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: What are the vertices and foci of the hyperbola (x - 9)2/25 - (y + 6)2/144 = 1 Show all work.

A: We have to find the vertices and foci of the given hyperbola.

Q: If A ABC is reflected across the line y-z+ 1, what are the coordinates of Point A post-reflection?…

A: In the question it is asked to show the reflection of the triangle shown in figure. It is asked to…

Q: Consider the paraboloid given by the equation z = x^2 + y^2. Find the coordinates of the vertex and…

A: A paraboloid is a quadric surface that has exactly one axis of symmetry and no center. The given…

Q: Describe what kind of conic section is the graph of 5x2 − 4xy + 8y2 − 36 = 0. by using linear…

A: We need to find the nature of the conic section for  the graph of 5x2-4xy+8y2-36 =0.

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. 3x* - g"+ 12 x +12y 2 -36=6

A: Let's find.

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

A:

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: 6. The z-axis. Answer:

A:

Q: How are the conics described in terms of a fixed point and a fixed line?

A: We need to describe the definition of conics in terms of a fixed point and fixed line.

Q: One 49 is 36 1 ♦ of the hyperbola

A:

Q: 3x2 − 6x − 4y + 8 = 0 identify the standard form, vertex, focus, ends of latus rectum, directrix;

A: the solution is following.

Q: Which equation would shift the parabola down 3 units? A y=z² B y=z² +3 C_y=(z-3)² Dy=(z+3)²³ E =…

A: which equation would shift the parabola down to 3 units.

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: A trapezoid is graphed on a coordinate grid and then reflected across the y-axis. Which rule…

A: As given:-  A trapezoid is graphed on a coordinate grid and then reflected across the y-axis

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

A:

Q: Ex. For the hyperbola *-= find the coordinates for the foci and vertices.

A:

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.