ShmoopTube

00:02

Here’s your shmoop du jour, brought to you by Dollar Signs.

00:05

Why can’t there be more of THOSE on the highway?

00:08

If x $ y is defined as x $ y equals the square root of x squared minus y squared,

00:18

and 13 $ y = 5, what is y?

00:22

And here are the potential answers…

00:26

Is it just us are you seeing dollar signs?

00:29

So we're given that x $ y equals the square root of x squared minus y squared.

00:34

So, 13 $ y is the square root of 13 squared minus y squared.

00:43

The given information tells us that 13 $ y equals 5.

00:47

This can be written as the equation square root of 13 squared minus y squared equals 5.

00:53

This gives us square root of 169 minus y squared equals 5.

00:59

Let’s get rid of the square root by squaring both sides.

01:02

This gives us 169 minus y squared equals 25.

01:07

We add y squared to both sides, then subtract 25 from both sides to get 144 equals y squared.

01:14

Now we can take the square root of 144 to get y equals 12.

01:18

BUT…we have to remember that negative 12 is also an answer, since a negative, when

01:23

squared, is positive.

01:24

The answer is (E).

Full Transcript