Please help and explain questions 20-22

Mathematics

1 answer:

zmey [24]3 years ago

6 0

Hello!

The formula for circumference is $2\pi r$ and the formula for area of a circle is $\pi r^{2}$ . Armed with these formulas, we can begin to find the circumferences and areas of the circles.

20.
C = $2 \pi r$
C = $2 \pi (6.5)$
C = $13 \pi$
C = 13(3.14)
C = 40.8

A = $\pi r^{2}$
A = $\pi (6.5)^{2}$
A = $\pi (42.25)$
A = 132.7

The circumference of the circle is 40.8 in and the area of the circle is 132.7 in².

21.
[Since we are given the diameter for this problem, to find the circumference, we no longer need to multiply the radius by 2 as in $2 \pi r$ because the diameter is the radius × 2. For $\pi r^{2}$ we do need to divide the diameter by 2.]

C = $15.7 \pi$
C = 49.3

A = $\pi r^{2}$
A = $\pi (7.85)^{2}$
A = $61.62 \pi$
A = 193.5

The circumference of the circle is 49.3 in and the area of the circle is 193.5 in².

And that is all there is to it. I hope this helps you! (:

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A partial proof was constructed given that MNOP is a parallelogram.

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A diagram of parallelogram MNOP is attached below

We have side MN || side OP and side MP || NO

Using the rule of angles in parallel lines, ∠M and ∠P are supplementary as well as ∠M and ∠N.

Since ∠M+∠P = 180° and ∠M+∠N=180°, we can conclude that ∠P and ∠N are of equal size.

∠N and ∠O are supplementary by the rules of angles in parallel lines
∠O and ∠P are supplementary by the rules of angles in parallel lines

∠N+∠O=180° and ∠O+∠P=180°

∠N and ∠P are of equal size

we deduce further that ∠M and ∠O are of equal size

Hence, the correct statement to complete the proof is

∠M ≅ ∠O; ∠N ≅ ∠P