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3 years ago

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Mary gets an annual salary of $56,780. if she is paid semimonthly, what is the amount of her semimonthly gross pay?

2 answers:

WITCHER [35]3 years ago

5 0

The answer is 2,365.83

Ulleksa [173]3 years ago

3 0

<span>There are 52 weeks in a year. Being paid biweekly means being paid every other week, or 26 times a year.

$567.20 * 26

There are 12 months in a year. If Mary is paid semimonthly, she is paid twice a month, or 24 times a year.

$56,780 / 24</span>

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If tanA+sinA=m and tanA-sinA=n.prove that m^2-n^2=4√mn

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and

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$\implies4\sqrt{mn}=4\sqrt{\tan^2A-\sin^2A}$

The expression under the square root can be rewritten as

$\tan^2A-\sin^2A=\dfrac{\sin^2A}{\cos^2A}-\sin^2A=\sin^2A\left(\dfrac1{\cos^2A}-1\right)=\sin^2A(\sec^2A-1)$

Recall that

$\sin^2A+\cos^2A=1\implies\tan^2A+1=\sec^2A$

so that

$\tan^2A-\sin^2A=\sin^2A\tan^2A$

and assuming $\sin A>0$ and $\tan A>0$ , we end up with

$4\sqrt{\tan^2A-\sin^2A}=4\tan A\sin A$

so that

$m^2-n^2=4\sqrt{mn}$

as required.

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