Answer:
20 because 40 is a positive and spent is negative
Step-by-step explanation:
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:
$19.15
Step-by-step explanation:
Equation 1: 8.50+4.25+4.25= 17.00 (price of the popcorn and drinks)
Equation 2: 17.00/7.89= 2.15 (how to find how much the tax is)
Solve: 17.00+2.15=19.15 (add the tax to how much the popcorn and drinks were)
The answer is, 4 + 8 + 12 + 16 ... rule is 4n.
Explanation:
one square has 4 toothpicks, then you added 4 picks (because you started with zero squares).
4 squares have 12 toothpicks, then you added 8 toothpicks to pass from one square to 4 squeres.
If you follow that reasoing you get to realize that the additions are 4, 8, 12, 16.
