All right. So this brushing me are after a both the area on a curse. Um, so in question, they were asked with the area under the curve between time with zero and time in calls for five. So I mean, we consider this to be your time, because five, uh, and we can kind of put this into three areas. So we got two rectangles. They're trying. So the first rec time goal is to buy two. So the area is gonna be, um, four plus on mrs. To this, rectangles will be to buy three go five, uh, plus six. Plus. Now, this triangle the the height. Ah. Is there three and the, um yeah, I just three in length is three. So, um, the area is gonna be 1/2 times nine, which is 4.5. The area is 14.5. So in part B were asked about the area between zero or sore between five and 10. So between five and 10 again are basically going to do the same thing. We got a little triangle, appear we've got a nice rectangle and another nice rectangle. So the smaller rectangle it is won by five. So area, it's areas five The triangle It's one by one. So it's area his 0.5 by one by one. I mean base and I have one. And then the big rectangle it is four Ah, by six. So the area is 24 so total area is 20 9.5. So now we and by so yes, O c So total from 0 to 10 which just add the 055 10 up. So that is gonna give us 44 and then lastly, in part D that ask us about the center of mass. So, um, the what this is really asking us is, um what, uh, X value is, um, half. Um, I want at up to what? X value is half of the total area under the curve. So, um, just by looking, um so Okay, it's a total area under a curve is 44 so x. So the center of mass is gonna be where up where the total, um, area under the curve above and below. It is 22. So, um, that if we we know going up to exceed six the area of the service 20 so and going up to seven, um, the area under the curve A's, um, you're gonna be Yes, we know that, um, it's gonna be between six. And seven. So now, um, we're gonna So yes. So now we're gonna get the ratio between six. And seven. So, um, we know, Yeah.