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Tanya [424]
3 years ago
10

Write an equation in standard form for the line that passes through (-1,-2) and (3.0)

Mathematics
1 answer:
Agata [3.3K]3 years ago
3 0

Answer:

y+2=1/2(x+1)

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(0-(-2))/(3-(-1))

m=(0+2)/(3+1)

m=2/4

m=1/2

y-y1=m(x-x1)

y-(-2)=1/2(x-(-1))

y+2=1/2(x+1)

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Step-by-step explanation:

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Veseljchak [2.6K]

For x between -\pi and \pi, we have

  • \cos x=\frac{\sqrt2}2=\frac1{\sqrt2} when x=\pm\frac\pi4;
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\cos x is continuous over its domain, so the intermediate value theorem tells us that

\cos x\ge\frac{\sqrt2}2

is true for -\frac\pi4\le x\le\frac\pi4.

For all x, we take into account that \cos x is 2\pi-periodic, so the above inequality can be expanded to

-\dfrac\pi4\le x+2n\pi\le\dfrac\pi4

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-\dfrac\pi4-2n\pi\le x\le\dfrac\pi4-2n\pi

To get the corresponding solution set for

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simply replace x with x+\frac\pi3:

-\dfrac\pi4-2n\pi\le x+\dfrac\pi3\le\dfrac\pi4-2n\pi

\implies\boxed{-\dfrac{7\pi}{12}-2n\pi\le x\le-\dfrac\pi{12}-2n\pi}

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