hectictar

Ohh... thank you

Aww you spent all that time typing and didn't post it?

Also I wasn't really really sure that they were the heights but it just kind of looked like they were. 

Is there a way to tell for sure?

Since 3² + 4² = 5², ABC is a right triangle with 3 as the height and 4 as the base.

So the area of ABC is (1/2)(4)(3) = 6 un.²

The lines AG, BG, and GC split the big triangle, ABC, into 3 equal pieces since they go from the vertices to the centroid.

The areas of ABG, BCG, and CAG, are all equal. They are all 6/3 = 2 un².

GR, GQ, and GP are all the heights of the 3 triangles. We know the bases and the areas, so just solve for the heights.

Triangle ABG:

2 = (1/2)(3)(GR)

4/3 = GR

Triangle BCG:

2 = (1/2)(4)(GP)

1 = GP

Triangle CAG:

2 = (1/2)(5)(GQ)

4/5 = GQ

4/3 + 1 + 4/5 = 47/15 = 31 and 2/15

I'm sorry I don't have an explanation, but I have an answer.

The four numbers are 21, 98, 219, and 461, so the largest is 461.

I found this by making a table and scrolling through to find all four of them.

Hey CPhill, I was trying to follow the Guest's work and it looks like the first step was square every term. I was just wondering is that really allowed??

0.6(7)^2 = (0.6)(7)(7) = 29.4

r(x) can be 0, 2, 4, and 6.

So the sum of all possible values of s(r(x)) = s(0) + s(2) + s(4) + s(6)

FREEEZE! there is no s(0) or s(6) because the domain of s(x) is {1,2,3,4}, so get rid of those.

s(2) + s(4)

= (2+1) + (4+1)

= 3 + 5

= 8

3y = 2x - 3

Divide everything by 3.

y = (2/3)x - 1

In this format, the coefficient of x is the slope. 2/3 is the slope.

Parallel lines have the same slope.

Plug in the point (-3, 4) using (2/3) as the slope and find the y-intercept, b.

4 = (2/3)(-3) + b

4 = -2 + b

6 = b

Parallel line: y = (2/3)x + 6

Perpendicular lines have a negative reciprocal slope.

Plug in the point (-3, 4) using (-3/2) as the slope and find the y-intercept, b.

4 = (-3/2)(-3) + b

4 = 9/2 + b

-1/2 = b

Perpendicular line: y = (-3/2)x - 1/2

Multiply out the denominator and combine like terms:

(x - 1)(x - 1) + (x + 1)(x + 1)

(x² - 2x + 1) + (x² + 2x + 1)

x² - 2x + 1 + x² + 2x + 1

2x²  + 2

Now set this equal to 0 and solve for x.

2x² + 2 = 0

2x² = -2

x² = -1

x = i

There are no real numbers that make the y undefined. So the domain is all real numbers.

( - ∞, ∞)

I had no idea how to do this one, but I think I understand it now!