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ollegr [7]
3 years ago
10

Solve the equation: sin(2x)= sin x

Mathematics
1 answer:
Anna [14]3 years ago
3 0

Answer:

Below

Step-by-step explanation:

sin(2x) = 2 ×cos(x)× sin(x)

● sin(x) = 2 × cos(x) × sin(x)

● 2 × cos(x) = 1

● cos (x) = 1/2

So we can deduce that:

● x = Pi/3 + 2*k*Pi

● or x = -Pi/3 + 2*k*Pi

K is an integer

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Jim needs to divide 762 coupon books equally among 9 stores. In which place is the first digit of the quotient? Select the word
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<span>Ayesha's right.  There's a good trick for knowing if a number is a multiple of nine called "casting out nines."  We just add up the digits, then add up the digits of the sum, and so on.  If the result is nine the original number is a multiple of nine.  We can stop early if we recognize if a number along the way is or isn't a multiple of nine.  The same trick works with multiples of three; we have one if we end with 3, 6 or 9.

So </span>1284673 <span>has a sum of digits 31 whose sum of digits is 4, so this isn't a multiple of nine.  It will give a remainder of 4 when divided by 9; let's check.

</span>1284673 = 142741 \times 9 + 4 \quad\checkmark<span>

</span>Let's focus on remainders when we divide by nine. The digit summing works because 1 and 10 have the same remainder when divided by nine, namely 1.  So we see multiplying by 10 doesn't change the remainder.  So 100 \times a + 10 \times b + c has the same remainder as a+b+c.

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It doesn't matter if the digits are larger or smaller or how many there are. We might want the first number bigger than the second so we get a positive difference, but even that doesn't matter; a negative difference will still be a multiple of nine. Let's pick a random number, reverse its digits, subtract, and check it's a multiple of nine:

</span>813219543092195 - 591290345912318 =  221929197179877 = 9 \times 24658799686653 \quad \checkmark

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