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
Slope formula: y2-y1/x2-x1
= 12-5/3-2
= 7/1
= 7
_____
Best Regards,
Wolfyy :)
This kind of problems requires to add the working velocities. The total velocity is the sum of the individual velocities.
Anita's velocity = 1 pool/8 hours
Chao's velocity = 1 pool/6 hours
Combined velocity 1/8 + 1/6 = (3 + 4)/24 = 7/24 pool/hour
Time = 1 pool / (7/24) pool/hour = 24/7 hour =3.43 hours
Four plus the absolute value of twenty-seven minus ten
The right answer is 4 hoped i helped