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Fed [463]
3 years ago
11

Simplify: 5(6-ab)+2(-7+3ab) =30-5ab -14 +6ab= 16+ab​

Mathematics
1 answer:
blagie [28]3 years ago
4 0

Answer:

-16-ab=0

Step-by-step explanation:

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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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3 years ago
T=v /6 + 5<br> a) Work out the value of T when v = 42
Leno4ka [110]

The value of T in the equation if v = 42 is 12

<h3>How to solve algebra</h3>

Given:

T= v /6 + 5

If v = 42, find T

  • substitute 42 for v in the equation

T= v /6 + 5

T = 42/6 + 5

  • solve the fraction first

T = 7 + 5

T = 12

Therefore, the value of T in the equation if v = 42 is 12

Learn more about algebra:

brainly.com/question/4344214

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