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2 years ago

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Find the exact value of sec(-4π/3

1 answer:

melisa1 [442]2 years ago

3 0

<span>Find the exact value of sec(-4π/3). Note that one full rotation, clockwise, would be -2pi. We have to determine the Quadrant in which this angle -4pi/3 lies. Think of this as 4(-pi/3), or 4(-60 degrees). Starting at the positive x-axis and rotating clockwise, we reach -60, -120, -180 and -240 degrees. This is in Q III. The ray representing -240 has adj side = -1 and opp side = to sqrt(3).

Using the Pyth. Theorem to find the length of the hypo, we get hyp = 2.

Thus, the secant of this angle in QIII is hyp / adj, or 2 / sqrt(3) (answer). This could also be written as (2/3)sqrt(3).

</span>

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Answer:

x=10

Step-by-step explanation:

We can use the Pythagorean theorem to find x

The height meets the base at a right angle

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Answer:

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Step-by-step explanation:

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1 year ago

Earth revolves around the Sun in 365 days, but the planet Mercury does so in only 88 days. Compared to Earth, how many more comp

Elena L [17]

Answer:

In a 1000 days Mercury will make 8.624 more revolutions than Earth!

Step-by-step explanation:

<u>Earth</u> takes 365 days to make a complete revolution.

we can say that the rotational speed of Earth is $\dfrac{1}{365}\frac{\text{rev}}{\text{day}}$

so, in a 1000 days how many revolutions will Earth have made?

$\dfrac{1}{365}\frac{\text{rev}}{\text{day}}\times(1000\,\text{day})$

see that the 'day's cancel out. Simply multiply the two numbers!

$2.739\text{rev}$

<u>Next, do the same for Mercury</u>

we can say that the rotational speed of Mercury is $\dfrac{1}{88}\frac{\text{rev}}{\text{day}}$

as it completes 1 revolution in 88 days.

so, in a 1000 days how many revolutions will Mercury have made?

$\dfrac{1}{88}\frac{\text{rev}}{\text{day}}\times(1000\,\text{day})$

multiplying by 1/88 by 1000 yields:

$11.363\text{rev}$

The Question is how many MORE complete revolutions will Mercury make in 1000 days?

We need to subtract the revolutions of Mercury with Earth to find how far ahead is Mercury from Earth

$11.363\text{rev} - 2.739\text{rev}$

$8.624\text{rev}$

In a 1000 days Mercury will make 8.624 more revolutions than Earth!

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2 years ago