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2 years ago

A circle with circumference 6 has an are with a 20° central angle.

Mathematics

2 answers:

Marysya12 [62]2 years ago

7 0

Answer:

AHH! Geometry!

Thanks!

The arc has a length of 1/3

Step-by-step explanation:

So you first start off with this:

$\frac{20}{360}$

This is because a circle is 360 degrees, and we are talking about a 20 degree arc.

Simplifying, we get $\frac{1}{18}$

So then, you multiply the circumference with this "factor"

$\frac{1}{18} *6=\frac{6}{18}=\frac{1}{3}$

Hope this helps!

P.S. Stay Safe during quarantine!

Igoryamba2 years ago

4 0

The length of the arc would be 1.05

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PLEASE HELP ME If 0 < z ≤ 90 and sin(9z − 1) = cos(6z + 1), what is the value of z? z = 3 z = 4 z = 5 z = 6

Burka [1]

Answer:

z = 6

Step-by-step explanation:

We know that ...

sin(x) = cos(90 -x)

Substituting (9z-1) for x, this is ...

sin(9z -1) = cos(90 -(9z -1))

But we also are given ...

sin(9z -1) = cos(6z +1)

Equating the arguments of the cosine function, we have ...

90 -(9z -1) = 6z +1

90 = 15z . . . . . . . . . add (9z-1) to both sides

6 = z . . . . . . . . . . . . divide by 15

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<em>Comment on the graph</em>

The attached graph shows 5 solutions in the domain of interest. These come from the fact that the relation we used is actually ...

sin(x) = cos(90 +360k -x) . . . . . for any integer k

Then the above equation becomes ...

90 +360k = 15z

6 +24k = z . . . . . . . . . for any integer k

The sine and cosine functions also enjoy the relation ...

sin(x) = cos(x -90)

sin(9z -1) = cos(9z -1 -90) = cos(6z +1)

3z = 92 . . . . . equating arguments of cos( ) and adding 91-6z

z = 30 2/3

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3 years ago

What is the unknown fraction? <br><br>6/10 + ____ = 62/100

sergeinik [125]

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6/10 is equivalent to 60/100.
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So, 6/10 + 1/50 = 62/100
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(Use 1/50 because that’s the simplified answer!)

I hope this made sense! Good luck!

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Paladinen [302]

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