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)
The property used in the equation is called Distributive property.
<h3>What is
Distributive property?</h3>
The distributive Property States that when a factor is multiplied by the sum/addition of two terms, it is essential to multiply each of the two numbers by the factor, and finally perform the addition operation.
Given an equation, 4 x (5 + 6) = (4 x 5) + (4 x 6)
The property used in this equation is distributive property.
a(b+c) = (a*b)+(a*c)
Hence, The property used in the equation is called Distributive property.
For more references on Distributive property, click;
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Answer:
x = 43
Step-by-step explanation:
x + 28 + 195 = 180
x + 223 = 180
x = 180 - 223
x = 43 (ANS)
I hope my answer is correct. If not I apologize.
Answer:
2.16666666667 or rounded to 2.17
Step-by-step explanation:
first you have to change the mixed number to an improper fraction which would be 13/6 and then divide the numerator by the denominator
8/4=12/x
Would be the ratio.
Solve it:
8/4 =12/x
2=12/x
2x=12
X=6
