A.Is 59.5 C. is 35.38 E. is 134.12 B. is 69.28 D. is 0.34 F. is 37.43100
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 is A, y = 65
The top angle is 50 because 180 - 130 = 50
Since the top angle is 50, the two bottom angles have to add up to 130. Since the bottom angles are the same, you can do 130 / 2 to find the angles which equals 65.
Answer:
2² * 3⁴ * x * y³
Step-by-step explanation:
<h3>Simplify:</h3>
First prime factorize 324
324 = 2 * 2 * 3 * 3 * 3 * 3
Now , write in exponent form:
324 = 2²*3⁴
324xy³ =2² * 3⁴ * x * y³
Answer:
g=4
Step-by-step explanation:
-6g + 36 = 12
-36 = -36
-6g = -24
------ -------
-6 -6
g=4
