Answer:
49/99
Step-by-step explanation:
Follow the first hint. Since there are two numbers that are repeating, the numerator will be 49. The denominator will have two nines.
Hope this helps!
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:
20%
Step-by-step explanation:
A pair of jeans cost $45 before the sale.
The sale is taking $9 off of the original price.
Then
$45 - 100%
$9 - x%
Write a proportion:
Cross multiply:
Step-by-step explanation:
c/(c - 5) = 4/(c - 4)
By Cross-multiplying,
We have c(c - 4) = 4(c - 5).
=> c² - 4c = 4c - 20
=> c² - 8c + 20 = 0
Since the discriminant is negative,
there are no real solutions for c.
However, there exist complex solutions for c.
Using the Quadratic Formula,
c = [8 ± √(-16)]/2
=> c = 4 ± √(-4)
=> c = 4 ± 4i or c = 4(1 ± i).
