Q(t) = 40((e^-t) - (e^-2t))
For q(t) to be maximum dq/dt = 0
dq/dt = 40(-(e^-t) + 2(e^-2t) = 0
2e^-2t - e^-t = 0
2e^-2t = e^-t
e^t = 2
t = ln 2
q(ln 2) = 40((e^(-ln 2) - (e^(-2ln 2)) = 40(1/2 - 1/4) = 40(1/4) = 10
Therefore, thw maximum amount of drug in the bloodstream at one time is 10 mg.
The speed of the cart begin to decrease at approximately: 3.5 minutes.
<h3>What is a Time-Speed Graph?</h3>
A typical time-speed graph shows the time on the x-axis and the speed on the y-axis. When the slope is rising, it means the speed is increasing. When the slope is horizontal, it means the speed is constant. When the slope falls or decline, it means speed is decreasing.
We are given a time-speed graph that shows the speed of a cart over a period of several minutes. Time in minutes is on the x-axis (horizontal axis) while speed in miles per hour is on the y-axis (vertical axis).
From the graph given, the speed of the cart started increasing up to about 3 minutes, since the line slopes upwards. Then, between 3 and 4 minutes, we have a horizontal line which starts to decline at approximately 3.5 minutes.
Therefore, we can conclude that the speed of the cart begin to decrease at approximately: 3.5 minutes.
Learn more about time-speed graph on:
brainly.com/question/3480245
#SPJ1
Answer:
(x - 8)(x + 4)
(x + 4)(x - 8)
Step-by-step explanation:
(x - 16)(x + 2)
= x2 + 2x - 16x - 32
= x2 - 14x - 32
(x + 2)(x - 16)
= x2 - 16x + 2x - 32
= x2 - 14x - 32
(x - 8)(x + 4)
x - 8)(x + 4) = x2 + 4x - 8x - 32
x - 8)(x + 4) = x2 + 4x - 8x - 32 = x2 - 4x - 32
( 30 + x)(x - 4)
= 30x - 120 + x2 - 4x
= x2 + 26x - 120
(x + 4)(x - 8)
(x + 4)(x - 8) = x2 - 8x + 4x - 32
(x + 4)(x - 8) = x2 - 8x + 4x - 32 = x2 - 4x - 32
(x - 4)(x + 8)
= x2 + 8x - 4x - 32
= x2 + 4x - 32
Let me think this again and I will get back later!! 2.234 graph
