You have to put the number in the graph
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:
<h2>
</h2>
Step-by-step explanation:
<em><u>Given</u></em><em><u>,</u></em>
Diameter of the bowl = 6 in
Radius of the bowl = 6 ÷ 2 = 3 in.
Height of the bowl = 2 in.
<em><u>Therefore</u></em><em><u>, </u></em>
Volume of the bowl to hold water ,
Answer:
So basically the answer is where the lines intersect if they do not intersect there is no solution if they are on top of one another it is infinite solutions
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
7+2n = 11
2n = 11-7
2n = 4
n = 4/2
therefore n = 2
