Could someone help me with this
1 answer:
Answer:
angle x is 130 degrees
Step-by-step explanation:
Recall that the addition of all central angles of the full circle should add up to . There are two angles that are explicitly given: MON =
, and POR =
. The other piece of information is that the arc from M to R is 4 times the length of the smaller arc From N to M, and therefore, their angles should keep the same proportion. That is: angle MOR should be 4 times angle MON, which in math terms will be: MOR = 4 x
, then MOR =
.
Now, since the addition of all angles should total , we can find what angle "x" measures:
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Answer:
Step-by-step explanation:
Given:
Since the equation is written in slope-intercept form, it is extremely easy to find the y-intercept. Slope-intercept form is written as:
Whereas:
y: range
m: slope
x: domain
b: y-intercept
With that in mind, we can immediately tell that 6 is the y-intercept.
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.