Okay, so we have a couple of inequalities. So we have, Um the 1st 1 is a hollow ball with, um So I write down how the ball hollow ball with diameter of 30 centimeters and thickness of 0.5 centimeters. So, um, right, this, um, in the Tootie's place first. So Well, I'll write a circle. Um, and then we converted to spherical. So we're in a circle. We know that we want, um, the diameter to be 30 swift 30 across. And it's gonna be a thickness of 0.5. So we want thickness to just be this outer part. So I have this outer part here, and we know that that's 0.5. So perverting this to a spirit kal important. Since it's the hollow ball, it's gonna spend the whole, um ah, data and five space so we can write it. But we don't have to. Um, but we can just right. The following is just described by since we know our diameter must be 30. We know our Max radius or Max row just 15 and then our thickness in out of this case corresponds to a You don't have to actually cut that in half because it's all around. So then this is just still 0.5 centimeters. So we can actually describe this entire ball using the inequality. Ro is in between 15 and 14.5 centimeters. So then what we like to do now is, um, right inequalities that described half of this. So we're going to say we cut it half way vertically. So we cut this vertically. Um, we end up with just this half. We'll go ahead and say, This is, um positive X and y. So we have Let's say this is positive X. So, um, we can go ahead and use our cornet space who describe a this hollow ball. We'll say it's right better. Who will say it's It's in this this plane So positive x in the positive X direction. So, um, by since fires angle with Z axis, it's still encompasses the entire identify, so we don't actually have to write that. And then we know it's different in x and y because data is different. So data ends up spanning negative Pirata, pirate or two. So this isn't negative to this estate. I see quite a negative. Prior to this line and right here this line is Paradies. You could deposit pirate too, so we can go ahead and say for our our half of the ball will say that this is described by these two inequalities the same as before With our radius that describes our actual sphere and the cut it in half. We'll show that how data must be between ah, pyre or two and native prior to And pirates too. And in for both cases. If you wanted to write that, you could, um if I just spanning from zero to pi And in the other case, um, data goes from zero to part 20 to 2 pi. So, um, to be as specific as possible, all you have to do is write these two qualities.