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3 years ago

Calculate the value of P and of Q that satisfy the following simultaneous linear equations.

Mathematics

1 answer:

luda_lava [24]3 years ago

5 0

0.5p -3q =11
5p +6q =2

1) ×-2

--> 3. -p +6q =-22

2) - 3)

6p =24

p =4

sub into 2)

5(4) +6q =2

20 +6q =2

6q =2 -20 =-18

q=-3

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The region bounded by the given curves is rotated about the specified axis. Find the volume V of the resulting solid by any meth

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Answer:

$\frac{128\pi}{3}$ cubic units

Step-by-step explanation:

We are given that a region bounded by a curves $x=(y-7)^2$

x=4 and about y=5

We have to find the value of volume of the resulting solid

To find the volume of resulting solid we are using cylinder method

Substitute the values of x then we get

$(y-7)^2=4$

$y-7=\pm2$

y-7=2 and y-7=-2

y=7+2=9 and y=-2+7=5

Radius of cylinder =r=y-5

and height =h= $4-(y-7)^2=4-y^2-49+14 y=-y^2+14 y -45$

Using cylinder method and integrate along y -axis from y=5 to y=9

Volume = $\int_{a}^{b}2\pi r h dy=\int_{5}^{9}2\pi(y-5)(-y^2+14 y -45) dy$

volume= $2\pi\int_{5}^{9}(-y^3+19y^2-115y+225)dy$

Volume = $2\pi[-\frac{y^4}{4}+19\frac{y^3}{3}-115\frac{y^2}{2}+225y]^9_5$

Volume = $2\pi[-\frac{6561}{4}+\frac{625}{4}+19(\frac{729-125}{3})-115(\frac{81-25}{2})+225(9-5)]$

Volume= $2\pi(-1484+\frac{11476}{3}-3220+900)$

Volume = $2\pi(\frac{11476}{3}-3804)$

Volume = $2\pi(\frac{11476-11412}{3})=\frac{128\pi}{3}$

Hence, volume of resulting solid = $\frac{128\pi}{3}$ cubic units

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3 years ago

Can anybody check and see if 11 and 12 are correct. I will Give Brainliest Answer.

alexgriva [62]

Answer:

These are correct! Nice Job!!

Step-by-step explanation:

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