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3 years ago

What is the square root of 49/19600 in fraction form

Mathematics

2 answers:

Afina-wow [57]3 years ago

7 0

Use a calculator and it would give you 1/20. Best of luck!

ratelena [41]3 years ago

4 0

Assuming you know the square root of 49(which is 7), we just need to find the square root of 19600.

We know that 19600 is quite a bit larger than 10000, so we can confirm that it's going to be than 100x100.

Know that, we can start with a larger number, such as 130x130. multiplying those together would equal 16900. We are getting closer now.

We now know that it is more than 130x130, so we just need to step it up a bit. So we'll do 140x140, which just happens to be 19600.

Now we have 7/140, so if we remove the zero from 140, we will have 7/14, and 7 goes into 14 twice. now we have 1/2, adding on the zero from before, we will end up with 1/20.

Leaving our final answer to be 1/20.

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Given sin(u)= -7/25 and cos(v) = -4/5, what is the exact value of cos(u-v) if both angles are in quadrant 3

solmaris [256]

Given:

$\sin (u)=-\dfrac{7}{25}$

$\cos (v)=-\dfrac{4}{5}$

To find:

The exact value of cos(u-v) if both angles are in quadrant 3.

Solution:

In 3rd quadrant, cos and sin both trigonometric ratios are negative.

We have,

$\sin (u)=-\dfrac{7}{25}$

$\cos (v)=-\dfrac{4}{5}$

Now,

$\cos (u)=-\sqrt{1-\sin^2 (u)}$

$\cos (u)=-\sqrt{1-(-\dfrac{7}{25})^2}$

$\cos (u)=-\sqrt{1-\dfrac{49}{625}}$

$\cos (u)=-\sqrt{\dfrac{625-49}{625}}$

On further simplification, we get

$\cos (u)=-\sqrt{\dfrac{576}{625}}$

$\cos (u)=-\dfrac{24}{25}$

Similarly,

$\sin (v)=-\sqrt{1-\cos^2 (v)}$

$\sin (v)=-\sqrt{1-(-\dfrac{4}{5})^2}$

$\sin (v)=-\sqrt{1-\dfrac{16}{25}}$

$\sin (v)=-\sqrt{\dfrac{25-16}{25}}$

$\sin (v)=-\sqrt{\dfrac{9}{25}}$

$\sin (v)=-\dfrac{3}{5}$

Now,

$\cos (u-v)=\cos u\cos v+\sin u\sin v$

$\cos (u-v)=\left(-\dfrac{24}{25}\right)\left(-\dfrac{4}{5}\right)+\left(-\dfrac{7}{25}\right)\left(-\dfrac{3}{25}\right)$

$\cos (u-v)=\dfrac{96}{625}+\dfrac{21}{625}$

$\cos (u-v)=\dfrac{1 17}{625}$

Therefore, the value of cos (u-v) is 0.1872.

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goldenfox [79]

Answer:

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Step-by-step explanation:

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