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Lostsunrise [7]
3 years ago
8

Find X. Round to the nearest tenth. Law of Cosines : c2 = 22 + b2 - 2ab cos C

Mathematics
1 answer:
fiasKO [112]3 years ago
7 0

Answer:

70.5°

Step-by-step explanation:

22² = (20)²+(18)² - 2(20)(18) cos X

484 = 400 + 324 - 720 cos X

-240 = -720 cosx

1/3 = cos X

cos^{-1}(\frac{1}{3}) = X

X = 70.52877937

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sin alpha = 7/25, alpha lies in quadrant ii, and cos beta = 2/5, beta lies in quadrant i. find cos(alpha-beta).
Ilia_Sergeevich [38]

Answer:

Therefore \cos(\alpha-\beta)=\frac{48+7\sqrt{25}}{125}

Step-by-step explanation:

Given values are

\sin \alpha=\frac{7}{25}

\cos \beta=\frac{2}{5}

\sin^2x+\cos^2=1

\cos \alpha=\sqrt{1-\sin^2\alpha}

\cos \alpha=\sqrt{1-(\frac{7}{25})^2}

\cos \alpha=\sqrt{1-\frac{49}{625}}

\cos \alpha=\sqrt{\frac{576}{625}}

\cos \alpha=\frac{24}{25}

\sin \beta=\sqrt{1-\cos^2\beta}

\sin \beta=\sqrt{1-(\frac{2}{5})^2}

\sin \beta=\sqrt{1-\frac{4}{25}}

\sin \beta=\frac{\sqrt{21}}{5}

\cos(\alpha-\beta)=\cos\alpha\cos\beta+\sin\alpha\sin\beta

\cos(\alpha-\beta)=\frac{24}{25}\times\frac{2}{5}+\frac{7}{25}\times\frac{\sqrt{21}}{5}

\cos(\alpha-\beta)=\frac{48+7\sqrt{25}}{125}

7 0
3 years ago
A nature museum has 2008 specimens of early birds, some with 222 wings and some with 444 wings. The specimens have a total of 40
ludmilkaskok [199]

Let's assume

number of birds with 2 wings is x

number of birds with 4 wings is y

A nature museum has 2008 specimens of early birds

so,

x+y=2008

Total of wings of 2 wings bird =2x

Total of wings of 4 wings bird =4y

The specimens have a total of 4384 wings

so, we get

2x+4y=4384

we can divide both sides by 2

x+2y=2192

so, we get system of equations as

x+y=2008

x+2y=2192

we can solve for x and y

We can subtract both equations

2008-y+2y=2192

y=184

x=2008-184

x=1824

y=184,\:x=1824

so,

number of birds with 2 wings is 1824

number of birds with 4 wings is 184.............Answer



5 0
3 years ago
Least to greatest 0.4, 5/8, 74%, 3/5
SashulF [63]

Answer:

0.4,3/5,5/8,74%

Step-by-step explanation:

Change them all into decimals.

Get 0.4,0.625,0.74,0.6

Then reorder and see what their original values were

5 0
3 years ago
Y&lt;=x-5, and y&lt;=-x-4 would be points (1,10)? or<br> (-1,10)<br> (10,1)<br> 1,-10)
weeeeeb [17]
It would be (1,-10) <===
4 0
3 years ago
Find the value of x in the triangle shown below.<br> =<br> २०<br> 14<br> 14<br> 50°<br> 18
Alexandra [31]

Answer:

x = 87

Step-by-step explanation:

37 + 56 = 93

triangles always equal to 180

180 - 93 = 87

5 0
2 years ago
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