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OverLord2011 [107]
2 years ago
7

Write the equation 2x-3y=6 in slope intercept form

Mathematics
1 answer:
Rasek [7]2 years ago
8 0

The slope-intercept form:

y=mx+b

m - slope

b - y-intercept

We have the equation in standard form.

2x-3y=6      <em>subtract 2x from both sides</em>

-3y=-2x+6      <em>divide both sides by (-3)</em>

y=\dfrac{2}{3}x-2

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Let R be the triangular region in the first quadrant with vertices at points (0,0), (a,0), and (0,b), where a and b are positive
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Answer:

volume of the solid generated when region R is revolved about the x-axis is π ₀∫^a ( \frac{-b}{a}x + b )² dx

Step-by-step explanation:

Given the data in the question and as illustrated in the image below;

R is in the region first quadrant with vertices; 0(0,0), A(a,0) and B(0,b)

from the image;

the equation of AB will be;

y-b / b-0 = x-0 / 0-a

(y-b)(0-a) = (b-0)(x-0)

0 - ay -0 + ba = bx - 0 - 0 + 0

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ay = -bx + ba

divide through by a

y = \frac{-b}{a}x + ba/a

y = \frac{-b}{a}x + b

so R is bounded by  y = \frac{-b}{a}x + b and y =0, 0 ≤ x ≤ a

The volume of the solid revolving R about x axis is;

dv = Area × thickness

= π( Radius)² dx

= π ( \frac{-b}{a}x + b )² dx

V = π ₀∫^a ( \frac{-b}{a}x + b )² dx

Therefore,  volume of the solid generated when region R is revolved about the x-axis is π ₀∫^a ( \frac{-b}{a}x + b )² dx

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You go to a restaurant with 3 friends the total bill is 90 you pay 6% tax and add 20% tip what do you pay
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You pay $38.16 for your bill unless your friends stiff you.
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