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:
The angle between the hands of a clock at 5:00 is 150
Step-by-step explanation:
hope this helped
Ok what else before I can help
lol i cant answer that im only in middle schoolStep-by-step explanation:
1) find the lcd the lcd is 12
2)rewrite the fractions 1/4 and 2/3 using 12 as the denominator (second column) you get 3/12 and 8/12
3) since its confusing to subtract 8/12 from 3/12 you need to borrow one form the 126 doing so is the same as taking 12/12 from 126 this change to 125 and the 12/12 adds to the 3/12 making it 15/12
4) subtract 8/12 form 15/12 to get 7/12
5) subtract 78 form 125 to get 47
6) the answer is 47 7/12
