When a certain drug is taken orally, the concentration of the drug in the patient's bloodstream after t minutes is given by
c(t) = 0.06t − 0.0002t2,
where 0 ≤ t ≤ 240 and the concentration is measured in mg/l.
when is the maximum serum concentration reached?
t = min
what is the maximum concentration?
/l

The time when the maximum serum concentration is reached is obtained by equating the derivative of C(t) to 0.
i.e. dC(t)/dt = 0.06 - 2(0.0002t) = 0.06 - 0.0004t = 0
0.0004t = 0.06
t = 0.06/0.0004 = 150
Therefore, the maximum serum concentration is reached at t = 150 mins

The maximum concentration = 0.06(150) - 0.0002(150)^2 = 9 - 0.0002(22,500) = 9 - 4.5 = 4.5
Therefore, the maximum concentration is 4.5mg/L

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12

If you make you answer for clear i can answer it : )