At 1:00 p.m., the water level in a pool is 13 inches. At 1:30 p.m., the water level is 18 inches. At 2:30 p.m.,the water level i
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Answer:
Step-by-step explanation:
If the bricklayer can construct the wall in its entirety in 3 hours, then he can get 1/3 of the job done in an hour.
If the apprentice can get the whole job done in 5 hours, then he can get 1/5 of the job done in an hour. If they both work together on said job, the equation is
and now we solve for x. Multiply everything by the LCM to get rid of the fractions. That would be 15x:
and doing that gives us
5x + 3x = 15 and
8x = 15 so
x = 1.875 hours which is 1 7/8 hours which is also 1 hour and 52 1/2 minutes.
Answer: About 72 feet
The more accurate value is roughly 71.7260397 feet (however, this value isn't fully exact either).
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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.
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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.
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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.
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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.
