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3 years ago

Using the slope formula, find the slope of the line through the points (0,0) and (5,10).

Mathematics

1 answer:

pychu [463]3 years ago

8 0

<h2>Answer:</h2>

First, we need to find the slope of the line using slope formula*.

$m = \frac{10 - 0}{5 - 0} = \frac{10}{5} = 2$

Slope of the line: 2

Second, we determine the y-intercept using the slope we just found, one of the given points, and slope-intercept form**.

$10 = 2(5) + b\\\\10 = 10 + b\\\\0 = b$

Because b = 0, this means that the y-intercept is the origin, (0,0), so it is not written in the equation.

Finally, we create the equation of the line.

$y = 2x$

Slope formula: y₂ - y₁/x₂ - x₁

Slope-intercept form: y = mx + b

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The distance between the baseball stadium and the airport is 1.6×10^6 centimeters.Which unit of measurement is most appropriate

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Tan(x+pi) + 2sin(x+pi)=0 can you help prove this and make the left side equal the right?

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This is not an identity but an equation. You're supposed to find the values of $x$ for which this is true. It is *not* true for all values of $x$ .

To see why:

$\tan x$ has period $\pi$ , which means $\tan(x+\pi)=\tan x$ .

The angle sum identity for $\sin x$ says that

$\sin(x+\pi)=\sin x\cos \pi+\cos x\sin\pi=-\sin x$

$\tan(x+\pi)+2\sin(x+\pi)=\tan x-2\sin x$

By definition of $\tan x$ ,

$\tan x=\dfrac{\sin x}{\cos x}$

and so

$\tan x-2\sin x=\sin x\left(\dfrac1{\cos x}-2\right)$

which is only 0 if either $\sin x=0$ (which only happens for certain values of $x$ ) or $\dfrac1{\cos x}-2=0\implies\cos x=\dfrac12$ (which also only happens for certain values of $x$ ). It's these values of $x$ you want to find.

$\sin x=0$ whenever $x$ is a multiple of $\pi$ , i.e. $x=n\pi$ for any integer $n$ .

If $0\le x$ , then $\cos x=\dfrac12$ is true for $x=\dfrac\pi3$ and $x=\dfrac{5\pi}3$ . Then to account for all other possible values, we add a multiple of $2\pi$ , so that $x=\dfrac\pi3+2n\pi$ or $x=\dfrac{5\pi}3+2n\pi$ for integers $n$ .

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3 years ago