Answer:
s = height above ground
s = 60 + 20 t - 4.9 t^2 (standard physics equation on earth)
at t = 0
s = 60 (clearly :)
now when does it hit the bleak earth?
That is when s = 0
4.9 t^2 - 20 t -60 = 0
solve quadratic and use the positive t (the negative t was back before you threw it if you had thrown it from the ground)
t = 6.09 or - 2.01
use t = 6.09
now to do the last part there are two obvious ways to get t at the peak
1. look for vertex of parabola
2. look for halfway between t = -2.01 and t = 6.09
I will do it the hard (11) waay by completing the square
4.9 t^2 - 20 t = -(s-60)
t^2 - 4.08 t = -.204 s + 12.2
t^2 - 4.08 t +2.04^2 = -.204 s +12.2 + 4.16
(t-2.04)^2 = -.204(s-80.2)
so
top at 80.2 meters at t = 2.04 s
===============
quick check on time
should be average of 6.09 and -2.01
=4.08 /2 = 2.04 check
Hold on just have to type before I can see the question
Answer:
150+55w
Step-by-step explanation:
150+55w
150 never changes
(55)(w), 55 changes depending on number of weeks
Answer:
y = 5cos(πx/4) +11
Step-by-step explanation:
The radius is 5 ft, so that will be the multiplier of the trig function.
The car starts at the top of the wheel, so the appropriate trig function is cosine, which is 1 (its maximum value) when its argument is zero.
The period is 8 seconds, so the argument of the cosine function will be 2π(x/8) = πx/4. This changes by 2π when x changes by 8.
The centerline of the wheel is the sum of the minimum and the radius, so is 6+5 = 11 ft. This is the offset of the scaled cosine function.
Putting that all together, you get
... y = 5cos(π/4x) + 11
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The answer selections don't seem to consistently identify the argument of the trig function properly. We assume that π/4(x) means (πx/4), where this product is the argument of the trig function.
