Question

find a number k>0 such that the area bounded by the curves y=X^2 and y=k-x^2 is 72 square units.

Answer 1

18. is the first guess :)
do u have choices ?

Answer 2

i dont have any choices., how did you got it?

Answer 3

actually, i use by formula :
area = (D * sqrt(D))/6a^2
with D =discriminant of quadratic equation
and D=b^2-4ac

Answer 4

here, known the area bouded of curves y = x^2 and y = k - x^2
first, we take y1 = y2 therefore
x^2 = k - x^2
2x^2 - k = 0
a = 2, b = 0, c = -k

Answer 5

so, the value of discriminant is
D=0^2 - 4(2)(-k) = 8k

Answer 6

area = (D * sqrt(D))/6a^2
72 = 8k sqrt(8k) / 6(2)^2
72 = 8k sqrt(8k) / 24
72 = k sqrt(8k) / 3
squaring to both sides, gives us
72^2 = k^2 (8k)/ 9
(9 * 8)^2 = 8k^3/9
9^2 * 8^2 = 8k^3/9
multiply both sides by 9/8, giving us
9^3 * 8 = k^3
9^3 * 2^3 = k^3
(9 * 2) ^3 = k^3
the finally, we get k=18

Answer 7

sorry, if my answer is wrong... but this is my opinion :)

Answer 8

would it have a shorter answer? like use integral?

Answer 9

its okay :)

Answer 10

yeah, this problem actually can solved by integration or by using formula above
but it is an easier than by integral :)

Answer 11

yeah, maybe this is a shorter answer