I think a) would be the answer. I proceeded by elimination: the domaine of the function goes from 3 and continues to infinity, so that leaves with a) and b) as possible answers. Both have the same range and both of their functions reflect over the x axis, so we have to compare the two answer by looking at the position of the function in the graph. The function is in the first quadrant (top right corner), so the position of the function has to be at our right, which leads us to a).
F(x) = 18-x^2 is a parabola having vertex at (0, 18) and opening downwards.
g(x) = 2x^2-9 is a parabola having vertex at (0, -9) and opening upwards.
By symmetry, let the x-coordinates of the vertices of rectangle be x and -x => its width is 2x.
Height of the rectangle is y1 + y2, where y1 is the y-coordinate of the vertex on the parabola f and y2 is that of g.
=> Area, A
= 2x (y1 - y2)
= 2x (18 - x^2 - 2x^2 + 9)
= 2x (27 - 3x^2)
= 54x - 6x^3
For area to be maximum, dA/dx = 0 and d²A/dx² < 0
=> 54 - 18x^2 = 0
=> x = √3 (note: x = - √3 gives the x-coordinate of vertex in second and third quadrants)
d²A/dx² = - 36x < 0 for x = √3
=> maximum area
= 54(√3) - 6(√3)^3
= 54√3 - 18√3
= 36√3.
Answer: 170% da da
Step-by-step explanation:
Some equivalent fractions of 1/6 are:
1/6 = 2/12 = 3/18 = 4/24 = 5/30 = 6/36 = 7/42 = 8/48 = 9/54 = 10/60 = 11/66 = 12/72 = 13/78 = 14/84 = 15/90 = 16/96 = 17/102 = 18/108 = 19/114 = 20/120 = 21/126 = 22/132 = 23/138 = 24/144 = 25/150 = 26/156 = 27/162 = 28/168 = 29/174 = 30/180 = 31/186 = 32/192 = 33/198 = 34/204 = 35/210 = 36/216 = 37/222 = 38/228 = 39/234 = 40/240
