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KatRina [158]
3 years ago
12

Solve for x: sinx-cosx=√2

Mathematics
1 answer:
kvv77 [185]3 years ago
6 0
<span>sinx - cosx =sqrt(2)
Taking square on both sides:
</span>(sinx - cosx)^2 =sqrt(2)^2<span>
sin^2(x) -2cos(x)sin(x) + cos^2(x) = 2
Rearranging the equation:
sin^2(x)+cos^2(x) -2cos(x)sin(x)=2
As,
</span><span>sin^2(x)+cos^2(x) = 1
</span><span>So,
1-2sinxcosx=2
 1-1-2sinxcosx=2-1
 -</span><span>2sinxcosx = 1
</span><span>Using Trignometric identities:
-2(0.5(sin(x+x)+sin(x-x))=1 
-sin2x+sin0=1
As,
sin 0 = 0
So,
sin2x+0 = -1
</span><span>sin2x = -1</span><span>
2x=-90 degrees + t360
Dividing by 2 on both sides:
x=-45 degrees + t180
or 2x=270 degrees +t360
x= 135 degrees + t180 where t is integer</span>
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Answer:

1024 cm²

Step-by-step explanation:

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Answer:

The faster computer can do the job in 20 mins on it own.

Step-by-step explanation:

Given:

Time taken by slower computer to do job on its own =30 minutes.

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We need to find the Time taken by faster computer to do job on its own.

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Let the the Time taken by faster computer to do job on its own be 'x'.

Now we know that;

Rate to complete the job is equal to number of jobs divided by time taken to complete the job.

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Now we can say that;

Rate of both the computers is equal to sum of Rate of faster computer and Rate of slower computer.

framing in equation form we get;

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Now denominator are same so we will solve the numerator.

\frac1x=\frac{5-2}{60}\\\\\frac1x=\frac{3}{60}\\\\\frac1x=\frac{1}{20}\\\\x=20\ mins

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