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denis-greek [22]
2 years ago
10

In circle M with m \angle LMN= 46m∠LMN=46 and LM=7LM=7 units, find the length of arc LN. Round to the nearest hundredth.

Mathematics
1 answer:
Rus_ich [418]2 years ago
4 0

Answer:

l =  5.62 units

Step-by-step explanation:

The formula for measuring the length of an arc is expressed as;

l = r \theta

r is the radius

\theta is the central angle in radians

r = LM = 7units

\theta = \frac{46 \pi}{180} \\\theta = \frac{23 \pi}{90} \\

Substitute into the formula

l = 7 \times \frac{23 \pi}{90}  \\l = 7 \times \frac{23 \times 3.14}{90}  \\l = 7 \times 0.8024\\l =  5.62 units

Hence the length of arc LN is 5.62 units to the nearest hundredth

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Ilya [14]

Answer:

6.13

Step-by-step explanation:

Using Sine Law we know that

\dfrac{a}{SinA}=\dfrac{b}{SinB}=\dfrac{c}{SinC}

Using your figure let's assign sides and angles:

A=? B = 60° C = 70°

a = 5 b = ? c = x

If we put that into our formula:

\dfrac{5}{Sin?}=\dfrac{?}{Sin60}=\dfrac{x}{Sin70}

Notice that we have too many unknowns. We need to complete at least one ratio to do this, so how do we do this?

Notice we have 2 angles given, so we solve for the third angle. The sum of all angles in any triangle is always 180°

∠A + ∠B + ∠C= 180°

∠A + 60° + 70° = 180°

∠A + 130° = 180°

∠A = 180° - 130°

∠A = 50°

Now we can use this to solve for x.

\dfrac{5}{Sin50}=\dfrac{x}{Sin70}\\\\\dfrac{(5)(Sin70)}{Sin50} = x\\\\\dfrac{4.6985}{0.7660}=x\\\\6.1338 =x

So the closest answer would be 6.13

5 0
3 years ago
Read 2 more answers
A series contains 18 numbers and has a sum of 4,185. The last number of the series is 275. What is the first number?
N76 [4]
If the series is made up of numbers in an arithmetic progression, you have

\displaystyle\sum_{n=1}^{18}a_n=\sum_{n=1}^{18}(a_1+(n-1)d)=18a_1+153d=4185

where a_1 is the first term and d is the common difference between terms.

Since the last term in the series is a_{18}=275, you have

a_{18}=a_1+(18-1)d\implies a_1+17d=275

Solve the system

\begin{cases}18a_1+153d=4185\\a_1+17d=275\end{cases}

and you'll find that the first term is a_1=190 (with d=5).
5 0
3 years ago
Please explain how to do this im confused
Anit [1.1K]

Answer:

70° , 70°

Step-by-step explanation:

The 2 angles are corresponding and are congruent, then

23x + 1 = 4 + 22x ( subtract 22x from both sides )

x + 1 = 4 ( subtract 1 from both sides )

x = 3

Then the angles are

23x + 1 = 23(3) + 1 = 69 + 1 = 70°

4 + 22x = 4 + 22(3) = 4 + 66 = 70°

8 0
2 years ago
Read 2 more answers
The number of tickets Ben can buy to the baseball game depends on the price of the tickets, p. he can afford lickets that cos $5
jonny [76]

Answer:IDK

Step-by-step explanation:I have the SAME QUESTION.

7 0
3 years ago
At a football stadium, 10% of the fans in attendance were teenagers. If there were 30 teenagers at the football stadium, what wa
JulijaS [17]

Answer:

i believe the answer to this is a total of 300 people because you multiply the ten percent into the 30 people which factors out some numerical values, so then your answer as i just said is 300 people in total attended the game.

Step-by-step explanation:

8 0
2 years ago
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