What is the equation for the line of reflection?
1 answer:
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The particular solution to the differential equation which describes the number of fish over time will be y = 40(0.99)^t.
<h3>What is an exponent?</h3>Consider the function:
y = a (1 ± r) ˣ
Where x is the number of times this growth/decay occurs, a = initial amount, and r = fraction by which this growth/decay occurs.
If there is a plus sign, then there is exponential growth happening by r fraction or 100r %
If there is a minus sign, then there is exponential decay happening by r fraction or 100r %
A population of endangered salmon, S(t), starts out with 40 fish and decreases proportionally at a rate of 0.01 fish per year. Let t be measured in years.
Let y be the number of fish over time (t).
Then we have
Then the particular solution to the differential equation which describes the number of fish over time will be y = 40(0.99)^t.
More about the exponent link is given below.
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<h2>Hello!</h2>
The answer is:
The center of the circle is the point (-9,-2) and the circle has a radius of 6 units.
<h2>Why?</h2>To solve the problem, we need to use the given equation which is in the general form, and then, use it transform it to the standard form in order to find the center of the circle and its radius.
So,
We are given the circle:
We know that a circle can be written in the following form:
Where,
h is the x-coordinate of the center of the circle
k is the y-coordinate of the center of the circle
r is the radius of the circle.
So, to find the center and the radius, we need to perform the following steps:
- Moving the constant to the other side of the equation:
- Grouping the terms (x and y):
- Completing squares for both variables, we have:
We need to sum to each side of the equation the following term:
Where, b, for this case, will the coefficients for both terms that have linear variables (x and y)
So, the variable "x", we have:
Where,
Then,
So, we need to add the number 81 to each side of the circle equation.
Now, for the variable "y", we have:
Where,
So, we need to add the number 4 to each side of the circle equation.
Therefore, we have:
Then, factoring, we have that the expression will be:
- Writing the standard form of the circle:
Now, from the simplified expression (after factoring), we can write the circle in the standard form:
Is also equal to:
Where,
Hence, the center of the circle is the point (-9,-2) and the circle has a radius of 6 units.
Have a nice day!