A rain gutter is made from sheets of aluminum that are 18 inches wide by turning up the edges to form right angles. Determine th
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Answer:
Step-by-step explanation:
Consider a sketch of the problem as shown in the picture, where:
- Blue line is given by y = 4x + 1.
- Point B is the center of the circle.
- Point A is (-3, 0).
Since the center of the circle lies on the line y = 4x +1 and is tangent to the x-axis at point A, then its radius BA is perpendicular to the x-axis. To find the coordinates of point B, we must replace x = -3 into the blue line equation: y = 4x(-3) + 1 = -11.
So, we know that the center of the circle is at B=(-3, -11). And furthermore, the radius BA is of length r=11.
Since the <em>general equation of the circle</em> of radius lenght r centered at (h, k) is given by
then with h = -3, k = -11 and r= 11, the equation of our circle is
We are given a relationship between the sides of a rectangle, that is, the length of one of its sides is 5 less two times its width, and we are asked to find an expression for the area. Let's remember that the area of a rectangle is equal to the product of the length of its side by its width. Let "w" be the length of the rectangle and "L" its lenght, then the area is given by the following formula:
We can use the relationship given in the problem, that is, its length being five less two times its width, that is:
Replacing in the formula for the area we get:
Now we use the distributive law: