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3 years ago

A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second.

Mathematics

1 answer:

scoray [572]3 years ago

3 0

Answer:

It makes 360 / 60 = 6 revolutions per second. 6 revolutions is 12π radians.

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How far does the tip of the minute hand of a clock move in 1 hour and 27 minutes if the hand is 2 inches long?

Nesterboy [21]

So, a full circle has 360°, thus when the minute hand does one hour, it does a full circle, therefore 360°.

now, how many degrees are there in 1 minute? well, there are 60 minutes in 360°, therefore there are 360/60 degrees in 1 minute, or 6°.

now, we know in 1 hour there are 360°, how many in 27 minutes? well, 27 * 6, or 162°. So after 1hr and 27min, the minute hand has done 360+162 or 522°.

we also know the minute hand is 2 inches long, thus

$\bf \textit{arc's length}\\\\
s=\cfrac{\pi \theta r}{180}\quad 
\begin{cases}
r=radius\\
\theta =angle~in\\
\qquad degrees\\
------\\
r=2\\
\theta =522
\end{cases}\implies s=\cfrac{\pi \cdot 522\cdot 2}{180}$

which is roughly 18 inches rounded up.

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3 years ago

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kicyunya [14]

With 21 marbles in the bag, and 9 of them green, her chances are 9/21 that she will pull a green marble. If you reduce 9/21 you get 3/7 which is the way the answer should be expressed (in lowest terms)

Answer Probability of green = 3/7

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Prove the identity.<br> tan(x − y) + tan(z − x) + tan(y − z) = tan(x − y) tan(z − x) tan(y − z)

Viktor [21]

Step-by-step explanation:

This is known as the triple tangent identity. Start with the fact that the three angles add up to 0.

(x − y) + (z − x) + (y − z) = 0

Subtract two terms to the other side and take the tangent:

x − y = -((z − x) + (y − z))

tan(x − y) = tan(-((z − x) + (y − z)))

Use reflection property:

tan(x − y) = -tan((z − x) + (y − z))

Now use angle sum identity:

tan(x − y) = -[tan(z − x) + tan(y − z)] / [1 − tan(z − x) tan(y − z)]

tan(x − y) = [tan(z − x) + tan(y − z)] / [tan(z − x) tan(y − z) − 1]

tan(x − y) [tan(z − x) tan(y − z) − 1] = tan(z − x) + tan(y − z)

tan(x − y) tan(z − x) tan(y − z) − tan(x − y) = tan(z − x) + tan(y − z)

tan(x − y) tan(z − x) tan(y − z) = tan(x − y) + tan(z − x) + tan(y − z)

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tinyurl.com/wpazsebu

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