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)
98 divided by 2 equals 49
55 divided by 5 equals 11
Answer is: 111.847
Method:
1 m/s = 2.23693629 mi/hr
Therefore ->
50 (m/s) * 2.23693629 (mi/hr) = 111.847 mi/hr
(Thanks to google)
Answer:
The correct answer is: 3x² (4x - 1) / (x - 4) (x - 3) ∧ restriction x ≠ 3, x ≠ 4, x ≠ 0 and x ≠ 1/4
Step-by-step explanation:
Given:
((16x² - 8x + 1) / (x² - 7x + 12)) : ((20x² - 5x) / 15x³) =
dividing with one fraction is the same as multiplying with its reciprocal value
((16x² - 8x + 1) / (x² - 7x + 12)) · (15x³ / (20x² - 5x))
First we need to factorize both numerators and denominators
16x² - 8x + 1 = (4x - 1)² This is square binomial
x² - 7x + 12 = x² - 4x - 3x + 12 = x (x - 4) - 3 (x - 4) = (x - 4) ( x - 3)
20x² - 5x = 5x (4x - 1)
(4x - 1)² / (x - 4) (x - 3) · 15x³ / 5x (4x - 1)
The existence of this rational algebraic expression is possible only if it is:
x - 4 ≠ 0 and x - 3 ≠ 0 and x ≠ 0 and 4x - 1 ≠ 0 =>
x ≠ 4 and x ≠ 3 and x ≠ 0 and x ≠ 1/4 This is restriction
Finally we have:
3 x² (4x - 1) / (x - 4) (x - 3)
God with you!!!
Answer:
Step-by-step explanation:
Sorry
