6. Sketch the region enclosed by the graphs of x =0, 6y-5x=0 and x+3y=21. Find the area

2 answers:

<span>Given three equations, x=0</span>

<span>6y-5x=0</span>

<span>x+3y=21</span>

<span> </span>

<span>The lines cross at:</span>

<span>x=0, y=0</span>

<span>x=0, y=7</span>

<span>x=6, y=5</span>

<span>so base of triangle is the y-axis between 0 and 7</span>

<span>height is x=6</span>

<span>area=6*7/2=20.5</span>

<span> </span>

<span>volume=1/3*(base area)*height</span>

<span>=1/3*(pi*6^2)*7</span>

<span>=84pi</span>

<span>=263.9</span>

X = 0 <span>6y - 5x = 0 so it intersects x=0 at (0,0) </span> <span>x + 3y = 21 </span>so it intersect x=0 at (0,7) multiply by 2 <span>2x + 6y = 42 subtracting 6y - 5x = 0 7x = 42 x = 6 so the third line intersects w second line at (6,5) 6. area of triangle = 1/2*base*height = 1/2*7*6 =21 7. volume = volume of 2 cones cone volume = 1/3*pi*radius^2*height lower cone: radius=6, height=5 upper cone: radius=6, height=7-5=2 volume = 1/3*pi*6^2*(5+2) =84pi =263.89 </span>

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