3 years ago

At this point i need help on this whole test lol. so pls help. math is literally my WORST subject

Mathematics

1 answer:

Sladkaya [172]3 years ago

6 0

Answer:

x=5

Step-by-step explanation:

x=5 because this triangle is an equilateral triangle (a triangle that has 3 equal sides) so if one side is five the others are also going to be 5

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Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 4 − 1 2

MissTica

Answer:

${\dfrac{127 \pi}{12}$

Step-by-step explanation:

The formula for the volume for a solid of revolution about the x-axis on an interval [a,b] is

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$\displaystyle V = \int_{1}^{2} \pi (4 - \frac{1}{2}x)^{2}dx = \pi \int_{1}^{2} \left(\dfrac{8-x }{2}\right)^{2}dx=\dfrac{\pi }{4}\int_{1}^{2} \left(8-x\right)^{2}dx\\\\=-\dfrac{\pi }{4}\times \dfrac{1}{3}\left[ 8 - x)^{3}\right]_{1}^{2}= -\dfrac{\pi }{12 }\left [512 - 192x + 24x^{2}-x^{3} \right ]_{1}^{2}\\\\=-\dfrac{\pi }{12}(512 - 384 + 96-8) + \dfrac{\pi }{12}(512 - 192 +24 -1)\\\\= -\dfrac{216\pi }{12} + \dfrac{343\pi }{12} = \mathbf{\dfrac{127 \pi}{12}\approx 33.25}$