Answer:
410.625
Step-by-step explanation:
The possible dimensions are -7 and -8 units.
Solution:
Area of the rectangular skateboard park =
To find the dimensions of the park.
Let us factor the polynomial:
15x can be written as 7x + 8x.
Take x common in 1st two terms and 8 common in next two terms.
Make sure that the remaining terms in the bracket should be equal.
Now, take the common term (x + 7) outside from both terms.
If the length of the park is -7 then the width is -8.
If the length of the park is -8 then the width is -7.
The possible dimensions are -7 and -8 units.
If you plot these points on a coordinate plane, you see that both vertices and foci lie on the y axis. This means that you have a vertical hyperbola, and the equation looks like this:
where h and k are the center. When you look at your graph, the origin is dead center between the vertices. (0, 0) is our h and k. Now we need a, b, and c. a is the distance between the center and the vertices, so our a = 4, and c is the distance between the center and the foci, so our c = 5. Use these in Pythagorean's Theorem to solve for b:
and
and b = 3. So we have all we need to do is replace all the variables. Our equation then would be this one:
or, simplified,