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Evgen [1.6K]
3 years ago
6

Unknown digit for 2.84 > 2.4 1 > 2.463

Mathematics
1 answer:
Bond [772]3 years ago
3 0

The digit _ that will make 2.4_1 be more than 2.463 must be 7, 8, or 9.

If the first number in your sequence is 2.48 (not 2.84), then the unknown digit must be 7.

2.48 > 2.471 > 2.463

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Simplify: cos2x-cos4 all over sin2x + sin 4x
GrogVix [38]

Answer:

\frac{\cos\left(2x\right)-\cos\left(4x\right)}{\sin\left(2x\right)+\sin\left(4x\right)}=\tan\left(x\right)

Step-by-step explanation:

\frac{\cos\left(2x\right)-\cos\left(4x\right)}{\sin\left(2x\right)+\sin\left(4x\right)}

Apply formula:

\cos\left(A\right)-\cos\left(B\right)=-2\cdot\sin\left(\frac{A+B}{2}\right)\cdot\sin\left(\frac{A-B}{2}\right) and

\sin\left(A\right)+\sin\left(B\right)=2\cdot\sin\left(\frac{A+B}{2}\right)\cdot\sin\left(\frac{A-B}{2}\right)

We get:

=\frac{-2\cdot\sin\left(\frac{2x+4x}{2}\right)\cdot\sin\left(\frac{2x-4x}{2}\right)}{2\cdot\sin\left(\frac{2x+4x}{2}\right)\cdot\cos\left(\frac{2x-4x}{2}\right)}

=\frac{-\sin\left(\frac{2x-4x}{2}\right)}{\cos\left(\frac{2x-4x}{2}\right)}

=\frac{-\sin\left(\frac{-2x}{2}\right)}{\cos\left(\frac{-2x}{2}\right)}

=\frac{-\sin\left(-x\right)}{\cos\left(-x\right)}

=\frac{-\cdot-\sin\left(x\right)}{\cos\left(x\right)}

=\frac{\sin\left(x\right)}{\cos\left(x\right)}

=\tan\left(x\right)

Hence final answer is

\frac{\cos\left(2x\right)-\cos\left(4x\right)}{\sin\left(2x\right)+\sin\left(4x\right)}=\tan\left(x\right)

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8 0
2 years ago
Desiree works 28 hours per week. She has a monthly income of $120 from investments. Desiree also plays in a band one night a wee
Oksi-84 [34.3K]
So hmmm let's see
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she plays on a band, and makes 200 a week, now, there are 52 weeks in a year, so her yearly income from band playing is 200 * 52, or
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her total annual income is 49696, now, if we subtract the band and investment income, we'd be left over with only what comes from her job payrate
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so, she makes from her job, $37856 annually

now, she only works 28 hours weekly, how much is that yearly?   well, 52 weeks in a year, she works 28*52 hours a year, let us divide 37856 by that

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51880 - 49696 = 2184

ok, so she wants $2184 annually more from her work
how much is that in the hours she works annually?  well 2184 ÷ ( 28 * 52)
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