#page 527

{[SLAY]: [Rot Ice Horror]}

The monster crawls towards you and smashes its claw against the face of the mech suit. It is close enough now that you can punch it directly in the face. 

The creature recoils in pain, and you drive the drill directly into its skull. The whirr mixes with the sickening crunch of flesh and exoskeleton.

The creature finally bursts into a collage of light and color. [The Rot Ice Horror]… is dead.

[You gained +1 Blessed Tear][You gained +1HP and +1MP]

The Mining mech has sustained too much damage and with a loud metallic groan it shuts down, this time for good. The sensation of control fades and it feels like dying. 

You scramble to find a way out of the tight confines of the mech’s enige but you can barely move. As you thrash about, a familiar feeling obscures your vision…

Everything goes dark…

{[You Have Reached: [Level 5]}

{[You now can invest your experience.]}

Leveling Up:You have [1] point to invest in:[The House of the North] [The House of the East][The House of the South]

You have [1] point to invest in:[The Sign of the Lion] {+1 Strength +5 Health} per point[The Sign of the Bull] {+1 Defense +1 Health regain} per point[The Sign of the Beetle] {+1 Spell Resistance +1 Mana regain} per point[The Sign of the Spider]{+1 Spell Power +5 Mana} per point

{The machine is devouring you soul as it shuts down… -2 MANA}

{You have 4 actions left before the Mining Mech consumes you.}

[STATUS] (new!)[QUESTS][MAP]

Hi Tasha,

Yeah, this is a pretty tough one. (For everyone else following along, here's my original solution.)

The two equations that are important come from the definitions of direct and inverse proportionality. Note: there are a number of ways to arrange the variables in these definitions; I'm placing them where I think they'll be helpful here.

In the equations above, a and b are variables and k is a constant. 

The question begins by telling us that x is inversely proportional to y, which means we can put y and x in for a and b in the general inverse proportionality form above: 

That's the relationship we know x and y have with each other. 

Now the question tells us that SOMETHING is directly proportional with 1/(x^2), and we need to figure out what. In other words:

Again, I'm just taking the standard direct proportionality form a = kb and putting 1/(x^2) in for b to get that. 

Now I need to get the relationship I know I have to look more like the relationship I know I want. This is why, in the other solution, I liken this to a solve for expressions question.

I have:

I want:

So first, I rearrange what I have a teeny bit. I just pull the k out of the numerator:

Now I'm already closer to what I want, right? If I square everything, I'm pretty much there!

There's one last tricky bit to this: the k^2. Remember, k is just a constant. So when we square it, it's still just a (probably different) constant. So the equation above still fits the definition of direct proportionality:

Therefore, y^2 is directly proportional to 1/(x^2).