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Answer
Length = 10 ft
Width = 5 ft
Explanation
Area of the rectangle given = 50 ft²
Let the width of the rectangle be x
So this means the length of the rectangle will be 3x - 5
What to find:
The dimensions of the rectangle.
Step-by-step solution:
Area of a rectangle = length x width
i.e A = L x W
Put A = 50, L = 3x - 5, W = x into the formula.
The quadratic equation can now be solve using factorization method:
Since the dimension can not be negative, hence the value of x will be = 5.
Therefore, the dimensions of the rectangle will be:
Answer:
Step-by-step explanation:
Assuming that the differential equation is
.
We need to solve it and obtain an expression for in order to complete the exercise.
First of all, this is an example of the logistic equation, which has the general form
.
In order to make the calculation easier we are going to solve the general equation, and later substitute the values of the constants, notice that and
and the initial condition
.
Notice that this equation is separable, then
.
Now, intagrating in both sides of the equation
.
In order to calculate the integral in the left hand side we make a partial fraction decomposition:
.
So,
.
We have obtained that:
which is equivalent to
Taking exponentials in both hands:
Hence,
.
The next step is to substitute the given values in the statement of the problem:
.
We calculate the value of using the initial condition
, substituting
:
and
.
So,
.
Finally, as we want the value of such that
, we substitute this last value into the above equation. Thus,
.
This is equivalent to . Taking logarithms we get
. Then,
.
So, the population of rats will be 200 after 25 months.