average rate change and secan line problem....

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

A: We need to choose correct option.