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.
My Question:
Is there any answer choices?
4x^2 + 5xy - y^2 = 6
Implicitly differentiating both sides,
4(2x) + 5(x y' + y) - 2yy' = 0
where y' = dy/dx
8x + 5xy' +5y -2yy' = 0
combining y' terms
y' (5x-2y) +8x +5y = 0
y'(5x-2y) = -(8x+5y)
dy/dx = -(8x+5y)/(5x-2y)
or
dy/dx = (8x+5y)/(2y-5x)
Answer:
The sale price was $67.20
Step-by-step explanation:
The sale price is 30% less than the original price. Symbolically,
Sale price: (100% less 30%) of $96, or
(1.00 - 0.30)($96), or 0.70($96) = $67.20
The sale price was $67.20
Answer:
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Step-by-step explanation:
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