A group of students were surveyed to find out if they like watching television or reading during their free time. The results of
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Whereas the density of the hemisphere at any point is proportional to it's density, then
The full answer in attachment, we use the partial integral using the <span>spherical coordinates,
and we find that </span>the mass of h = <span>πK/2</span>
The full answer in attachment, we use the partial integral using the <span>spherical coordinates,
and we find that </span>the mass of h = <span>πK/2</span>
The graph of is a horizontal line. So the area under
on [0, 8] is equal to the area of a rectangle with length 8 and height 2, or 16.
The graph of is the upper half of a circle with radius
. It's symmetric about
, so on the interval [0, 8], we're considering a quarter of the circle. The area of such a sector is
.
Then use the fact that the definite integral is distributive over sums, meaning