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3 years ago

11

JUliet is trying to increase her savings account and she decides that she is going

1 answer:

antiseptic1488 [7]3 years ago

3 0

Set up an automatic transfer from her checking to savings account once a month.

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Emilio's vegetable patch is 7 yards wide and 15 yards long. Emilio wants to build a fence

madam [21]

It would cost $132. 7+7+15+15X3=132

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2 years ago

I can’t figure this out

ella [17]

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Step-by-step explanation:

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1 year ago

If you work 40 hours per week at $13.00 per hour and save 10% of your gross earnings, how much will you save per week?

Vesna [10]

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3 years ago

Find the 11th term of the geometric sequence 1,3,9, ...

ad-work [718]

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2 years ago

Read 2 more answers

Pls, can you help me? thx.<br><img src="https://tex.z-dn.net/?f=%20%5Ccos%28x%20%2B%20%5Cfrac%7B%5Cpi%7D%7B3%7D%29%20%5Cgeqslant

Veseljchak [2.6K]

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

$\cos x=\frac{\sqrt2}2=\frac1{\sqrt2}$ when $x=\pm\frac\pi4$ ;
$\cos x=1$ for $x=0$ ; and
$\cos x=0$ for $x=\pm\frac\pi2$

$\cos x$ 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

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

where $n$ is any integer. Equivalently,

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

To get the corresponding solution set for

$\cos\left(x+\dfrac\pi3\right)\ge\dfrac{\sqrt2}2$

simply replace $x$ with $x+\frac\pi3$ :

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

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

7 0

3 years ago