SOLUTION: Shade the region satisfying each given inequality . {{{ y>=1+sqrt(9-x^2) }}}

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Question 1051947: Shade the region satisfying each given inequality .
+y%3E=1%2Bsqrt%289-x%5E2%29+
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Work through the algebraic steps to find x%5E2%2B%28y-1%29%5E2%3E=9 and make a sketch of this circle centered at (0,1) with radius of 3. BETWEEN the x-intercepts, y values will be positive or 0.

What are the x-intercepts, where y=0?
y=0=sqrt%289-x%5E2%29%2B1
-1=sqrt%289-x%5E2%29
x%5E2-9=-1
x%5E2=8
x=0%2B-+2%2Asqrt%282%29
Some steps here were omitted.

Between inclusive, -2sqrt%282%29 and 2sqrt%282%29, y will be positive or 0. You would shade the region ABOVE the circle for x values between and including those two values.


Note that neither of these graphs look the way they need to be. You want to shade ONLY the region between the x-intercepts ABOVE AND INCLUDING the circle. (My use of the site's code is just not right, or I do not yet know this code well enough.)

graph%28300%2C300%2C-5%2C5%2C-5%2C5%2Cx%5E2%2B%28y-1%29%5E2%3E=9%29

graph%28300%2C300%2C-5%2C5%2C-5%2C5%2Cy-1%3E=sqrt%289-x%5E2%29%29