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.
Step-by-step explanation:
step 1. an example of difference of squares (dos) is (x + y)(x - y) = x^2 - y^2.
step 2. dos must have only 2 square rootable terms and a "-" between them.
step 3. 196x^2 - 121y^2 = (14x + 11y)(14x - 11y) works!
step 4. 5x^2 - 245 = 5(x^2 - 49) = 5(x + 7)(x - 7) works!
step 5. 27w^5 - 75w = 3w(9w^4 - 25) = 3w(3w^2 + 5)(3w^2 - 5) works!
step 6. x^4 - 100y^2 = (x^2 - 10y)(x^2 + 10y) works!
B. Because you can easily just eat at home and avoid paying to eat
Answer: 138
Step-by-step explanation:
