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Instructions: Write out your solutions, scan them as a pdf, and upload them to COTROnline by the date posted. If you require extra time, you must email me before the due date. No extensions will be given after the due date except in extenuating circumstances. Leave all solutions exact unless otherwise specified. Include sketches of your areas - I am particularly interested in the 2D "shadows" of the shapes. Questions: 1. Find the centroid of the region between the x-axis and the arch y = sinx, 0≤x≤ π. 2. Find the moment of inertia with respect to the y-axis of a thin sheet of constant density 8 = 1 gm/cm² bounded by the curve y = (sin² x)/x² and the interval T ≤ x ≤ 27 of the x-axis. 3. Find the mass of a thin plate occupying the smaller region cut from the ellipse x² + 4y² = 12 by the parabola x = 4y2 if the density is 8(x, y, z) = 5x kg/m². 4. Sketch the graph described by the following cylindrical coordinates and describe the shape in words. (a) z = r (b) 1 ≤ r ≤ 2,0 ≤ 0 ≤ π/3 (c) 0 ≤r ≤ 3, -π/2 ≤ 0 ≤ π/2, 0≤ % ≤r cos 5. Sketch the graph described by the following spherical coordinates and describe the shape in words. (a) = π/6 (b) 1≤p ≤ 2 seco, 0≤ ≤ π/4 6. Evaluate the integral 7. Evaluate the integral p3п/2 (a) 8(r, 0, 2) = % (b) 8(r, 0, 2) = r 0/п 3√4-r² √4-r2 z dz r dr de L L 5 5p³ sin³ dp do do o 8. A solid is bounded on the top by the paraboloid z = ³, on the bottom by the plane z = 0, and on the sides by the cylinder r= 1. Find the centre of mass and the moment of inertia about the z-axis if the density is

Instructions: Write out your solutions, scan them as a pdf, and upload them to COTROnline by the date posted. If you require extra time, you must email me before the due date. No extensions will be given after the due date except in extenuating circumstances. Leave all solutions exact unless otherwise specified. Include sketches of your areas - I am particularly interested in the 2D "shadows" of the shapes. Questions: 1. Find the centroid of the region between the x-axis and the arch y = sinx, 0≤x≤ π. 2. Find the moment of inertia with respect to the y-axis of a thin sheet of constant density 8 = 1 gm/cm² bounded by the curve y = (sin² x)/x² and the interval T ≤ x ≤ 27 of the x-axis. 3. Find the mass of a thin plate occupying the smaller region cut from the ellipse x² + 4y² = 12 by the parabola x = 4y2 if the density is 8(x, y, z) = 5x kg/m². 4. Sketch the graph described by the following cylindrical coordinates and describe the shape in words. (a) z = r (b) 1 ≤ r ≤ 2,0 ≤ 0 ≤ π/3 (c) 0 ≤r ≤ 3, -π/2 ≤ 0 ≤ π/2, 0≤ % ≤r cos 5. Sketch the graph described by the following spherical coordinates and describe the shape in words. (a) = π/6 (b) 1≤p ≤ 2 seco, 0≤ ≤ π/4 6. Evaluate the integral 7. Evaluate the integral p3п/2 (a) 8(r, 0, 2) = % (b) 8(r, 0, 2) = r 0/п 3√4-r² √4-r2 z dz r dr de L L 5 5p³ sin³ dp do do o 8. A solid is bounded on the top by the paraboloid z = ³, on the bottom by the plane z = 0, and on the sides by the cylinder r= 1. Find the centre of mass and the moment of inertia about the z-axis if the density is

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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1:16 Done Math_202_Homework_15_6_7_7... Instructions: Write out your solutions, scan them as a pdf, and upload them to COTROnline by the date posted. If you require extra time, you must email me before the due date. No extensions will be given after the due date except in extenuating circumstances. Leave all solutions exact unless otherwise specified. Include sketches of your areas - I am particularly interested in the 2D "shadows" of the shapes. Questions: 1. Find the centroid of the region between the x-axis and the arch y = sinx, 0≤x≤ π. 2. Find the moment of inertia with respect to the y-axis of a thin sheet of constant density 8 = 1 gm/cm² bounded by the curve y = (sin² x)/x² and the interval ≤ x ≤ 2π of the x-axis. 3. Find the mass of a thin plate occupying the smaller region cut from the ellipse x² + 4y² = 12 by the parabola x = 4y2 if the density is 8(x, y, z) = 5x kg/m². 4. Sketch the graph described by the following cylindrical coordinates and describe the shape in words. (a) z = r (b) 1 ≤r ≤ 2,0 ≤ 0 ≤ π/3 (c) 0 ≤r ≤ 3, -π/2 ≤0 ≤ π/2, 0≤ z≤r cos 5. Sketch the graph described by the following spherical coordinates and describe the shape in words. (a) = π/6 (b) 1 ≤p ≤ 2 seco, 0≤ ≤ π/4 6. Evaluate the integral Math 202 Homework Ch 15.6, 15.7 Andrea Hyde 7. Evaluate the integral 9 (a) 8(r, 0, z) = z (b) 8(r, 0, 2) = r [" Lola Lav 4-r2 8. A solid is bounded on the top by the paraboloid z = r³, on the bottom by the plane z = 0, and on the sides by the cylinder r= 1. Find the centre of mass and the moment of inertia about the z-axis if the density is z dz r dr de r3п/2 1 [/2" ["5p³ sin³ o dp do do 0 1 Q
Transcribed Image Text:1:16 Done Math_202_Homework_15_6_7_7... Instructions: Write out your solutions, scan them as a pdf, and upload them to COTROnline by the date posted. If you require extra time, you must email me before the due date. No extensions will be given after the due date except in extenuating circumstances. Leave all solutions exact unless otherwise specified. Include sketches of your areas - I am particularly interested in the 2D "shadows" of the shapes. Questions: 1. Find the centroid of the region between the x-axis and the arch y = sinx, 0≤x≤ π. 2. Find the moment of inertia with respect to the y-axis of a thin sheet of constant density 8 = 1 gm/cm² bounded by the curve y = (sin² x)/x² and the interval ≤ x ≤ 2π of the x-axis. 3. Find the mass of a thin plate occupying the smaller region cut from the ellipse x² + 4y² = 12 by the parabola x = 4y2 if the density is 8(x, y, z) = 5x kg/m². 4. Sketch the graph described by the following cylindrical coordinates and describe the shape in words. (a) z = r (b) 1 ≤r ≤ 2,0 ≤ 0 ≤ π/3 (c) 0 ≤r ≤ 3, -π/2 ≤0 ≤ π/2, 0≤ z≤r cos 5. Sketch the graph described by the following spherical coordinates and describe the shape in words. (a) = π/6 (b) 1 ≤p ≤ 2 seco, 0≤ ≤ π/4 6. Evaluate the integral Math 202 Homework Ch 15.6, 15.7 Andrea Hyde 7. Evaluate the integral 9 (a) 8(r, 0, z) = z (b) 8(r, 0, 2) = r [" Lola Lav 4-r2 8. A solid is bounded on the top by the paraboloid z = r³, on the bottom by the plane z = 0, and on the sides by the cylinder r= 1. Find the centre of mass and the moment of inertia about the z-axis if the density is z dz r dr de r3п/2 1 [/2" ["5p³ sin³ o dp do do 0 1 Q
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