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3 years ago

what are the smallest values of p and r that satisfy the definitions for parallel lines and perpendicular lines?

Mathematics

1 answer:

Feliz [49]3 years ago

4 0

Answer:

p = 2

r = 4

Step-by-step explanation:

If you're doing parallel it needs to be like "side by side." The least you can do is 2 because you'll need at least one other line to be beside the original.

Perpendicular lines are intersecting, so if you intersect them as a plus sign, you'll make at least four right angles.

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Andrea enjoys running. She keeps a daily journal to record how far she runs. She wears a pedometer to calculate the exact distan

Neko [114]

Answer:

14.225 kilometers.

Step-by-step explanation:

Monday 3.6

Tuesday 4.705

Wednesday 5.92

By using the addition operation, the total distance, in kilometers, that Andrea ran over the three days will be :

3.6 +4.705 +5.92=14.225

Hence, the total distance that Andrea ran over the three days = 14.225 kilometers.

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3 years ago

In the xy-plane above, o is the center of the circle, and the measure of

Marina86 [1]

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3 years ago

INFO: The chairs are evenly spaced around

lana66690 [7]

Answer: About 72 feet

The more accurate value is roughly 71.7260397 feet (however, this value isn't fully exact either).

======================================================

Explanation:

Check out the diagram below. It's effectively the same diagram your teacher provided, but I've added points M and N. I've left out any unnecessary lines.

M = center of the circle
N = location where the cable is anchored to the ground

We're told that "(the length of cable from) E to the ground is 35 feet", so this is the red portion of cable that I've marked this as NE = 35, ie segment NE is 35 feet long. We're also told that NF = 40 feet, which is also shown in red.

The blue portions are chords of the circle. We're given one chord as LE = 80 ft, while the other chord JF is what we want to find out.

-----------------

What we need to find is the radius of this circle. Right away, it's not clear what the radius is; however, we can use the chord LE = 80 to help find it.

It turns out that the chord length c is connected to the radius r and central angle theta like so:

c = 2*r*sin(0.5*theta)

where theta must be in radian mode. The central angle subtends the arc that forms the chord in question.

If we started at point L, and counted the number of spaces to get to E while going clockwise, then we can see that there are 5 spaces

Those five spaces could be written as

The jump from L to A
The jump from A to B
The jump from B to C
The jump from C to D
The jump from D to E

Or you could mark it as such on the diagram for a visual reference. Overall, the circle has been cut into 12 equal slices. So going from L to E, going clockwise, will have us take up 5/12 of the full circle.

There are 2pi radians in a full circle, meaning the central angle LME is (5/12)*2pi = 5pi/6 radians.

-----------------

Plug theta = 5pi/6 and c = 80 into the formula mentioned. Isolate the radius.

c = 2*r*sin(0.5*theta)

80 = 2*r*sin(0.5*5pi/6)

80 = 2*r*sin(5pi/12)

80 = 2*r*0.9659258

80 = 2*0.9659258*r

80 = 1.9318516r

1.9318516r = 80

r = 80/1.931 8516

r = 41.4110483

The radius is approximate. The radius is in feet. Make sure your calculator is in radian mode.

-----------------

Now that we know the radius, we can determine how long chord JF is.

The central angle for chord JF is angle JMF

If we start at J and go to F, along the shorter path, then we've gone 4 spaces. This is 4/12 = 1/3 of the full circle. So the radian measure of angle JMF is (1/3)*2pi = 2pi/3 radians.

So,

c = 2*r*sin(0.5*theta)

c = 2*41.4110483*sin(0.5*2pi/3)

c = 71.7260397

Chord JF is roughly 71.7260397 feet long.

When rounding to the nearest foot, that's about 72 feet.