Show that 155 can be express as the sum of a power of 2 and a cube number?
1 answer:
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Part A
Answers: The braking distance is 25 meters for the dry road, 80 meters for the wet road, 140 meters for the icy road
As expected, the worse the conditions, the longer the skid.
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Explanation:
First locate the speed 50 km/hr. So you'll look at the horizontal axis which is the speed or velocity axis. The value 50 is at the midpoint between 40 and 60. Draw a vertical line straight up and down as far as you can go in both directions. Then mark the points of intersection between the vertical line and the various curves. Finally, draw horizontal lines from each of the points so you can see what the y coordinates are.
Check out figure 1 (attached image) to see a visual of what I'm referring to.
The points of intersection are roughly: (50,25) and (50,80) and (50,140). The first y values is an approximate guess because the visual graph given isn't perfectly lined up. The value is somewhere between 20 and 30 so 25 seems like a good compromise.
Therefore the braking distances are roughly 25, 80 and 140 for the dry, wet and icy roads (in that order).
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Part B
Answers: The top speeds required are 30 km/hr for the icy road, 45 km/hr for the wet road, 70 km/hr for the dry road
These are max speeds allowed so that the braking distance is 60 meters or less. This is the inverse order of part A. The worse conditions require a slower speed.
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Explanation:
We go in reverse of part A. Instead of looking on the x axis, we start with the y axis. Locate 60 on the y axis (which is the braking distance axis) which is between 40 and 80. In figure 2 (also attached), I draw a red horizontal line to start things off. Then I mark the points between each curve and the horizontal line. The last step is to drop vertical lines to the x axis to figure out the x coordinate of each red point.
The x coordinates are: 30, 45, 70
The 45 comes from the fact that it seems to be at the midpoint of 40 and 50 (this is a guess really).
So this means that a vehicle on an icy road can go at most 30 km/hr. A car on a wet road can't go faster than 45 km/hr. Finally a car on a dry road can have a top of speed of 70 km/hr. All of these road conditions will have a braking distance of 60 meters or less.
