For this weeks reflection please explain how you can use a triple integral to determine the volume of a rectangular box. Don't just provide the integral but also give an explanation in your own words on why the integral determines the volume. Volume length width height

Q: 1 D 1 4 -1 -2 (b) Your friend attempted part (a) and obtained a negative value. "That doesn't make…

A: As per the question we have to find the double integral analytically and deduce that the value is…

Q: The equation y^2+(x-2)^2=1 is the equation of a circle of radius 1 centered at (2,0). Rotating it…

A: The equation y2+(x-2)2=1 is the equation of a circle of radius 1 centered at (2,0). Rotating it…

Q: 4. SET-UP the double integral that solves for the volume of the solid: *+2 = 4 2 +y = 4

A: Given that

Q: Give an equation representing the area of the strip you would use in a Riemann sum representing the…

A: Let, the length of the strip = wThen the pythagoruse theorem gives, h2 + w22 = 72 ⇒ w = 249 -…

Q: Textbook D Videos [+] Evaluate the integral below by interpreting it in terms of areas. In other…

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Q: Read all directions and answer the questions the best that you can. and reasonable work is expected…

A: Solving Part(1) To determine: Volume of the solid obtained by rotating  y=x2+2 andy=6…

Q: 3. The base of a solid S is a circle with equation g2 +y? = 9. The parallel cross- %3D sections…

A: Consider the given equation of the circle x2+y2=9, that is, r= 3 since the general form of the…

Q: Recall from the Volume and Average Value section in the previous chapter that volume could be found…

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Q: 5. SET-UP the double integral that solves for the volume of the solid: 3 3x+ 2y+ 4z 12

A: The solid is bounded by the triangle and the planes x=0,y=0, z=0

Q: Write an example (applications) that explain, how triple integrals can be used on communications?…

A: See the attachment

Q: Evaluate the integral. Please specify the formula or equation you used to answer the question. Thank…

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Q: Identify the expression below that represents the volume of the solid obtained by rotating about the…

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Q: Find the volume of the region between the cylinders a? + y? = 49 and a? + z? = 49. %3D %3D

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Q: www ......... ....... Write and evaluate the definite integral that represents the volume of the…

A: Given; So, y=25-x2y2=25-x22y2=25-x2x2=25-y2x=±25-y2   Use the disc method to calculate the area of…

Q: Evaluate the integral. Please specify the formula or equation you used to answer the question. Thank…

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Q: Let A be the area in the first quadrant boundedby the y-axis, the curve y = z 2, and the curvey -z2…

A: Given: the curves y = x2 and the curve y = 12 x2 + 4  To Find: The volume obtained by rotating this…

Q: (30z² – 16 dr Evaluate the integral:

A: The given integral is ∫30x2-16x4dx. Apply trigonometric substitution: x=4secu⇒dx=4secutanudu…

Q: Calculate the volume of the body of revolution we get by rotating R about the x-axis.

A: Given lines are: y=x-4 and y=x-2. The intersection point of these two lines is:…

Q: 6.) y = x³ + 1, y = 0, x = 1 around x = 2.

A: Shell method: Let a region R is bounded by the vertical axis x=a and x=b and let g(x) represents the…

Q: Y = 5x , Y = X^5,  around 15   Rotate this region about a horizontal or vertical line that is NOT…

A: Consider the provided question, Given equation of the curve y=5x, y=x5  around 15 We need to rotate…

Q: write a triple integral that calculates the volume for a quadratic surface  estimate the volume to…

A: Let's Solve,

Q: The shape below is rotated around the x-axis. Calculate the volume of the shape that is created.…

A: given shape is rectangle. now if this rectangle rotated around x-axis then it will make cylinder…

Q: a) Write the integral(s) that you would use to find the area of the region. b) Write the integral(s)…

A: Definition used -       The area between the two curve f(x) and g(x)-…

Q: Michael feel a plastic ball with air until it is a sphere with a radius of 6 cm what is the volume…

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Q: Find the volume obtained by rotating the region between the curves y = 3x and y = x² about the line…

A: Answer is : 22.5 pi  or 70.6858347058

Q: (c) Find the surface area of this torus. Hint: You will need to write down formulas for the surface…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: csc³ ÷w cot³ ÷w dx 4 4 3

A:

Q: In the diagram, the purple solid S is a portion of a sphere cut off by a plane. S R Find a formula…

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Q: / Fullscreen 2. Find the area between the parabola y = x² – 1 and the line y = x + 5. Use…

A: We have to find the area between the parabola y=x2-1 and the line y=x+5 .

Q: Sketch the region of integration and evaluate the following integral by re-

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Q: Find the area of the region enclosed by the curves y = x and y = x2, over 0 < x < 2.

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Q: 5. Evaluate the improper integral: op- -20 1+e

A: It is improper of first kind, limit if integration is infinity

Q: A torus is formed by revolving the region bounded by the circle x? + y? = 49 about the line x = 8…

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Q: Write, but do not evaluate, an integral expression that gives the volume of each solid. The base of…

A: Here, the objective is to write the integral for volume of the solid.

Q: The region in the graph shown to the right is to be revolved about the x-axis to generate a solid.…

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Q: Write and evaluate the definite integral that represents the volume of the solid formed by revolving…

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Q: - 29 Evaluate the integral: x²/æ² + 4

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Q: PLEASE ANSWER LETTER B AND SHOW GRAPH Evaluate the Iterated Integral  The Second Proposition of…

A: To find the volume of the solid that is obtained by rotating the below curve about the y axis using…

Q: 2.) y = x² + 2, y = 6 around y = 6.

A: Given: y=x2+2, y=6 around y=6 To find:  Set up an integral that represents the volume for all of…

Q: 4.) y = Vr, y = 3, x = 0 around the y axis

A: Integrated about y axis

Q: Setup, but do not evaluate, a triple integral that represents the volume of the wedge in the first…

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Q: Write a definite integral that represents the area of the region. (Do not evaluate the integral.) y,…

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Q: Write and evaluate the definite integral that represents the volume of the solid formed by revolving…

A: Given: y= 36-x2 To find: Volume of solid formed by revolving the region about the  y - axis.

Q: Read all directions and answer the questions the best that you can. and reasonable work is expected…

A: Note: There are multiple questions. Few questions has multiple subparts. No specific question has…

Q: 14. The Great Pyramid at Giza in Egypt has a square base about 750 feet on each side, and is about…

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Q: The density of oil in a circular oil slick on the surface of the ocean at a distance r meters from…

A: to calculate the exact value of total mass of the oil if the slick extends from 10000 meters from…

Q: Y1 = x² + 2x + 2 Y2 = 2x + 11 xp 18 y2 16- 14 12 10 y 8- 6 -2 2 4

A:

Q: 2. */4-x a) Integral Number in the attached Table: b) Values of the constants: a = d = (Fill in the…

A: The solution of the problem is given in the next steps.

Q: The half cylinder shown below has diameter 6m (radius 3m) and length 7m. 7 m a) On your paper find a…

A: Given the half-cylinder with the diameter 6 m (radius 3 m) and length 7 m. (a) The volume of the…

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.