Q3: Find the points on the surface x^2+z^2-630, closest to the origin.

Q: What is the maximum vertical distance between the line y = x + 30 and the parabola y = x2 for -5 s x…

A: given, equation of line is y = x + 30 and equation of parabola is  we have to find maximum vertical…

Q: Explain why the curve of intersection of the surfaces x2 + 3y2 − 2z2 + 2y = 4 and 2x2 + 6y2 − 4z2 −…

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Q: Identify and sketch the surfaces x2 + y2 - z2 = 4

A: Given, The surface is x2 + y2 - z2 = 4

Q: Describe and sketch the surface x + 2y + 3z = 6

A: Given

Q: Sketch the surface.......... ASSORTED ............... 4y2 + z2 - 4x2 = 4

A: Given :             The given function is 4y2 + z2 - 4x2 = 4 And can be written as,…

Q: Find the volume of the largest rectangular box in the first octant with three faces in the…

A: The given equation of plane is : x+2y+3z=6 x=6-2y-3z                   …(1) Volume of a rectangular…

Q: Determine the diameter of a hole that is drilled vertically through the center of the solid bounded…

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Q: Sketch the surfaces 1. 9x2 + y2 + z2 = 9  2. 4x2 + 9y2 + 4z2 = 36

A: Using graphing calculator to graph them. 9x^2 + y^2 + z^2 = 9

Q: Identify and sketch the surfaces 4x2 + 4y2 + z2 = 4

A:

Q: Describe the relationship between the graphs of the quadric surfaces x2 + y2 - z2 + 2z = 1 and x2 +…

A: Given: The quadratic surfaces,   To describe the relationship between given two graphs and to state…

Q: Describe and sketch the surface 4x2 + y2 = 4

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Q: There is a line through the origin that divides the region bounded by the parabola y=4x−6x2y=4x-6x2…

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Q: Sketch the surfaces ASSORTED 4y2 + z2 - 4x2 = 4

A: Given:  And can be written as,  Therefore, The obtained function is in the form of Hyperboloid…

Q: Find the volume of the largest rectangular box in the first octant with three faces in the…

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Q: Describe and sketch the surface (x2/16) + (y2/9) + z2 = 1

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Q: Sketch the surface with equation x^2 + y^2 + 2z^2 − 1 = 0.

A: The given equation is x2+y2+2z2-1=0

Q: What is the maximum vertical distance between the line y = x + 6 and the parabola y x2 for -2 < x<…

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Q: 4. Engineers are building a parabola shaped satellite dish, shape is formed by rotating y = ax²…

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Q: Sketch the surface: x + 2y + 3z = 12.

A: First find the intersection of plane with axis then draw the plane.

Q: Identify and sketch the surfaces x2 + z2 = y2

A: Given surface is x2+z2=y2. The given equation is in the form of x2a2+z2c2=y2. So, the given surface…

Q: Find the volume of the largest rectangular box in the first octant with three faces in the…

A: We have to find the volume of the largest rectangular box in the first octant with three faces in…

Q: Classify and sketch the surface x − y2 − 4z2 = 0.

A: The surface is given as x-y2-4z2=0. Rewrite the equation x-y2-4z2=0 as follows. x-y2-4z2=0x=y2+4z2…

Q: A rectangle is inscribed in a parabola y²=8x with one of its vertical side passes through the point…

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Q: Determine the diameter of a hole that is drilled vertically through the center of the solid bounded…

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Q: What is the maximum vertical distance between the line  y = x + 12  and the parabola  y = x2 for…

A: See the attachment

Q: Find the area of the surface generated by revolving the curve y=x^3/18, 0(<=)x(<=) 2 square root 2,…

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Q: Use disk method and draw a graph. √(9-y^2 ),y=1,y=3,x=0 about the y-axis

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Q: the solid cut from the first octant by the surface z = 81-x2-y

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Q: Sketch the surfaces ASSORTED 16x2 + 4y2 = 1

A: we have to sketch the the surface 16x2+4y2=1

Q: What is the name of the surface defined by the equation x2 y

A: Given Equation is :                                  y=x24+z28y=2x2+z282x2+z2=8y   Since,…

Q: Sketch the surface x = 2y2 +3z2

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Q: Identify and sketch the surfaces z = - (x2 + y2)

A: Identify and sketch the surfaces z = - (x2 + y2)

Q: What is the average distance between the parabola y = 7x(20 – x) and the x-axis on the interval…

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Q: Sketch the region in the xy  -plane defined by the equation or inequalities. -1 &lt;=y&lt;=3

A: -1≤y≤3

Q: draw vertical and horizontal traces to identify the surface y = x^2 + 9z^2

A: The graph of the given surface is

Q: Plot the surface of 6a2- 2x4- y?z2 = 0, for -10 <x, y, z < 10

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Q: Find the slope of the surface z = 3x/y at the point (5,2,15/2) in the x- and y- directions.

A: Given data is: z=3xy  To find the slope of the surface z at the point 5,2,152 in the x and…

Q: Describe and sketch the surface 16x2 + 16y2 − 9z2 = 0

A: Given surface 16x2+16y2-9z2=0

Q: Sketch the surface = 2y + 32².

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Q: There is a line through the origin that divides the region bounded by the parabola y=8x−4x2y=8x-4x2…

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Q: Sketch the section of the surface at y 0. -6 -4 -2 6. -2 2 -6 -4 -6 -4 -2 -6 -4

A: The objective of the question is sketch the section of the surface at y=0.

Q: Calculate the point on the surface z =1 - x2 - y2 that has a maximum value for the sum of its…

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Q: Q1/ Use traces to sketch and identify the surface z2 - 4x2 - y² = 4

A: Let's find.

Q: What is the average distance between the parabola y = 10x(22 - x) and the x-axis on the interval…

A: From the average of a curve to x axis in an interval.

Q: Sketch the section of the surface at x = 0. y - 252 = 25 -12- -8 12 -6 -4 -6 12 -4 -8 -12 6 4 4 -6-4…

A: topic - hyperbola y2-25z2= 25 is a hyperbola with vertex are (0,5,0) and (0,-5,0)

Q: The area of the surface obtained by rotating the curve y = 36-x2, -6<xS6 about the x-axis is

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Q: Sketch the graph of -x + 9y² – 4z² = 36 and identify the surface. %3D

A: Given a function in terms of x, y and z. Here x and y are independent variables and z is a dependent…

Q: Sketch the surfaces ASSORTED x2 + y2 = z

A: we have to sketch the surface x2 + y2 = z.

Q: Find the minimum distance from the point to the surface z = √4 - 2x - 2y. (Hint: To simplify the…

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Q: What is the maximum vertical distance between the line y = x + 6 and the parabola y = x< for -2 <x<…

A: To Find

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.