00:01
So in this problem, we're given this function.
00:03
Y equals the square root of 81 minus x squared, all divided by 3, minus 0 .4 cosine of 8 pi x.
00:14
We're first asked to kind of describe this and then graph it using a graphing utility.
00:20
Well, first of all, we can't take the square root of a negative number.
00:46
That means that 81 minus x squared has to be greater than equal to zero.
00:52
So move the 81 to the other side.
00:54
So that's negative x squared is greater than equal to negative 81.
00:59
Take the negative off.
01:01
X squared is greater than equal to 81, multiply them by negative one on both sides.
01:06
And so then x is greater than equal to plus or minus nine.
01:12
Well, i shouldn't say it this way.
01:18
What i should say is that negative 9 is less than or equal to x is less than or equal to 9.
01:50
Yeah, because i messed up right here, didn't i? whenever you do the negative, multiply that negative 1, you have to switch the inequality around.
01:57
Okay, so x is between negative 9 and 9 from that.
02:01
Now the next thing we can talk about is this cosine of 8 pi x...