I NEED HELP! Find the quotient using scientific notation. (6 x 10^7) / (2 x 10^3)

1 answer:

8 0

Solution :
$\dfrac{6 \times {10}^{7} }{2 \times {10}^{3} } = 3 \times {10}^{4}$

$6 \div 2 = 3 \\ 7 - 3 = 4$

Answer : 3 x 10^4

Hope this helps. - M

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At what point does the curve have maximum curvature? y = 9 ln(x) (x, y) =

Andrews [41]

y = 9ln(x)
y' = 9x^-1 =9/x
y'' = -9x^-2 =-9/x^2

curvature k = |y''| / (1 + (y')^2)^(3/2)

= |-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,

we find where k' = 0. 
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.

x=9/√2=6.36

y=9 ln(x)=9ln(6.36)=16.66

the answer is
(x,y)=(6.36,16.66)

7 0

3 years ago

What is the point-slope equation of the line with a slope 4/3 that goes through the point (-4,6)?

Sever21 [200]

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