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
Answer:
28
Step-by-step explanation:
40% 6th graders of 70 total = 28 6th graders
40% 6th graders + 20% 7th graders = 60%
100% - 60% = 40% 8th graders
40% are 8th graders therefore the answer is 28
Answer:
10 people lesser.
Step-by-step explanation:
Initially, it 15 people get off but 9 people get picked up, hence losing 6 people. If 4 more people get off, it has then lost 10 people total.
The original number of passengers on the bus decreased by 10 after the second stop
Assume that the total passengers on the bus before 2:30 was x
Now, at 2:30:
15 passengers got off and 9 got on.
This means that:
number of passengers = x - 15 + 9
number of passengers = x -6
10 minutes later:
4 passengers got off the bus
This means that:
number of passengers = (x-6) - 4
number of passengers = x - 10
The original number of passengers on the bus decreased by 10 after the second stop.
Answer:
Step-by-step explanation:
735$
