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
<em>while the two were at the movies Katie spent $40.00</em>
Answer:
8
Step-by-step explanation:
For the smallest possible length, this has to be one of the shorter sides. Let the length of this side be x.
So, by the triangle inequality theorem, 1+x>8, which means x>7.
So, the smallest possible whole number length is 8.
Answer:
21
Step-by-step explanation:
Since Lilly has read 7/8 of her book (aka 147 pages), divide 147 by 7 and you get 21.
This means 1/8=21
Since she has read 7/8 of the book, and the full book is 8/8, 8/8-7/8= 1/8
Meaning she has 1/8 of the book left to read.
As said before, 1/8 =21
Thus, she has 21 pages left to read.
6 strawberries.
one plum= 32 calories
one strawberry=4 calories
total calories=56
56-32=24
24 calories come from the strawberries
24÷4=6
Therefor 6 strawberries
