You will upload the answer to this question here. Consider the solid object under z = x +3y+4 and above the closed region below. x = y- 1

Q: (b) Find the equation of the sphere in R³ that has the diameter from A(1, 2, -1) to B(5,-2,0).

A: Part (b):- Given co-ordinates of diameter are  A1, 2, -1   to   B5, -2,  0.

Q: 1. Classify the equation Zxx + XZyy = 0 and find the regions that the equation is hyperbolic,…

A: Consider a second order partial differential equation A(x,y)Zxx + B(x,y)Zxy +C(x,y)Zyy+…

Q: Find the area of each of the following surfaces.   The portion of the sphere with equation x 2+y 2+z…

A: Given, x2+y2+z2=16 , lies inside  x2+y2=9 surface area =2∬1+zx2+zy2dxdy…

Q: 1. Find the points on the surface a² +9y² +92² = 4 which are closest to and farthest from the point…

A: The given surface is x2+9y2+9z2=4 and point (0,2,0). To find the point which is closest to and…

Q: Find the area of the surface. The part of the surface z = 5 + 3x + 3y² that lies above the triangle…

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Q: 2. Suppose you revolved the triangular region bound by the axes and the line 4x + 3y = 12 completely…

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Q: Find the centroid of the area shown in figure 1.

A: The figure is  There are four rectangles 1, 2, 3, 4.

Q: Derive the formula V sphere 3

A: We have to derive the formula                                                VSphere=43πr3

Q: 4 1z = 4 –y? x = 4- 3 2 z + y = 2 z = y

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Q: The equation x2 + xy + y² = 1 determines an below. ellipse in the xy-plane shown

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Q: 2. Find the area of the part of the sphere x² + y² + z² = 4z that lies inside the paraboloid z = x²…

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Q: In each of the following cases, draw each solid Q bounded by the surfaces whose equations are given…

A: We are given four surfaces.   y=x2 , the parabola. 4z+3y=12, the slanting plane. y=4, a plane 4…

Q: • What is/are the trace(s) of the surface (x – 1)? 22 = 1 on the rz-plane? 36 a. hyperbola b.…

A: For the given surface

Q: Draw a sketch of the cylinder z = -4 - y2.

A: A cartesian coordinate system contains two mutually perpendicular number lines named x-axis and…

Q: 1. If 4 = xy i+yzj+zxk, find curl4 and curl curl A at points (1,2, –3).

A: Given that A = xy i + yzj + zxk and find curlA and curlcurlA at point (1,2,-3). Here i attached…

Q: F9-3. Determine the centroid y of the shaded area. 2m y 23 1 m F9-3 1 m

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Q: Write an equation for the level surface of f(x, y, z) = r² + 10y? + 20z2 corresponding to the level…

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Q: x² 6. Find the area of the largest rectangle that can be inscribed in the ellipse =1. 9. 4 Hint: Use…

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Q: QUESTION 5 What are the x-traces of the surface x2+ y2 +z=5? O a. Circles. O b. Elipses. O.…

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Q: A company that sells copier machines has collected data from 45 recent calls on users to perform…

A: Given that,  X = number of copiers serviced, Y = total number of minutes spent by service person,X¯…

Q: The surface 2x2 -2y² – 2z² =1 is identified as

A: The given surface is qudratic surface. Different qudratic surfaces 1)Ellipsoid 2)Hyperboloid in one…

Q: The surface x2+y?+z?-4x-2z+5=0 is: O an elliptic paraboloid O a point O no graph O a hyperboloid of…

A: Please see the below picture for detailed solution.

Q: Part A: Sofia transformed figure PQR into P'Q'R'. Which of the following represents her…

A: Given,          P-4,-8 , Q-8,-2 and R-2,2 form figure PQR.

Q: 71 D The region D above lies between the two red lines 3 and the red parabola y = x². It can be…

A: Mention the functions and the x and y coordinates on the given graph.

Q: Which of the following represents the radius of the sphere whose equation is x² + 8x +y2 – 16y +z² –…

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Q: 3. Find the points on the surface z = = xy + 2 that are closest to the origin.

A: Let g(x,y,z) be the constraint function and f(x,y,z) be the function whose extreme values to…