y = 9ln(x)
<span>y' = 9x^-1 =9/x</span>
y'' = -9x^-2 =-9/x^2
curvature k = |y''| / (1 + (y')^2)^(3/2)
<span>= |-9/x^2| / (1 + (9/x)^2)^(3/2)
= (9/x^2) / (1 + 81/x^2)^(3/2)
= (9/x^2) / [(1/x^3) (x^2 + 81)^(3/2)]
= 9x(x^2 + 81)^(-3/2).
To maximize the curvature, </span>
we find where k' = 0. <span>
k' = 9 * (x^2 + 81)^(-3/2) + 9x * -3x(x^2 + 81)^(-5/2)
...= 9(x^2 + 81)^(-5/2) [(x^2 + 81) - 3x^2]
...= 9(81 - 2x^2)/(x^2 + 81)^(5/2)
Setting k' = 0 yields x = ±9/√2.
Since k' < 0 for x < -9/√2 and k' > 0 for x >
-9/√2 (and less than 9/√2),
we have a minimum at x = -9/√2.
Since k' > 0 for x < 9/√2 (and greater than 9/√2) and
k' < 0 for x > 9/√2,
we have a maximum at x = 9/√2. </span>
x=9/√2=6.36
<span>y=9 ln(x)=9ln(6.36)=16.66</span>
the
answer is
(x,y)=(6.36,16.66)
Answer:
95/351
Step-by-step explanation:
the first thing you must do is to add 140 and 94 and 22 together
you get 256
then you subtract 351 with 256 and get 95
and then you do this
95/351
Answer:
x times (x+1).
If it's wrong, then I'm an idiot.
Step-by-step explanation:
Answer:
d) All of the above
Step-by-step explanation:
A one way analysis of variance (ANOVA) test, is used to test whether there's a significant difference in the mean of 2 or more population or datasets (minimum of 3 in most cases).
In a one way ANOVA the critical value of the test will be a value obtained from the F-distribution.
In a one way ANOVA, if the null hypothesis is rejected, it may still be possible that two or more of the population means are equal.
This one way test is an omnibus test, it only let us know 2 or more group means are statistically different without being specific. Since we mah have 3 or more groups, using post hoc analysis to check, it may still be possible it may still be possible that two or more of the population means are equal.
The degrees of freedom associated with the sum of squares for treatments is equal to one less than the number of populations.
Let's say we are comparing the means of k population. The degree of freedom would be = k - 1
The correct option here is (d).
All of the above
