Answer:
A(t) = 300 -260e^(-t/50)
Step-by-step explanation:
The rate of change of A(t) is ...
A'(t) = 6 -6/300·A(t)
Rewriting, we have ...
A'(t) +(1/50)A(t) = 6
This has solution ...
A(t) = p + qe^-(t/50)
We need to find the values of p and q. Using the differential equation, we ahve ...
A'(t) = -q/50e^-(t/50) = 6 - (p +qe^-(t/50))/50
0 = 6 -p/50
p = 300
From the initial condition, ...
A(0) = 300 +q = 40
q = -260
So, the complete solution is ...
A(t) = 300 -260e^(-t/50)
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The salt in the tank increases in exponentially decaying fashion from 40 grams to 300 grams with a time constant of 50 minutes.
Answer:
7.5 units squared
Step-by-step explanation:
Equation for solving the area is A = 1/2h(b1 + b2).
The bases here have a length of 4 and 1, so we add them together. The height is 3, so our equation is 1/2 * 3(5) = 7.5
Answer:
I cant see the question
Step-by-step explanation:
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Answer:
( 3 / 4) * λ = - 1 - - > λ = - ( 4 / 3)
y = - ( 4 / 3) * x + 6
