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3 years ago

Explain the Proof for Lemis Theorm

Mathematics

1 answer:

11111nata11111 [884]3 years ago

3 0

You mean Lami’s Theorem?

Consider the figure. Three concurrent forces net to static equilibrium at the origin. Let's assume for simplicity force a is along the positive x axis.

We have equilibrium when the components of force balance in both dimensions. In particular in the y dimension,

$b \sin C = c \sin B$

$\dfrac{b}{\sin B} = \dfrac{c}{\sin C}$

We're free to move our coordinate system around to make any of the force vectors the x axis and then we'd get the same sine balance as in the Law of Sines for the remaining pair of sides.

$\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}$

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If the length of side a is 16 centimeters, the length of side b is 10 centimeters, and m = 42°, what is the measure of ? Round y

kupik [55]

Answer:Substitute the given values in the Law of Sines and find that the measure is 24.72°

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4 years ago

ccording to the U.S. National Weather Service, at any given moment of any day, approximately 1000 thunderstorms are occurring wo

viva [34]

Answer:

The critical value of z for 99% confidence interval is 2.5760.

The 99% confidence interval for population mean number of lightning strike is (7.83 mn, 8.37 mn).

Step-by-step explanation:

Let X = number of lightning strikes on each day.

A random sample of n = 23 days is selected to observe the number of lightning strikes on each day.

The random variable X has a sample mean of, $\bar x=8.1\ mn$ and the population standard deviation, $\sigma=0.51\ mn$ .

The (1 - α)% confidence interval for population mean μ is:

$CI=\bar x\pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

Compute the critical value of z for 99% confidence interval is:

$z_{\alpha/2}=z_{0.01/2}=z_{0.005}=2.5760$

*Use a z-table.

The critical value of z for 99% confidence interval is 2.5760.

Compute the 99% confidence interval for population mean number of lightning strike as follows:

$CI=\bar x\pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}\\=8.1\pm2.5760\times\frac{0.51}{\sqrt{23}}\\=8.1\pm0.2738\\=(7.8262, 8.3738)\\\approx(7.83, 8.37)$

Thus, the 99% confidence interval for population mean number of lightning strike is (7.83 mn, 8.37 mn).

The 99% confidence interval for population mean number of lightning strike implies that the true mean number of lightning strikes lies in the interval (7.83 mn, 8.37 mn) with 0.99 probability.

3 0

3 years ago

Which is the graph of g(x) = ⌈x + 3⌉?

77julia77 [94]

ANSWER

$\boxed {D}$

EXPLANATION

The given function is,

$g(x) = ⌈x + 3⌉$

The parent function of this ceiling function is

$g(x) = ⌈x ⌉$

When this function is shifted horizontally 3 units to the left, we obtain the transformed function,

$g(x) = ⌈x + 3⌉$

The correct answer is option D.

See attachment.