Ihave three (copied below)

-when solving a radical equation, beth and kelly came to two different conclusions. beth found a solution, while kelly's solution did not work in the equation.

create and justify two situations: one situation where beth is correct and a separate situation where kelly is correct.

-a dirt bike racer wants to plan a path between a giant boulder and a fence that lines his property. using these as the focus and directrix, how can the racer plan a parabolic path that will be equidistant from the boulder and the fence at all times? describe your method in full sentences.

-joselyn is a manager at a sign painting company. she has three painters, allen, brianne, and charles. allen can complete a large project in 16 hours. brianne can complete the same sized project in 18 hours. charles is new, so no one knows how long it will take him.

joselyn assigns them all a large project to complete together. explain to joselyn how this project can tell her how long it would take charles if he worked by himself. use complete sentences.

-The two situations; one situation where Beth is correct and a separate situation where Kelly is correct, can be:
sqrt(x) = -2  and   sqrt(x) = 2

- For a given point, called the focus, and a given line not through the focus, called the directrix, a parabola is the locus of points such that the distance to the focus equals the distance to the directrix. So by definition, if you create a parabola for the focus (the rock) and define the fence as the "line not through the focus" that is:
y = (1/4f)*x^2 where f is 1/2 perpendicular distance from the rock to the fence. 

-Allen can complete 1/16 of the project per hour Brianne can complete 1/18 of the project per hour Charles can complete 1/x Together they can accomplish 1/16 + 1/18 + 1/X per hour. we need a common denominator, which is

288X = 18x+16x+288288x
Choose t as the time it takes them all, so 1/t is the hourly rate.
 
1/t =18x+16x+288288x
or
t =288x18x+16x+288

Once the project is completed, Jocelyn will have t, so she will only need to solve for x in this equation to find out the rate 1/x for Charles working by himself