Find the 15th term of the arithmetic sequence x + 3, – X – 1, -3x – 5,...

Mathematics

1 answer:

tatuchka [14]3 years ago

5 0

Answer:

-53-27x

Step-by-step explanation:

Answer attached...

Hope it helps :)

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What kind of angle is this and how do you work it out?

Lostsunrise [7]

Well x is an obtuse angle

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7 0

3 years ago

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Stells [14]

Answer:

x = 60

Step-by-step explanation:

(x+22) + (x+6) + (x-28) = 180

x + 22 + x + 6 + x - 28 = 180

x + x + x + 22 + 6 - 28 = 180

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x = 60

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3 years ago

If sinθ = -1/2 and θ is in Quadrant III, then tanθ = _____.

Gnom [1K]

Answer: $\tan \theta=\dfrac{1}{\sqrt3}.$

Step-by-step explanation: Given that

$\sin\theta=-\dfrac{1}{2}$ and $\theta$ lies in Quadrant III.

We are to find the value of $\tan \theta.$

We will be using the following trigonometric identities:

$(i)~sin^2\theta+\cos^2\theta=1,\\\\(ii)~\dfrac{\sin\theta}{\cos{\theta}}=\tan \theta.$

We have

$\tan\theta\\\\\\=\dfrac{\sin\theta}{\cos\theta}\\\\\\=\dfrac{\sin\theta}{\pm\sqrt{1-\sin^2\theta}}\\\\\\=\pm\dfrac{-\frac{1}{2}}{\sqrt{1-\left(\frac{1}{2}\right)^2}}\\\\\\=\pm\dfrac{\frac{1}{2}}{\sqrt{1-\frac{1}{4}}}\\\\\\=\pm\dfrac{\frac{1}{2}}{\frac{\sqrt3}{2}}\\\\\\=\pm\dfrac{1}{\sqrt3}.$