What is the 24th term of the arithmetic sequence where a1 = 8 and a9 = 56?

Mathematics

1 answer:

luda_lava [24]3 years ago

4 0

Since this is an arithmetic sequence it would just be 8 x 24 which is 192

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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
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3 years ago

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MaRussiya [10]

I can’t see the exact numbers because the pic is blurry but here’s how to solve it.

The three angles in a triangle always add up to 180. So subtract the angle that’s given and you’ll have the sum of the two other angles. Since it’s an equilateral triangle, the other two angles are the same.
So write the equation 2(whatever the angle is) = the number you get when you do 180-the given angle

For example (I’m not sure these numbers are right because the pic is blurry)
2(9x+7)=114
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The answer to the first part is (4,1).
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Answer:

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