The Lagrangian is
It has critical points where the first order derivatives vanish:
From the first two equations we get
Then
At these critical points, we have
(maximum)
(minimum)
Arithmetic sequence: must have a constant common difference.
3/20-1/10=(3-2)/20=1/20
5/30-3/20=(10-9)/60=1/60
Difference is not constant, so no.
Geometric sequence: must have a common ratio
30/20 / (1/10) = 15
5/30 / (3/20) = 100/90 = 10/9
ratio is not constant, so no.
The answer is (c) neither geometric nor arithmetic
Answer:
x=12
Step-by-step explanation:
Simplifying
30 + 4x + 2 = 8 + 6x
Reorder the terms:
30 + 2 + 4x = 8 + 6x
Combine like terms: 30 + 2 = 32
32 + 4x = 8 + 6x
Solving
32 + 4x = 8 + 6x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-6x' to each side of the equation.
32 + 4x + -6x = 8 + 6x + -6x
Combine like terms: 4x + -6x = -2x
32 + -2x = 8 + 6x + -6x
Combine like terms: 6x + -6x = 0
32 + -2x = 8 + 0
32 + -2x = 8
Add '-32' to each side of the equation.
32 + -32 + -2x = 8 + -32
Combine like terms: 32 + -32 = 0
0 + -2x = 8 + -32
-2x = 8 + -32
Combine like terms: 8 + -32 = -24
-2x = -24
Divide each side by '-2'.
x = 12
Simplifying
x = 12
12 out of 18. This is because there is 6 red marbles and 18 of them all together. The question states the probability of the red marble NOT being chosen therefore you need to take away 6 from 18 leaving you with 12. I hope this made sense :)
Your radius would have to be 1.91
