Weeks : 1 2 3 4 5
number of insects : 4 8 16 32 64
each week ur insect collection doubled...so by week 5, u had 64 insects in ur collection
To figure ut the roots use the quadratic formula
x = [-b +- sqrt(b^2-4ac)]/2a
x = [-k +- sqrt(k^2-4(1)(5)]/2(1)
x = [-k + sqrt(k^2 - 20)]/2 or [-k - sqrt(k^2 - 20)]/2
So the question says these roots differ by sqrt 61, so let's subtract each
[-k + sqrt(k^2 - 20)]/2 - [-k - sqrt(k^2 - 20)]/2
well the k's cancel in the beginning and we are left with 2sqrt(k^2 - 20)/2, and the 2 on top and bottom reduce to
sqrt(k^2 - 20), so this equals sqrt 61
Set equal and solve
sqrt(k^2 - 20) = sqrt(61)
k^2 - 20 = 61
k^2 = 81, so k = +9 or -9
The greatest value therefore is k = +9.
2.443 x 10^6
Hope it helps! :)
Step-by-step explanation:
x= 180-109 = 71°
y= 360-81-71-100= 108