First take the derivative of the Y w.r.t t
so
dy/dt =50(-1) (1 + 6e^(-2t))^(-2) . (6e^(-2t) . (-2)
=600 e^(-2t) / (1 + 6e^(-2t))^2
to find that where it is maximum we take the drivative again
d²y/dt² = 600 e^(-2t) . (-2) . (1 + 6e^(-2t))^(-2) + 600 e^(-2t) . (-2) (1 + 6e^(-2t))^(-3) . (-12 e^(-2t)) = [-1200 e^(-2t) (1 + 6e^(-2t)) + 1200 e^(-2t) . 12e^(-2t)] / (1 + 6e^(-2t))^3 = 1200 e^(-2t) [6e^(-2t) - 1] / (1 + 6e^(-2t))^3 which will be 0 when 6e^(-2t) = 1, so e^(-2t) = 1/6 => -2t = ln (1/6) = -ln 6 => t = (1/2) ln 6
for value of y we know that
6e^(-2t) = 1, so y = 50 / (1 + 6e^(-2t)) = 50 / (1 + 1) = 25. So the coordinates are ((ln 6) / 2, 25).
Answer:
9.42
Step-by-step explanation:
The circumference of a circle is calculated using the following formula:
C=2πr (C: circumference, r : radius)
radius here is 6 and π is given as 3.14
2*(3.14)*6 = 18.84 now divide this by 2 to find the length of semicircle
18.84/2 = 9.42
So.. take a peek at the picture... let's get two points from it, hmm say 0,4 notice it touches the y-axis there, and say hmmm -4, 1, almost at the bottom of the line
once you get the slope and solve for "y", that'd be the equation of the line.
Answer:
22/25
Step-by-step explanation:
