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A research lab is mixing two chemical solutions, A and B, to create a new compound.
Solution A has a concentration modeled by the function
C_A (t)=0.8t+5.3
where t is time in minutes.
Solution B has a concentration modeled by
C_B (t)=1.2t-3.7.
At a certain time t=x, the lab technician records the following conditions:
The average concentration of the two solutions at time xis equal to 27.25555:
(C_A (x)+C_B (x))/2= ????.
At the same time, the difference between the concentration of Solution B and Solution A is exactly 0.5times the natural logarithm of e^2:
C_B (x)-C_A (x)=0.5ln(e^2).
Question: Using the two conditions above, solve the system of equations to find the value of x. If you do the algebra correctly, your final numerical answer for xwill be:
??????
AND SOLVE THIS ONE!
A spacecraft is adjusting its trajectory using two short engine burns.
The velocity change from the first burn (in "m/s" ) as a function of burn time t(in seconds) is
Δv_1 (t)=1.8t-12.7.
The velocity change from the second burn is
Δv_2 (t)=-0.9t-35.4.
Mission control wants to find a specific time t=x(in seconds) such that:
The sum of the two velocity changes equals -213.5036:
Δv_1 (x)+Δv_2 (x)=-213.5036.
At the same time, the difference between the first and second burn is exactly