What’s the test about you didn’t put anything?
The answer is B. Corresponding
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.
It's not a multiple choice answer is it?
Explanation:
A "common denominator" is the least common multiple (LCM) of the denominators of the rational expressions involved. As such it can be found as the product of the unique factors of those denominators, each to its highest power.
For example, the common denominator for fractions with denominators of 20 and 25 will be 100. It can be found by considering the factors ...
20 = 2² × 5
25 = 5²
The unique factors here are 2 and 5, each with a highest power of 2. The product of these unique factors to their highest powers is ...
2²·5² = 4·25 = 100.
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Using this method of finding the LCM, it is essential that we know the factors of the numbers.
The LCM can also be found as the product of the numbers, divided by their greatest common factor (GCF). For this method, too, you need to know factors of the numbers involved--or, at least, the greatest common factor.
For the above example numbers, the GCF is 5, so their LCM is ...
20·25/5 = 500/5 = 100
