3 years ago

I need help with my algerbra

Mathematics

1 answer:

Molodets [167]3 years ago

5 0

I can help you what problem??

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7m - 6 + 3m + 7 = 21

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Find the volume of the solid whose base is the region Ix I Iy I < 1 and whose vertical cross sections perpendicular to the y-

gavmur [86]

Answer:

volume of the solid = $\frac{\pi }{3}$

Step-by-step explanation:

As given , the region : |x| + |y| $\leq$ 1

when y $\geq$ 0 ,

|x| + y = 1

⇒|x| = 1 - y

when y ≤ 0 ,

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⇒|x| = 1 + y

The given region is the rectangle with sides (0, 5) , (0, -5), (5, 0), (-5, 0)

As given , the vertical cross section are semicircle

As we know that the area of semi circle = $\frac{1}{2}$ $\pi x^{2}$

Now,

Volume = $\int\limits^0_-1 {\frac{\pi }{2} (1+y)^{2} } \, dy$ + $\int\limits^1_0 {\frac{\pi }{2} (1-y)^{2} } \, dy$

= $\frac{\pi }{2} (\frac{(1+y)^{3} }{3} )$ - $\frac{\pi }{2} (\frac{(1-y)^{3} }{3} )$

= $\frac{\pi }{6}$ [1-0] - $\frac{\pi }{6}$ [0-1]

= $\frac{\pi }{6} + \frac{\pi }{6} = 2\frac{\pi }{6} = \frac{\pi }{3}$

⇒volume of the solid = $\frac{\pi }{3}$

4 0

3 years ago

Thank you so much. (20 characters required)

padilas [110]

#3.
√18²-5.7² Second Choice

#4
l²=5²+4² = 25+16 = = 41
l=√41
l= 6.4

Second Choice

#5 Only A --- First choice

#7 6 ----- Third choice

#8 V= $\pi r^2(h)= \pi 10^2(3) = 314(3)=$ 942 units³ ---Second choice

6 0

2 years ago