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4 years ago

What is 6.6 repeating as a fraction

Mathematics

1 answer:

Nana76 [90]4 years ago

4 0

6 7/10 maybe i dont know...................

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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,

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

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

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

Read 2 more answers

A caterpillar moves across the grass at a rate of 423 feet every 7 minutes. How fast does the caterpillar move in feet per minut

bija089 [108]

If it moves 423 feet in 7 minutes, you divide 423 by 7 to see how much it moves per minute, which is Around 60.4 feet per minute

7 0

3 years ago

Mikey bikes 12 miles in 2 hours. How many miles does Mikey bike in an hour?

Ad libitum [116K]

Answer:

6 miles

Step-by-step explanation:

2 hours can be made into 1 hour by dividing by 2. In order to keep the ratio, you also have to divide the miles by 2, giving you 6.

2:12

1:6

7 0

3 years ago

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Tina had $47.10 in her bank account on Monday. She withdrew $25 on Monday and also made a deposit of an amount d that she cannot

nalin [4]

The correct answer is a. 47.10 - 25 + d = 97.43.

This is because you have to subtract the $25, because it is a withdrawal, or taking out of money.
This rules out options C and D.

Also, Tina made a deposit of an amount that she can't remember. A deposit is adding a certain amount of money, so you have to +d.

This rules out option B.

The only option left is option A, which makes complete sense.

4 0

3 years ago

Actually help pls people have been typing random stuff

agasfer [191]

Answer:

reading, chores, and then homework

Step-by-step explanation:

just accept it

3 0

3 years ago

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