When Spherius dips through Flatland, his cross section appears as a circle whose circumference is becoming larger, then shrinking, and finally disappearing. Describe the cross-sections of a 3-D cube as it passes through Flatland "edge-first". What if the 3-D cube passes through Flatland "corner-first"?

Q: Consider the following equation of a circle written in expanded form. x² + y² + 4x+10y = - 4 Whic…

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Q: There is a parabola which has a minimum where the two lines 3x+6y-1=0 and 2x+ y-2=0 intersect. The…

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Q: Determine the focus of the parabola (y + 2)2 = -16(x 3). O(7.2) O(6.3) O (3,-2) O (1-2)

A: We have to find the focus of the given parabola. The solution is following.

Q: 16X2 + 25Y2 + 160X + 200Y + 400 = 0 hub a.(5.4) B. (5, - 4) C. (-5, -4) D. (-5, 4) Vertex A) C=3…

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Q: The surface of a mountain is modeled by the equation h(x, y) = 7500 – 0.001x2 - 0.004y2. A mountain…

A: Given the surface of a mountain is modeled by the equation h(x,y)=7500−0.001x2−0.004y2

Q: 2) Graph the equation 3 x + 4 y = 12.

A: The given equation is  3 x + 4 y = 12

Q: How do you write an equation of a sphere with a given center and radius?

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Q: :- x(4 + 9) – z ( 9+ ) – + 7)x - 15 + Graph the following equation in three dimensions (6+ 9.5)y…

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Q: The graph of x2+y2+z2-14y=0 is a sphere. what are the center and radius of the sphere?

A: Given    Equation of sphere  x2+y2+z2-14y=0To calculate:-     Center  and  radius  of the sphere.

Q: Hey, isn't a hyperbola supposed to be the to minus each other instead of plus?

A: yes you are write there is minus sign instead of plus please find below step wise solution

Q: Find the center and radius of a sphere given by equation 3x +3y² +3z? =10+6y+12z.

A: We have to find

Q: What is the equation for a sphere centered at the point (4,-3,-7) with a radius of 5.

A: The general equation for a sphere in three dimensions is given by (x - h)^2 + (y - k)^2 + (z - l)^2…

Q: Which quadric surfaces have both hyperbolas and parabolas as traces?

A: Consider the given: The intersection of a three-dimensional surface and a plane is called a trace.…

Q: we have two parabolas and both have same directrix line, different focus points. How do we know…

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Q: Find the distance from (-5,9, –12) to each of the following: 1. The xy-plane. Answer:

A: Given point :-  (-5,9,-12) To find:- Distance of given point to plane xy

Q: Complete the equation for the circle with center (6, 2) and radius 8. Choose... O 2 +( Choose.. O2-…

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Q: Let 4x^2+3y^2+8x-6y=5 find the center and foci. Graph

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Q: Exercise 5. Find the equation of the circumference whose center is on the y-axis and that passes…

A: We have to Find the equation of the circumference whose center is on the y-axis and that passes…

Q: Graph x = 2 and y = 3 and z = -3 in a 3-D rectangular coordinate system.

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Q: ODELING REAL LIFE A charm bracelet costs $65, plus $25 for each charm. The equation -25x +y = 65…

A: a) Given that, the function is -25x+y=65. -25x+y=65y=65+25x Let x=0 then the value of y is…

Q: q13.2 You have been given the following equation of a sphere (x^2) + (y^2) + (z^2) - 6x + 4z = 3…

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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.