The graphs of y = |x-20| + |x+18| and y = x+c intersect at exactly one point. Find the value of c. Show your work.
Round 2
An open can of oil is accidentally dropped into a lake; assume the oil spreads over the surface as a circular disk of uniform thickness whose radius increases steadily at the rate 10 cm/sec. At the moment when the radius is 1 meter, the thickness of the oil slick is decreasing at the rate 4 mm/sec; how fast is it decreasing when the radius is 2 meters? (Watch the units!)
Round 3
A gravitational force of magnitude F acts vertically downward on a block resting on
a plane. The plane makes an angle of θ with the horizontal. What is the magnitude of the
component of the gravitational force acting parallel to the plane?
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C= 38
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Didn't show your work. 0 credit.
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o crap....sorry
XD
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welp, it's 20 obviously
Edit: I'm stupid, c = 18 actually
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That is correct. 18
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Please keep your eyes on your own paper.
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Oi, you better not be collaborating with Mr. Cheats up top.
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With all due respect sir, just because I was caught cheating 57 times during last 3 months, doesn't mean I always cheat. Besides, rules are meant to be broken anyway.
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y = |x-20| + |x+18| can be written as 3 equations depending on the value of x.
When x < -18, y = -2x + 2
When -18 ≤ x ≤ 20, y = 38
When x > 20, y = 2x - 2.
Because y = x + c has a slope of 1, there is only one possible value for x in order to only have a single intersection, which is when x = 20. Any other value of x would result in 2 points of intersection. Plugging this back into our equation, we now have our point of (20,38). Plugging this into our second equation, we can now solve for c.
y = x + c
38 = 20 + c
c = 18
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Nicely done. +5 points.
Comments
-- A pleasure to have in class.
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Wow this comments are definitely not why I am here for :D
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Mind the chitchat.
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Sorry the caputere is wrong, the intersection between y and x is (y,x) = (38,0)
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Put your phone away.
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The constant will be 18
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Alright, who has my answer key? 0 points.
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my dog ate the answer ;)
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It also took a bite out of your grade.
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look on that it was A++ and now its A+, im fine with that (so is my dog ;))
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Ex. 2
At first, I tried using integrals and differential equtions, but discovered, that MS Paint is not a suitable for this task and eventually - gave up. However, now that I think about it solution could be this:
R1 = 1m, R2 = 2m. Because perimeter of a circle is 2 x pi x radius, then for R2 perimeter is twice as much as for R1. So thickness decreasing speed (T) would be double (2xT1).
However, at R2 you are drawing oil from is 4 times the area you were drawing at R1, making it 4 times less draining for any oil covered area (so T=2x T1 x 0.25)
The last thing to mention, is that at R2 due to area being 4 times larger than at R1 and V of entire oil being constant, the height of oil disc is 4 times less, so any new oil spread requires 4 times less height to be made (at moment of R2), so it can be created at 1/4 the speed of T
Therefore, full answer should be T=T1 x2x0.25x0.25 = T1/8 = 0.5 mm/sec
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Don't forget that the problem asks for the rate at which it decreases. Make sure it's negative next time around.
Nicely done. +5 Points
Extra Credit for using in-class application: Microsoft Paint +1 Point
Comments
-- Talks too much. Otherwise, a pleasure to have in class.
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Oh, come on, it's right there in the definition of T - "thickness decreasing speed".
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