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?
C= 38
Comment has been collapsed.
Didn't show your work. 0 credit.
Comment has been collapsed.
o crap....sorry
XD
Comment has been collapsed.
welp, it's 20 obviously
Edit: I'm stupid, c = 18 actually
Comment has been collapsed.
That is correct. 18
Comment has been collapsed.
Please keep your eyes on your own paper.
Comment has been collapsed.
Oi, you better not be collaborating with Mr. Cheats up top.
Comment has been collapsed.
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.
Comment has been collapsed.
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
Comment has been collapsed.
Nicely done. +5 points.
Comments
-- A pleasure to have in class.
Comment has been collapsed.
Wow this comments are definitely not why I am here for :D
Comment has been collapsed.
Mind the chitchat.
Comment has been collapsed.
Sorry the caputere is wrong, the intersection between y and x is (y,x) = (38,0)
Comment has been collapsed.
Put your phone away.
Comment has been collapsed.
The constant will be 18
Comment has been collapsed.
Alright, who has my answer key? 0 points.
Comment has been collapsed.
my dog ate the answer ;)
Comment has been collapsed.
It also took a bite out of your grade.
Comment has been collapsed.
look on that it was A++ and now its A+, im fine with that (so is my dog ;))
Comment has been collapsed.
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
Comment has been collapsed.
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.
Comment has been collapsed.
Oh, come on, it's right there in the definition of T - "thickness decreasing speed".
Comment has been collapsed.