Using separation of variables, solve the differential equation db/dt = -k(b-24) for b

b(0)=28

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There isn't enough information to determine the value of . It is thus treated as a non-zero constant. (In case that , .)

Step-by-step explanation:

Start by separating the two differentials, and . Multiply both sides of this equation by the denominator to obtain

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Separate the variables. Move all terms that involve to the side with ; move all terms that involve to the side with .

Divide both sides with assuming that it is not equal to zero.

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Note that the first derivative of with respect to is just . Hence, leaving the constant on the side with could potentially simplify the calculations.

Integrate both sides.

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The left-hand side is similar to the first-derivative of a logarithm with as its base. .

Apply -substitution to the denominator . Let . Then since the expression is linear with a coefficient of .

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The given condition implies that .

The right-hand side is constant. Only linear expressions can produce a first-derivative of a constant. .

Hence .

The constant only needs to appear on one side of the equation.

is the inverse of . Hence . Place both sides of the equation as the exponent of :

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Apply the given initial condition of and to find the value of :

Hence . Add to both sides of the equation to obtain

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Apparently, the value of is dependent on that of . Hence the function expression:

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answer is 144

step-by-step explanation:

translate k to n and reflect across the line containing jk.