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Yuri [45]
3 years ago
7

I rlly rlly rlly need help! Complete the following proof. Given: Points R, S, T, Q on circle O Prove: m\overarc RS + m\overarc S

T + m\overarc TQ + m\overarc RQ

Mathematics
1 answer:
harina [27]3 years ago
8 0

Answer:

m(\widehat {RS})+m(\widehat{ST})+m(\widehat{TQ}) + m(major\ arc RQ) = 360\ degree

Step-by-step explanation:

As we can see in the figure that

The R, S, T ,and Q are the points on the circle O.

Also

The measurement of the circular arc is equivalent to the measurement of the angle at the center of the arc

So by this

m(\widehat{RS})=m(\angle ROS)

m(\widehat{ST})=m(\angle SOT)

m(\widehat{TQ})=m(\angle TOQ)

m(major arc RQ) = m(∠QOR)

So,

m(\widehat {RS})+m(\widehat{ST})+m(\widehat{TQ}) + m(major\ arc RQ) = m(\angle ROS)+m(\angle SOT)+m(\angle TOQ)+m(\angle QOR)

And as we know that

All angles sum = 360°

Therefore

m(\widehat {RS})+m(\widehat{ST})+m(\widehat{TQ}) + m(major\ arc RQ) = 360\ degree

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Answer:

Step-by-step explanation:

Question says that it uses 120 feet of fencing material to enclose three sides of the play area. This means there are 3 sides. Putting this into equation, we have something like this.

120 = L + 2W

Where

LW = area.

Again, in order to maximize the area with the given fencing, from the equation written above, then Width, w must be = 30 feet and length, l must be = 60

On substituting, we have

A = LW = (120 - 2W) W

From the first equation, making L the subject of the formula, we have this

L = 120 - 2W, which then we substituted above.

On simplification, we have

L = 120W -2W²

Differentiating, we have

A' = 120 - 4W = 0

Remember that W = 30

So therefore, L = 120 - 2(30) = 60 feet

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