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2 years ago

Convert the following repeating decimals to

Mathematics

1 answer:

adoni [48]2 years ago

3 0

16/99

8/9

2/9

do the last three have a decimal in the start?

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Six less than the product of four and a number xx.

Lunna [17]

Is the number xx? I would take it as x.

Product for four and x. = 4x

Six less than product = 4x - 6

4 0

4 years ago

PROVE THAT:<br><br>cos 20° - sin 20° = \sqrt{2}sin25°<br><br>

Lemur [1.5K]

Answer:

See below.

Step-by-step explanation:

$\cos(20)-\sin(20)=\sqrt{2}\sin(25)$

First, use the co-function identity:

$\sin(90-x)=\cos(x)$

We can turn the second term into cosine:

$\sin(20)=\sin(90-70)=\cos(70)$

Substitute:

$\cos(20)-\cos(70)=\sqrt{2}\sin(25)$

Now, use the sum to product formulas. We will use the following:

$\cos(x)-\cos(y)=-2\sin(\frac{x+y}{2})\sin(\frac{x-y}{2})$

Substitute:

$\cos(20)-\cos(70)=-2\sin(\frac{20+70}{2})\sin(\frac{20-70}{2})\\\cos(20)-\cos(70) =-2\sin(45)\sin(-25)\\\cos(20)-\cos(70)=-2(\frac{\sqrt{2}}{2})\sin(-25)\\ \cos(20)-\cos(70)=-\sqrt{2}\sin(-25)$

Use the even-odd identity:

$\sin(-x)=-\sin(x)$

Therefore:

$\cos(20)-\cos(70)=-\sqrt{2}\sin(-25)\\\cos(20)-\cos(70)=-\sqrt{2}\cdot-\sin(25)\\\cos(20)-\cos(70)=\sqrt{2}\sin(25)$

Replace the second term with the original term:

$\cos(20)-\sin(20)=\sqrt{2}\sin(25)$

Proof complete.

4 0

4 years ago

A book sold 34,600 copies in its first month of release. Suppose this represents 8.6% of the number of copies sold to date. How

NemiM [27]

Answer:402325.6

Step-by-step explanation:

let a be the total sales till date

8.6% of a=34600

8.6/100 x a=34600

0.086 x a=34600

divide both sides by 0.086

(0.086 x a)/0.086=34600/0.086

a=402325.6

8 0

4 years ago

Read 2 more answers

What 3 numbers can you times to get 9

Masja [62]

Answer:

3x3x1

9x1x1

9x.5x2

3 0

4 years ago

A cylindrical container holding sugar has a height of 14 inches and a diameter of 6 inches. Which of the following is the closes

Anna35 [415]

I have a lot to say I don’t think you

4 0

3 years ago