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:
C. 33 square feet.
Step-by-step explanation:
to get the area of irregular polygon.
divide the area into two parts (see attached image)
total area = A1 + A2
where A = 1/2 base x height
total area = ( 1/2 * 6 * 8) + (1/2 * 6 * 3)
total area = 24 + 9
total area = 33 square feet.
therefore the answer is C. 33 square feet.
Answer: a. p = c/5 - 43 b. 17 people
Step-by-step explanation:
c= 5p + 215
A) a said solve for p so we will solve for p in the equation.
c= 5p + 215 First Subtract 215 from both sides
-215 -215
c - 215 = 5p Now divide both sides by 5.
p = c/5 - 43
B) If c is the total cost of hosting a birthday party then we will input 300 into the equation for c and solve for p.
300 = 5p + 215 First subtract 215 from both sides
-215 -215
85 = 5p Divide both sides by 5
p = 17
This means 17 people can attend the meeting if Allies parents are willing to spend $300.
Use the formula a^2+b^2=c^ which is 7.21
1-0.15=0.85
36.21/0.85=42.6=ANSWER
