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Kay [80]
3 years ago
8

When the smaller of two consecutive integers is added to fivefive times the​ larger, the result is 5959. find the integers?

Mathematics
1 answer:
dangina [55]3 years ago
5 0
X + 5(x + 1) = 59
6x + 5 = 59
6x = 54
x = 9 

The 2 integers are 9 and 10
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Please help ASAP!
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First, recall that

\sin(-\theta)=-\sin\theta

So if \sin(-\theta)=\dfrac15, then \sin\theta=-\dfrac15.

Second,

\tan\theta=\dfrac{\sin\theta}{\cos\theta}

We know that \tan\theta>0 and \sin\theta, which means we should also have \cos\theta.

Third,

\sin^2\theta+\cos^2\theta=1\implies\cos\theta=\pm\sqrt{1-\sin^2\theta}

but as we've already shown, we need to have \cos\theta, so we pick the negative root.

Finally,

\tan\theta=\dfrac{\sin\theta}{\cos\theta}\iff\dfrac6{\sqrt{12}}=\dfrac{-\frac15}{\cos\theta}\implies\cos\theta=-\dfrac1{5\sqrt3}

Unfortunately, none of the given answers match, so perhaps I've misunderstood one of the given conditions... In any case, this answer should tell you everything you need to know to find the right solution from the given options.

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Could you check my answer, whether I done it right or wrong?
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