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)
His estimate is reasonable. But only if Michael is less than 2 years old.
Answer:
z = 61
Step-by-step explanation:
The exterior angle is congruent (equal to) the sum of the 2 farthest angles from it, so you can set the equation like this:
z + z - 11 = z + 50
Add like terms, which would be the 2 "z's" on the left side:
2z - 11 = z + 50
Then subtract the z on the right side from both sides:
2z - 11 = z + 50
-z -z
___________
z - 11 = 50
Add 11 to both sides:
z - 11 = 50
+ 11 +11
________
z = 61
Answer:
T=29.95a + 13.95c
Step-by-step explanation:
For this equation let a=amount of adult tickets, c=amount of children tickets, and T=the total cost. Since each adult ticket costs 29.95 dollars that needs to be multiplied by the number of adult tickets to see how much was spent on adults, the same goes for the price and number of children tickets. Finally, both of those totals need to be added together to see how much is spent overall for all of the guests.
