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sweet [91]
2 years ago
11

The following differential equation is separable as it is of the form dP/dt = g(P)h(t).

Mathematics
1 answer:
dedylja [7]2 years ago
7 0

Answer:

P(1-P) = Ae^t

Step-by-step explanation:

given differential equation is

\frac{dP}{dt} =P-P^2\\\frac{dP}{dt} = g(P) h(t)\\g(P) = P-P^2\\h(t) = 1

So this is separable

We separate as

\frac{dP}{P-P^2} =1dt\\\frac{dP}{P(1-P)} =1dt

Resolve into partial fractions to solve this

dP(\frac{1}{P}+ \frac{1}{1-P} ) = 1dt\\ln P(1-P) = t+C\\P(1-P) = Ae^t

So solution isP(1-P) = Ae^t

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Answer:

Measure of EF: 1.98

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Trick I learned that's very helpful when solving these problems: SOH (Sine, Opposite, Hypotenuse)- CAH (Cosine, Adjacent, Hypotenuse)- TOA (Tangent, Opposite, Adjacent)

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you're starting with angle D which is 26 degrees. You have the measure of the Hypotenuse (DF) and you're trying to find the measure of EF (the segment opposite the angle) so you would use Sine

to do the equation, i'm going to use x in place of EF. 0.44 = sin(26)

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Equation:

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trying to find hypotenuse and you already have the adjacent angle so you would use cosine. Using y in place of AB. 0.616 = sin(52)

cos(angle) = (adjacent)/(hypotenuse)

cos(52) = 10/y      <------ divide by y

y*0.616 = 10       <------------ divide by 0.616

y = 10/0.616    <----------- next you'll divide 10 by 0.616

y = 6.16    <-----------answer

MEASURE OF HI

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tan(angle) = (opposite)/(adjacent)

tan(42) = 11/z   <------------ multiply z on both sides

z*0.90 = 11  <--------- divide by 0.90 to get z by itself

z = 11/0.90    <-------- divide 11 by 0.90

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