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balu736 [363]
3 years ago
6

Convert the equation, x - 2y = 6, into slope-intercept form.

Mathematics
1 answer:
MArishka [77]3 years ago
6 0

Answer:

\boxed {y = -\frac{1}{2}x + 3}

Step-by-step explanation:

Convert the equation from <u>Standard Form</u> to <u>Slope-Intercept Form</u>:

Ax + By = C  ⇒  y = mx + b

-The following equation:

x - 2y = 6

-Solve:

x - 2y = 6

x - x - 2y = 6 - x

2y = -x + 6

\frac{2y}{2} = \frac{-x}{2} + \frac{6}{2}

\boxed {y = -\frac{1}{2}x + 3}

So, the equation in Slope-Intercept Form is y = -\frac{1}{2}x + 3.

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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}

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\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

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<h2 /><h2><u>8 is answer</u></h2>
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