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3 years ago

In circle "R" below, determine the length of arc AB if BR = 5 units.

Mathematics

2 answers:

ki77a [65]3 years ago

7 0

See the pic, I'd solved in it.

riadik2000 [5.3K]3 years ago

4 0

$l=2 \pi r( \frac{degrees}{360} )$

$l=2 \pi$ × 5 × $\frac{135}{360}$ = 11.78

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Given the hyperbola y = 1/x, find the area under the curve between x = 5 and x = 33 to 3 sig. dig. namely: integral subscript 5

Shtirlitz [24]

Answer:

(b) ln(33/5)

Step-by-step explanation:

$\int\limits_{5}^{33} \frac{1}{x} \, dx = \ln(x) \Big|\limits_{5}^{33} = \ln(33) - \ln(5) \\\\= ln(33/5)$

Remember that in general

$\ln(a) - \ln(b) = \ln(a/b)$

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2 years ago

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stiks02 [169]

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2 years ago

What is the median for this set of numbers 10,9,23,68,70,4,12,4

vesna_86 [32]

Answer:

Step-by-step explanation:

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2 years ago

Find gradient xe^y + 4 ln y = x² at (1, 1)

cricket20 [7]

$xe^y+4\ln y=x^2$

Differentiate both sides with respect to x, assuming y = y(x).

$\dfrac{\mathrm d(xe^y+4\ln y)}{\mathrm dx}=\dfrac{\mathrm d(x^2)}{\mathrm dx}$

$\dfrac{\mathrm d(xe^y)}{\mathrm dx}+\dfrac{\mathrm d(4\ln y)}{\mathrm dx}=2x$

$\dfrac{\mathrm d(x)}{\mathrm dx}e^y+x\dfrac{\mathrm d(e^y)}{\mathrm dx}+\dfrac4y\dfrac{\mathrm dy}{\mathrm dx}=2x$

$e^y+xe^y\dfrac{\mathrm dy}{\mathrm dx}+\dfrac4y\dfrac{\mathrm dy}{\mathrm dx}=2x$

Solve for dy/dx :

$e^y+\left(xe^y+\dfrac4y\right)\dfrac{\mathrm dy}{\mathrm dx}=2x$

$\left(xe^y+\dfrac4y\right)\dfrac{\mathrm dy}{\mathrm dx}=2x-e^y$

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{2x-e^y}{xe^y+\frac4y}$

If y ≠ 0, we can write

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{2xy-ye^y}{xye^y+4}$

At the point (1, 1), the derivative is

$\dfrac{\mathrm dy}{\mathrm dx}\bigg|_{x=1,y=1}=\boxed{\dfrac{2-e}{e+4}}$

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3 years ago

The mean high temperature on a particular day in January is 31 degrees F and the standard deviation is 8.7 degrees. One year, th

Basile [38]

Answer:

The Z-score for that day's temperature is 2.41, and since Z > 2, this temperature is significantly high.

Step-by-step explanation:

Z-score:

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

If $|Z| > 2$ , the measure X is significantly high(Z > 2) or significantly low(Z < -2).