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Jobisdone [24]
3 years ago
9

Uhh i guess you just find x ..

Mathematics
1 answer:
zaharov [31]3 years ago
6 0
X = 3.5

This is because PQRS is similar to JKLM, hence RS is similar to LM.

RS is half of LM
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The question is not clear. You have indicated the original function as 12sin(0) - 9sin²(0)

If so, the solution is trivial. At 0, sin(0) is 0 so the solution is 0

However, I will assume you meant the angle to be \theta rather than 0 which makes sense and proceed accordingly

We can find the maximum or minimum of any function by finding the first derivate and setting it equal to 0

The original function is

f(\theta) = 12sin(\theta) - 9 sin^2(\theta)

Taking the first derivative of this with respect to \theta and setting it equal to 0 lets us solve for the maximum (or minimum) value

The first derivative of f(\theta) w.r.t \theta is

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And setting this = 0 gives

12\cos\left(\theta\right)-18\cos\left(\theta\right)\sin\left(\theta\right) = 0

Eliminating cos(\theta) on both sides and solving for sin(\theta) gives us

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This is the maximum value that the function can acquire. The attached graph shows this as correct

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