WEBVTT
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we know the formula for point slope form is why
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minus y wan is m times x minus X one
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, which means the why is m which is the
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slope comes Xmas X one plus y one correct plug
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. And now what the problem has given us.
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And we see this essentially means that if we because
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this is a hat is the settling of a cross
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section and this is half of that length, we
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know that doubling it would give us the value we
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need, which is going to be SFX essentially.
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So doubling this gives us a minus B times h
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of acts must be So what essentially means that when
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we double that we multiplied this whole thing by two
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. We just crossed off all the twos. Right
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. Okay, now that we have this, we
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know that we have toe again. We're gonna be
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getting the volume. So V is from zero to
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h r squared D backs. Now we established what
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us is. We just figured that out. So
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plug in a menace, be over H of ax
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, plus b. Remember, it's squared. This
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is us. A square just means we have the
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squared now remember, when we integrate, we use
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the power rule, which means we increased the experiment
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by one and we divide by the new expert.
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So again we're dividing by the new exponents and then
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for terms such as B squared. As you can
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see, we have added a X on because that's
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what we do. We integrate when we have a
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constant just becomes the new coefficient, so plugging in
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, we know we have 1/3. This could be
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pulled out. It's the constant times H that's common
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in these two terms. A squared plus a B
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plus B squared. Remember, you're gonna need to
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use the foil method from algebra, which you should
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have learned. No, given this we know.
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But as a promise, Miss Fei ai is B
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, which means V is 1/3 h times a squared
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plus eight times A, which is a squared again
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, plus a squared like this, which simplifies to
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simply h a squared because it's just one plus one
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plus 1/3 which is 3/3 which is just one was
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just a J squared. That's explanation for why,
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and then we know if h zero there if a
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zero, then we have 1/3 H B Square because
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they've said that a a zero, As we can
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see, this is the pyramid volume formula with the
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base that is a square, so equal sides equal
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angles. So what this means is that we end
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up with V is 1/3 age times a squared,
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plus a B plus B squared. This is the
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formula. And as we said, if A's be
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, then we have a rectangular box with a zero
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, then we have a pyramid.