If you have ever seen a pinball machine, you would know that it is shaped like a rectangular box. Since a rectangle has two sets of equal parallel lines, then you would have to know the length and the width. Its perimeter is equal to the total length of all sides. Thus, the equation is 2L + 2W = 172 inches. However, since there is no other data other than the perimeter, I can't give a definite numerical answer. The only answer I could give is in variables. Thus, the length of the pinball machine is
2L = 172 - 2W
L= 86 - W
First of all, I'm going to assume that we have a concave down parabola, because the stream of water is subjected to gravity.
If we need the vertex to be at
, the equation will contain a
term.
If we start with
we have a parabola, concave down, with vertex at
and a maximum of 0.
So, if we add 7, we will translate the function vertically up 7 units, so that the new maximum will be 
We have

Now we only have to fix the fact that this parabola doesn't land at
, because our parabola is too "narrow". We can work on that by multiplying the squared parenthesis by a certain coefficient: we want

such that:
Plugging these values gets us

As you can see in the attached figure, the parabola we get satisfies all the requests.
By applying the knowledge of similar triangles, the lengths of AE and AB are:
a. 
b. 
<em>See the image in the attachment for the referred diagram.</em>
<em />
- The two triangles, triangle AEC and triangle BDC are similar triangles.
- Therefore, the ratio of the corresponding sides of triangles AEC and BDC will be the same.
<em>This implies that</em>:
<em><u>Given:</u></em>

<u>a. </u><u>Find the length of </u><u>AE</u><u>:</u>
EC/DC = AE/DB



<u>b. </u><u>Find the length of </u><u>AB:</u>

AC = 6.15 cm
To find BC, use AC/BC = EC/DC.




Therefore, by applying the knowledge of similar triangles, the lengths of AE and AB are:
a. 
b. 
Learn more here:
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The x intercepts must be 1 and -4, so C.
So, this means that you are multiplying both of the numerators and denominators together to get the product