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AlekseyPX
3 years ago
9

Jim has $4,200 in his checking account to pay his rent. Each month, $600 is taken out of the account

Mathematics
1 answer:
Allushta [10]3 years ago
5 0

Answer:4200-600m=1800

Step-by-step explanation:

4200-600m=1800

Subtract 4200 from 1800

-600m=-3600

Divide both sides by -600

m=6

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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}}

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On further simplification, we get

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

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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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50 is 20% of what number
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