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

b(0)=28

.

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

.

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.

.

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.

.

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 .

.

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 :

.

.

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

Hence . Add to both sides of the equation to obtain

.

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

.

i think the correct option is the second option.

first, you divide the triangle in two, tô form a retangle triangle. after, using pythagoream theorem:

18^2 = 14^2 + (x/2)^2

(x^2/4) + 196 = 324

x^2/4 = 324 - 196

x^2/4 = 128

x^2 = 512

x = √512

x = √2^9

x = 16√2 cm

i hope i you.