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:
This means that you should do what is possible within parentheses first, then exponents, then multiplication and division (from left to right), and then addition and subtraction (from left to right).
Step-by-step explanation:
Answer:
4.67 inches
Step-by-step explanation:
Shanna is planning a trip from Dallas, Texas, to San Diego, California.
She will travel about = 1,400 miles
The scale of a map is 300 miles = 1 inches
The trip of 1,400 miles = 
= 4.66666 inches ≈ 4.67 inches
Her trip is 4.67 inches far on the map.
x = 8
Explanation:
AE = 3x - 4
EC = x + 12
SInce diagonals AC and DB intersect at E
it means the lines which meet at the intersection E are equal. A and C meet at E which gives AE and EC
AE = EC
3x - 4 = x + 12
collect like terms:
3x - x = 12 + 4
2x = 16
divide both sides by 2:
2x/2 = 16/2
x = 8
