I need help with this question it's really important for a important grade pls help if can.

3 regions are defined in the figure find the volume generated by rotating the given region about the specific line

anastassius [24]

The volume generated by rotating the given region $R_{3}$ about OC is $\frac{4}{g} \pi$

<h3>Washer method</h3>

Because the given region ( $R_{3}$ ) has a look like a washer, we will apply the washer method to find the volume generated by rotating the given region about the specific line.

solution

We first find the value of x and y

$y=2(x)^{\frac{1}{4} }$

$x=(\frac{y}{2} )^{4}$

$y=2x$

$x=\frac{y}{2}$

$\int\limits^a_b {\pi } \, (R_{o^{2} } - R_{i^{2} } ) dy$

$R_{o} = x = \frac{y}{2}$

$R_{i} = x= (\frac{y}{2}) ^{4}$

$a=0, b=2$

$v= \int\limits^2_o {\pi } \, [(\frac{y}{2})^{2} - ((\frac{y}{2}) ^{4} )^{2} ) dy$

$v= \pi \int\limits^2_o= [\frac{y^{2} }{4} - \frac{y^{8} }{2^{8} }} ] dy$

$v= \pi [\int\limits^2_o {\frac{y^{2} }{4} } \, dy - \int\limits^2_o {\frac{y}{2^{8} } ^{8} } \, dy ]$

$v=\pi [\frac{1}{4} \frac{y^{3} }{3} \int\limits^2_0 - \frac{1}{2^{8} } \frac{y^{g} }{g} \int\limits^2_o\\v= \pi [\frac{1}{12} (2^{3} -0)-\frac{1}{2^{8}*9 } (2^{g} -0)]\\v= \pi [\frac{2}{3} -\frac{2}{g} ]\\v= \frac{4}{g} \pi$

A similar question about finding the volume generated by a given region is answered here: brainly.com/question/3455095

6 0

2 years ago

Lauren has an above-ground pool. To keep the pool's skimmer working well, the water level must be 4 inches from the top of the p

KIM [24]

Answer:

1885.5 m^3 of water

Step-by-step explanation:

I'll assume this is the complete question

Lauren has an above-ground pool. To keep the pool's skimmer working well, the water level must be 4 inches from the top of the pool. When the pool is filled to this recommended level, approximately how many cubic feet of water will it contain? Use π = 3.14

The pool forms a cylinder with a radius of 12 feet and a height of 4.5 feet.

height of pool = 4.5 ft

radius of pool $12^{2}$ = 12 ft

height of water is 4 inches below pool top

12 inches make 1 ft

4 inches = 4/12 ft = 0.33 ft

Therefore, height of water = 4.5 - 0.33 = 4.17 ft

volume of the water in this section of the cylinder will be equal to the volume of the cylinder formed

volume of cylinder formed by the water = volume of water = π $r^{2}$ h

volume = 3.14 x $12^{2}$ x 4.17 = 1885.5 m^3 of water

3 0

3 years ago

6 8/10 + 1 7/10 = please help meee

balandron [24]

Answer:

8.2

Step-by-step explanation:

Hope this helps....

6 0

2 years ago

Read 2 more answers

Hey some help please and thank.

tatyana61 [14]

Think of how many there are. im not sure if you put these into ratios or not...

like for number 3 think of how many numbers 1-9 are multiples of three

1 2 3 4 5 6 7 8 9

and once you get that number you make it out of 9 because there were 9 numbers

Example

3:9 3/9

for questions one and two its out of 52 and if you don't know how many clubs and hearts are in a deck you can look it up and put it in a ratio with 52

7 0

3 years ago

A total of 65 pounds of iceberg lettuce heads are purchased for use in a banquet of 120 people. If 6 ounces of cleaned chopped l

makvit [3.9K]

65 lbs= 1040 oz

120 people x 6 oz = 720 oz

1040-720 = 320 oz or 20 lbs left

6 0

3 years ago

I need help with this question it's really important for a important grade pls help if can.​

I need help with this question it's really important for a important grade pls help if can.