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5 months ago

How do you find the derivative of 1/logx?

Mathematics

1 answer:

valentina_108 [34]5 months ago

5 0

The derivative of 1/logx is With the chain rule.

1log(x)=log(x)−1 is ,= -1xlog(x)2 .

The by-product of logₐ x (log x with base a) is 1/(x ln a). Here, the thrilling issue is that we have "ln" withinside the by-product of "log x". Note that "ln" is referred to as the logarithm (or) it's miles a logarithm with base "e".

The by-product of 1/log x is -1/x(log x)^2. Note that 1/logx is the reciprocal of log.

$With the chain rule. \\ 1log(x)=log(x)−1 \\ So you follow the chain rule to the electricity after which to the log: \\ ddxlog(x)−1=−1⋅log(x) \\ \\−2⋅ddxlog(x) \\ =−1log(x)21x \\ =−1xlog(x)2 .$

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The mean sat verbal score is 486, with a standard deviation of 95. use the empirical rule to determine what percent of the score

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Find the z-scores for the two scores in the given interval.

$z=\frac{x-\mu}{\sigma}$

For the score x =391, $z=\frac{391-486}{95}=\frac{-95}{95}=-1$ .

For the score x = 486, $z=\frac{486-486}{95}=0$

Now you want the area (proportion of data) under the normal distribution from z = -1 to z = 0. The Empirical Rule says that 68% of the data falls between z = -1 to z = 1. But the curve is symmetrical around the vertical axis at z = 0, so the answer you want is HALF of 68%.

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3 years ago

Evaluate the polynomial 6x - y for x = 3 and y =4

Mashcka [7]

6 x 3 is 18. y is equal to 4. 18 minus 4 is 14. The answer is 14.

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2 years ago

Archimedes calculated the volume of a sphere by comparing it to what solid? prism cylinder pyramid box

Stella [2.4K]

<h2>Answer:</h2>

cylinder

<h2>Step-by-step explanation:</h2>

Archimedes was a brilliant mathematician. This man rose the formula of the volume of a sphere by comparing this shape to a cylinder. The volume of a sphere is hard to calculate by comparing this object to a cube. So Archimedes imagined cutting a sphere into two halves, called hemispheres. So an hemisphere gave him a flat surface, which is easier to work with. Therefore, if he'd find the volume of a hemisphere, then he'd multiply the result by 2 and would get the volume of a sphere. Then he imagined a hemisphere within a cylinder as the one shown below. Also, he imagined a cone within the same cylinder. <em>What did he find? </em>He found that the volume of the hemisphere should be equal to the volume of the cylinder minus the volume of the cone:

$V=\pi r^3-\frac{1}{3}\pi r^3 \\ \\ V=\frac{2}{3} \pi r^3$

Then the volume of a sphere is twice this volume:

$\boxed{V=\frac{4}{3} \pi r^3}$

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2 years ago

For the given function, find the vertical and horizontal asymptotes f(x)= x2+3/ x2-9

Ratling [72]

Set the denominatior equal to zero to find vertical asymptotes. Horizontal take the highest degree of the top and divide it by the highest degree of the bottom.
${x}^{2} - 9 = 0 \\ {x}^{2} = 9 \\ x = 3 \\ x = - 3 \\ \\ \frac{ {x}^{2} }{ {x}^{2} } = 1 \\ y = 1$
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Horizontal : y=1

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2 years ago

You have a jar containing 55 coins, consisting entirely of nickels and quarters, worth a

yawa3891 [41]

Answer: 22 quarters

Step-by-step explanation:

Let N be the number of nickels.

Then the number of quarters is (55-N)

The nickels contribute 5N cents to the total.

The quarters contribute 25*(55-N) cents to the total.

5N + 25*(55-N) = 715

5N + 1375 - 25N = 715

-20N = 715 - 1375 = -660

$N=\frac{-660}{-20}$

$=33$

$55-33=22$

So there is 22 quarters inside the jar.

Check to see if my answer is correct-

33*5 + 22*25 = 715 cents

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2 years ago