A Stability cable is attached to the top of an electricity pole and then stretched to the ground. The pole is 4.5m tall while it he cable has a length of 6m. How far from the base of the pole is the cable attached to the ground

3.96 meters

Step-by-step explanation:

Draw a Right triangle as the one shown in the image attached, where "x" is the distance from the base of the pole to the point in which the cable is attached to the ground.

In this case you need to use the Pythagorean Theorem. According to this theorem:

Where "a" is the hypotenuse and "b" and "c" are the legs of the Right triangle.

If you solve for one of the legs, you get:

In this case, you can identify that:

Substituting values, you get the following result:

(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