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2 years ago

State the domain of the rational function. (2 points)

Mathematics

1 answer:

ELEN [110]2 years ago

8 0

Answer:

All real numbers except $4$ .

Step-by-step explanation:

The given function is

$f(x)=\frac{6}{4-x}$

This is a rational function.

The domain of a rational function is all real numbers except values that will make the denominator zero.

The denominator of the given function is $4-x$ .

So the domain is all real numbers except

$4-x=0$

We solve for $x$ to obtain,

$4=x$ or $x=4$ .

Therefore the domain is all real numbers except $x=4$ .

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If sinA+cosecA=3 find the value of sin2A+cosec2A

Irina18 [472]

Answer:

$\sin 2A + \csc 2A = 2.122$

Step-by-step explanation:

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$\csc A = \frac{1}{\sin A}$ (1)

$\sin^{2}A +\cos^{2}A = 1$ (2)

Now we perform the operations: $f(A) = 3$

$\sin A + \csc A = 3$

$\sin A + \frac{1}{\sin A} = 3$

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$\sin^{2}A -3\cdot \sin A +1 = 0$ (3)

By the quadratic formula, we find the following solutions:

$\sin A_{1} \approx 2.618$ and $\sin A_{2} \approx 0.382$

Since sine is a bounded function between -1 and 1, the only solution that is mathematically reasonable is:

$\sin A \approx 0.382$

By means of inverse trigonometrical function, we get the value associate of the function in sexagesimal degrees:

$A \approx 22.457^{\circ}$

Then, the values of the cosine associated with that angle is:

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