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: 4w-14
Step By step explanation: 4(w-2)-6= 4w-8-6= 4w-14
B is the only rational answer.
Answer:
the cubes are 1 in on all sides
but...
since there's gaps its more likely that there a 1/2 in or 3/4 in
Step-by-step explanation:
12/12=1
Answer:
width of one box = 1.25 inches
Step-by-step explanation:
Given data:
12 congruent boxes
Length = 25 inches
height = 2 feet
Volume = 9000 cubic inches
First change the height into inches
1 foot = 12 inches
therefore 2 feet = 24 inches
Volume = Length * width * height
9000 = 25 * width * 24
9000 = 600 * width
width = 9000/600
width = 15 inches
width of one box = width of all boxes / number of boxes
width of one box = 15/12
width of one box = 1.25 inches
