Raymond is designing a ceramic pot on a coordinate system where each unit corresponds to 1 millimeter. The neck of the pot has edges with the shape of a hyperbola, where the asymptotes y = 2.75x and y = -2.75x are followed. If the closest
that any part of the neck edges comes to the center of the neck is 32 millimeters, write an equation for the hyperbola used
to model the edges.

9514 1404 393

  x^2/1024 -y^2/7744 = 1

Step-by-step explanation:

The parent hyperbola relation is ...

  x^2 -y^2 = 1

This has asymptotes of y = ±x and x-intercepts of ±1.

For the given hyperbola, we want to scale x by a factor of 32, and y by a factor that is 2.75 times that, or 88. Then the equation could be written as ...

  (x/32)^2 -(y/88)^2 = 1

More conventionally, the denominator is shown at full value:

  x^2/1024 -y^2/7744 = 1

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0

(3x-8) or (3x+8)

step-by-step explanation: