Which situation could be described by the expression m – 1.85?
2 answers:
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Answer
X1= 3-2 root3 x2= 1 x3=5 x4= 3 +2 root 3
First swap the sides then simplify the equation
Collect like terms
Move all the expression to the left to equal 0
Then collect like terms again
Reorder the terms from ^2 to ^4
Factor the expression
Change the signs
Separate into possible cases
Then sold the equation to equal 0
Then check solutions by subbing them in as x
Then you should have 4 perfect answers
X1= 3-2 root3 x2= 1 x3=5 x4= 3 +2 root 3
First swap the sides then simplify the equation
Collect like terms
Move all the expression to the left to equal 0
Then collect like terms again
Reorder the terms from ^2 to ^4
Factor the expression
Change the signs
Separate into possible cases
Then sold the equation to equal 0
Then check solutions by subbing them in as x
Then you should have 4 perfect answers
Answer:
The value of x that gives the maximum transmission is 1/√e ≅0.607
Step-by-step explanation:
Lets call f the rate function f. Note that f(x) = k * x^2ln(1/x), where k is a positive constant (this is because f is proportional to the other expression). In order to compute the maximum of f in (0,1), we derivate f, using the product rule.
We need to equalize f' to 0
- k*(2x ln(1/x) - x) = 0 -------- We send k dividing to the other side
- 2x ln(1/x) - x = 0 -------- Now we take the x and move it to the other side
- 2x ln(1/x) = x -- Now, we send 2x dividing (note that x>0, so we can divide)
- ln(1/x) = x/2x = 1/2 ------- we send the natural logarithm as exp
- 1/x = e^(1/2)
- x = 1/e^(1/2) = 1/√e ≅ 0.607
Thus, the value of x that gives the maximum transmission is 1/√e.