Answer:
Solutions are 2, -1 + 0.5 sqrt10 i and -1 - 0.5 sqrt10 i
or 2, -1 + 1.58 i and -1 - 1.58i
(where the last 2 are equal to nearest hundredth).
Step-by-step explanation:
The real solution is x = 2:-
x^3 - 8 = 0
x^3 = 8
x = cube root of 8 = 2
Note that a cubic equation must have a total of 3 roots ( real and complex in this case). We can find the 2 complex roots by using the following identity:-
a^3 - b^3 = (a - b)(a^2 + ab + b^2).
Here a = x and b = 2 so we have
(x - 2)(x^2 + 2x + 4) = 0
To find the complex roots we solve x^2 + 2x + 4 = 0:-
Using the quadratic formula x = [-2 +/- sqrt(2^2 - 4*1*4)] / 2
= -1 +/- (sqrt( -10)) / 2
= -1 + 0.5 sqrt10 i and -1 - 0.5 sqrt10 i
<span>Number of bowls left after 1 hour =
x - x/3 - 1/3 = 2x/3 - 1/3
</span><span> Number of bowls left after 2 hours = (2x/3 - 1/3) -
(2x/3 - 1/3)/2 - 1/2
= 2x/6 - 1/6 - 1/2
= 2x/6 - 4/6
= x/3 - 2/3
keep doing this untill u reach 0 bowls left
and then u'll get ur answer
</span>
answer is C
He made an error in Step 3. He should have subtracted 2 from both sides.
Step-by-step explanation:
horizontal line I believe
