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3 years ago

Find the distance between the points (-2, -4) and (-6, -8). Round your answer to to the nearest tenth.

Mathematics

1 answer:

Lyrx [107]3 years ago

8 0

Answer:

d=5.7

Step-by-step explanation:

$d=\sqrt{(x2-x1)^{2} +(y2-y1)^{2} }$

$d=\sqrt{-6(-2)^{2}+(-8-(-4)^{2} }$

$d=\sqrt{(-6+2){^{2}+(-8+4)^{2} } }$

d= $\sqrt{(-4)^{2}+(-4)^{2} }$

d= $\sqrt{16+16}$

d= $\sqrt{32}$

d=5.656 =5.7

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Step-by-step explanation:

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2 years ago

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

Irina18 [472]

Answer:

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

Step-by-step explanation:

Let $f(A) = \sin A + \csc A$ , we proceed to transform the expression into an equivalent form of sines and cosines by means of the following trigonometrical identity:

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

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

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

$\sin A + \csc A = 3$

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

$\sin ^{2}A + 1 = 3\cdot \sin A$

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

$\cos A \approx 0.924$

Now, we have that $f(A) = \sin 2A +\csc2A$ , we proceed to transform the expression into an equivalent form with sines and cosines. The following trignometrical identities are used: