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Artyom0805 [142]
3 years ago
6

Can somebody help with numbers 19-24

Mathematics
1 answer:
Gemiola [76]3 years ago
5 0
19-20 idk but ik the others
21.)0.785
22.)0
23.)-14.5
24.)7.838
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Solve the system of linear equations for x and y.(cos θ)x + (sin θ)y=1(−sin θ)x + (cos θ)y = 0x=y=
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Answer:

\bold{x =cos\theta}\\\bold{y=sin\theta}

Step-by-step explanation:

The given system of linear equations is:

(cos\theta)x+(sin\theta)y=1\\(-sin\theta)x+(cos\theta)y=0

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For this, let us multiply the first equation by sin\theta and second equation by cos\theta

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(cos\theta.sin\theta)x+(sin\theta.sin\theta)y=sin\theta\\\Rightarrow (cos\theta.sin\theta)x+(sin^2\theta)y=sin\theta ....... (1)\\\\(-sin\theta.cos\theta)x+(cos\theta.cos\theta)y=0\\\Rightarrow (-sin\theta.cos\theta)x+(cos^2\theta)y=0 ..... (2)

Now, let us add (1) and (2):

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Using the equation:

(-sin\theta)x+(cos\theta)y=0

Putting value of y:

\Rightarrow (-sin\theta)x+(cos\theta)sin\theta=0\\\Rightarrow (sin\theta)x=(cos\theta)sin\theta\\\Rightarrow x = cos\theta

So, the answer to the system of linear equations is:

\bold{x =cos\theta}\\\bold{y=sin\theta}

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