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Elena L [17]
3 years ago
6

Determine the length of arc JL.

Mathematics
1 answer:
aleksandr82 [10.1K]3 years ago
6 0

The length of arc JL is \frac{25}{18} \pi  So option c is correct.

<u>Solution:</u>

Given, from the diagram, radius of the given circle is 2 units.

And, the angle between the radius JK and KL is 125 degrees.

We have to find the length of the minor arc formed by JL

The length of arc is given as:

\text { Length of arc }=2 \pi r\left(\frac{\theta}{360}\right)

where \theta is angle between radii formed by points with centre

Now the length of arc JL is:

=2 \pi \times 2 \times \frac{125}{360}=4 \pi \times \frac{125}{360}=\pi \times \frac{125}{90}=\frac{25}{18} \pi

Hence, the length of are JL is \frac{25}{18} \pi so option c is correct.

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1. You are given the 3rd and 5th term of an arithmetic sequence. Describe in words how to determine the general term.
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Step-by-step explanation:

1. In an arithmetic sequence, the general term can be written as

xₙ = y + d(a-1), where xₐ represents the ath term, y is the first value, and d is the common difference.

Given the third term and the fifth term, and knowing that the difference between each term is d, we can say that the 4th term is x₃+d and the fifth term is the fourth term plus d, or (x₃+d)+d =

x₃+2d. =x₅ Given x₃ and x₅, we can subtract x₃ from both sides to get

x₅-x₃ = 2d

divide by 2 to isolate d

(x₅-x₃)/2 = d

This lets us solve for d. Given d, we can say that

x₃ = y+d(2)

subtract 2*d from both sides to isolate the y

x₃ -2*d = y

Therefore, because we know x₃ and d at this point, we can solve for y, letting us plug y and d into our original equation of

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2.

Given the third and fifth term, with a common ratio of r, we can say that the fourth term is x₃ * r. Then, the fifth term is

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square root both sides

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