Suppose we want to form a conic container by rolling up a circular sector of radius 10. We want to find the central angle (theta) such that it maximizes the volume of the cone. Find the radius and the height of the cone and then express the volume as a function of theta. Make sure you state the domain.

Q: A line segment of length a + b runs from the x-axis to the y-axis. The point P on the segment lies a…

A: Given A line segment of length a + b runs from the x-axis to the y-axis. The point P on the segment…

Q: Describe concentrically?

A: Concentrically means circles having a common center. If number of circle that have a common center…

Q: Describe and graph (using a computer) the surfaces d) 4y² + z² − x − 16y - 4z + 20 = 0 e) x² - y² +…

A: The given surfaces are: d  4y2+z2-x-16y-4z+20=0e x2-y2+z2-2x+2y+4z+2=0f  fx,y=1x-y2 We have to…

Q: ed Deve 38-0- a (3 -2 1 b. Compute the vales of a and b for which the system 5-8 9 1 (i) a unique…

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Q: hoose the letter of the correct answer. There could be multiple answers and none of the choices.…

A: The solid can have a base in any of the planes in the coordinate axis. The cross-section can be…

Q: Use the parametric equations of an ellipse, x = 5 cos(0), y = 3 sin(0), 0 ≤0≤2π, to find the area…

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Q: Mr. Yang's rugby team is facing the fighting bees next week. For the equation (x^2/a^2)+(y^2/b^2)=1…

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Q: Convert to standard from and give the center and radius: x^2+ Y^2 - 2x +6y - 1=0

A: x-h2 +y-k2 =r2 (h , k) is centre and r is radius .

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A: Given : information of a figure to be drawn on the graph. Cylindrical pool: depth=5m , diameter=60m…

Q: Write the equation of the sphere with centre at ( 0,0,0) and radius = 2

A: The center of the sphere is:(h, k, j)=(0, 0, 0)The radius of the sphere is:r=2

Q: Explain what it means for a surface to be orientable.

A: They are the surfaces for which we can define clockwise consistently. e.g. Cylinder and spheres are…

Q: ank is 10 meters above the street l o that the truck can pass under the

A: Given, Span= 24 meters, Height= 16 meters.

Q: 2. A light bullb is designed as a sphere of radius a inch with the bottom sliced off to fi. onto a…

A: We need to find surface area of spherical part.

Q: What is the definition of a parabolic cylinder?

A: The parabolic cylinder functions are the solutions to the differential equation d2ydx2 + ax2 + bx +…

Q: What quadric surface is the following an equation for and how do you know? -9x^2-3x+y^2+z^2= 1/4

A: The given quadratic equation is .We know that the quadratic surface of the form  form a cone.

Q: y=8-4x² - 9z²

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Q: Write the equation of a sphere of radius 3 in all three coordinates--cartesian, cylindrical, and…

A: It is given that the radius of sphere is 3 .We have to find the equation of sphere in all three…

Q: *Challenge: For a given triangle, if the centroid is at (-2,5) and the orthocenter is at (-8,13),…

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Q: Describe the usual orientation of a closed surface such as a sphere.

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