What is the reciprocal of 3 3/7

Mathematics

2 answers:

aleksandrvk [35]2 years ago

8 0

24/7 is the correct answer

never [62]2 years ago

3 0

To find the reciprocal of 3 3/7,
1) convert 3 3/7 into the improper fraction 24/7.
2) Invert this improper fraction 24/7. You'll get 7/24.

This the desired reciprocal.

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Question 1: Paul leaves £4000 in the bank for two years.

Marta_Voda [28]

Answer:

4410

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8 0

2 years ago

If sin(x) = 5/13, and x is in quadrant 1, then tan(x/2) equals what?

Rufina [12.5K]

$x$ is in quadrant I, so $0$ , which means $0$ , so $\dfrac x2$ belongs to the same quadrant.

Now,

$\tan^2\dfrac x2=\dfrac{\sin^2\frac x2}{\cos^2\frac x2}=\dfrac{\frac{1-\cos x}2}{\frac{1+\cos x}2}=\dfrac{1-\cos x}{1+\cos x}$

Since $\sin x=\dfrac5{13}$ , it follows that

$\cos^2x=1-\sin^2x\implies \cos x=\pm\sqrt{1-\left(\dfrac5{13}\right)^2}=\pm\dfrac{12}{13}$

Since $x$ belongs to the first quadrant, you take the positive root ( $\cos x>0$ for $x$ in quadrant I). Then

$\tan\dfrac x2=\pm\sqrt{\dfrac{1-\frac{12}{13}}{1+\frac{12}{13}}}$

$\tan x$ is also positive for $x$ in quadrant I, so you take the positive root again. You're left with

$\tan\dfrac x2=\dfrac15$