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3 years ago

What is the measure of angle x? Enter your answer in the box. x = ( )°

Mathematics

2 answers:

Over [174]3 years ago

5 0

90 - 47 = 43

x = 43
vertical angles are equal

hope it helps

Alexandra [31]3 years ago

3 0

We know that angles on a straight line sum to 180°, and we can see that 90° has already been defined on the left top left hand, leaving us with 90° on the top right hand. We are given 47°, so that must mean that the angle between the right angle and the 47° angle is:
90-47= 43°
Opposite angles around a 360° point are equal, and we see that angle x is opposite the 43° that we just found out. Therefore, x= 43°

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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

Lubov Fominskaja [6]

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

3 0

3 years ago

Please answer the image below .

mojhsa [17]

There u just needed to search the formula

8 0

3 years ago

Read 2 more answers

How to solve approximate square roots

Murljashka [212]

Just follow this operation.
Find the two perfectly squared factors the multiple to your number.
Take the square root of those perfect factors then multiple them.