Answer:
x = (1/2) (-9 ± √73)
Step-by-step explanation:
Using completing the square method
x²+9x+2=0
x²+9x = -2 (complete the square by adding (9/2)² to both sides)
x²+9x + (9/2)² = -2 + (9/2)²
( x + (9/2) )² = -2+ (9/2)²
( x + (9/2) )² = -2+ (81/4)
( x + (9/2) )² = 73/4
x + (9/2) = ± √(73/4)
x + (9/2) = ± √(73) / 2
x = -(9/2) ± √(73) / 2 (factorize out (1/2) )
x = (1/2) (-9 ± √73)
There are 4 As and 3 Bs, so the ratio of Bs to the total number of As and Bs is ...
... (count of Bs) : (count of As + count of Bs)
... = 3 : (4 + 3)
... = 3 : 7
Expressed as a fraction, this is
... 3/7
Answer:
3V
r = ∛ ( ---------- )
4π
Step-by-step explanation:
Please, enclose the fraction 4/3 inside parentheses, to eliminate any possibility of misreading this fraction. Also note that this formula MUST include "pi," symbolized by π.
V = (4/3) π r³ This formula does NOT include "m," which is a unit of measurement, not a variable.
Our task is to solve this formula for the radius, r.
Divide both sides by (4/3) π, to isolate r³. This results in:
v (4/3) π r³
------------- = -----------------
(4/3) π (4/3) π
V 3V
Then r³ = -------------- = --------
(4/3) π 4π
and r is found by taking the cube root of the above result:
3V
r = ∛ ( ---------- )
4π
