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3 years ago

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I need help with this please help

1 answer:

Firlakuza [10]3 years ago

5 0

Answer:

Step-by-step explanation:

Hope fhat hep,ed skdnfsu. Soidhf scodfiysldm vij fhu idnvcmdlc

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Save me the headache

maxonik [38]

$(9\sin2x+9\cos2x)^2=81$

Taking the square root of both sides gives two possible cases,

$9\sin2x+9\cos2x=9\implies\sin2x+\cos2x=1$

or

$9\sin2x+9\cos2x=-9\implies\sin2x+\cos2x=-1$

Recall that

$\sin(\alpha\pm\beta)=\sin\alpha\cos\beta\pm\cos\alpha\sin\beta$

If $\alpha=2x$ and $\beta=\dfrac\pi4$ , we have

$\sin\left(2x+\dfrac\pi4\right)=\dfrac{\sin2x+\cos2x}{\sqrt2}$

so in the equations above, we can write

$\sin2x+\cos2x=\sqrt2\sin\left(2x+\dfrac\pi4\right)=\pm1$

Then in the first case,

$\sqrt2\sin\left(2x+\dfrac\pi4\right)=1\implies\sin\left(2x+\dfrac\pi4\right)=\dfrac1{\sqrt2}$

$\implies2x+\dfrac\pi4=\dfrac\pi4+2n\pi\text{ or }\dfrac{3\pi}4+2n\pi$

(where $n$ is any integer)

$\implies2x=2n\pi\text{ or }\dfrac\pi2+2n\pi$

$\implies x=n\pi\text{ or }\dfrac\pi4+n\pi$

and in the second,

$\sqrt2\sin\left(2x+\dfrac\pi4\right)=-1\implies\sin\left(2x+\dfrac\pi4\right)=-\dfrac1{\sqrt2}$

$\implies2x+\dfrac\pi4=-\dfrac\pi4+2n\pi\text{ or }-\dfrac{3\pi}4+2n\pi$

$\implies2x=-\dfrac\pi2+2n\pi\text{ or }-\pi+2n\pi$

$\implies x=-\dfrac\pi4+n\pi\text{ or }-\dfrac\pi2+n\pi$

Then the solutions that fall in the interval $[0,2\pi)$ are

$x=0,\dfrac\pi4,\dfrac\pi2,\dfrac{3\pi}4,\pi,\dfrac{5\pi}4,\dfrac{3\pi}2,\dfrac{7\pi}4$

5 0

3 years ago

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A standard deck of 52 cards has four queens. two cards are randomly drawn in succession, without replacement, from a standard de

AnnyKZ [126]

There are a total of 4 queens in a standard deck of 52 cards. The probability that the 2 consecutive draws are queen is:

Probability = (4 / 52) * (3 / 51)

<span>Probability = 12 / 2652 = 0.004</span>

3 0

4 years ago

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Use two unit multipliers to convert 1250 square inches to square feet

Fiesta28 [93]

12 inches = 1 foot
144 square inches = 1 square foot
1250 square inches = 1250/144 = 8.68 square feet

4 0

4 years ago

PLEASE HELP!!!!

Paraphin [41]

Answer:

yes

Step-by-step explanation:

1 is smaller than ten

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3 years ago

What is 1+2+3+4+5+6+7?

Elan Coil [88]

Answer:

28

Step-by-step explanation:

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3 years ago

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