A conical glass, 10cm high and 8cm in diameter at the top is filled with an exquisite wine to a depth of 9cm. If a 3cm side (edge) ice cube is added to the cup, use the total differential to decide the validity of the statement that the cup spills.

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: (a) With 10 rectangles using left endpoints, how many rectangles are contributing negative area…

A: Given the function y=2cosx and the interval [-4.02,4.02]. So a=-4.02 and b=4.02. Number of…

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: 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: What must be the measure of ZX in order for ARST to be similar to AxYZ?

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Q: A closed rectangular box is to have an inside length of 8 meters, an inside width of 5 meters, an…

A: We need to find the material needed to make a container.

Q: If each of the dimensions of a rectangular box is measured with an error not exceeding 1%, what i…

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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: The height and base radius of a circular cylinder are measured as 15 cm and 4 cm, respectively, with…

A: Note the formula and result . Volume of cylinder is . Suppose f and g is a differentiable function…

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: The radius of a circular disk is measured and found to be 20cm, with a max error in measurement of…

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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: One side of a right triangle is known to be 20 cm long and the opposite angle is measured as 17°,…

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Q: The length and width of a rectangle are measured as 35 cm and 28 cm, respectively, with an error in…

A: To determine the maximum error in the area.

Q: The edges of a cube are found to be 10cm with an error ± 0.03cm The volume of the cube is then…

A: Let the side of the cube = s = 10 cmError in the side = ds = ±0.03 cmNow,Volume of the cube = V =…

Q: The length and width of a rectangle are measured as 25 cm and 36 cm, respectively, with an error in…

A: Given length of a rectangle, l =25 cm           Width of a rectangle, w=36 cm We know that,  Area of…

Q: The illumination of an object by a light source is directlyproportional to the strength of the…

A: Given that: The illumination of an object by a light source is directly proportional to the strength…

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: The radius of a circular disk is given as 24 cm with a maxi -mum error in measurement of 0.2 cm.(a)…

A: The radius of a circular disk is given as 24 cm with a maximum error in measurement of 0.2 cm. Let…

Q: two metal strips are measured as 6.21cm and 1.529cm  correct to two and three decimals places…

A: Given that: Length of two metal strips are 6.21 cm and 1.529 cm

Q: A snail slid 7 cm down a stalk and climbed 5 cm back up. Hlow far was the snail below its original…

A: Given : A snail moves 7 cm down then moves 5 cm up.

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: 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: 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: A ladder 3.9 m long is placed in a vertical plane which is at right angle to the vertical wall, the…

A: Given :                     The height of the ladder = 3.9m                     Let x…

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: 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: An astronaut using a camera measures the radius of Earth as 4000 mi with an error of ±80 mi. Use…

A: Please see the explanation below

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 country with one of the highest population densities is San Wan​, where approximately 34,000…

A: Population density is the number of people divided by the size of the area. Here, number of…

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: A ball is shot straight up into the air with initial velocity of 47 ft/sec. Assuming that the air…

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Q: The edge of a cube was found to be  60cm with a possible error of 0.1 cm. Use differentials to…

A: The volume of cube, V = x3, where x is the edge of the cube.

Q: A ball is shot from the ground straight up into the air with initial velocity of 42 ft/sec. Assuming…

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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: 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: A computerized spin balance machine rotates a 25-inch-diameter tire at 480 revolutions per minute.…

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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: an ice cube is shrinking uniformly at a rate of 8 cubic inches per hour. when the cube has a volume…

A: We are given the rate of change of volume of ice cube is shrinking uniformly at a rate of 8 cubic…

Q: The measurement of the side of a square floor tile is 10 inches, with a possible error of 1/32 inch.…

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Q: A toxic radioactive substance with a density of 9 milligrams per square cm is detected in the…

A: It is given that, A toxic radioactive substance with a density of 9 milligrams per square cm is…

Q: 7, If a snowball melts so that its surface area decreases at a rate of 3 cm2/min, find the rate at…

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Q: A linear density of a rod of length 16 m is given by p(x)=25sqrt x+4 measured in kilograms per…

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Q: 2. Air is leaking from a spherical-shaped advertising balloon at the rate of 26 cubic feet per…

A: Let r be the radius and v be the volume of balloon, Given dvdt=26 cf/minuteswe know…

Q: The length and width of a rectangle are measured as 38 cm and 34 cm, respectively, with an error in…

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Q: An automobile weighing 4500 lb is driven down a 5° incline at a speed o 60 mi/h when the brakes are…

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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…

Q: the width and length of rectangle are measure in cm as 6 and 18 respectively with an error of at…

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