Find the equation of the line with slope m=53 that contains the point (−6,−12).
1 answer:
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Answer:
<em>The circle has a radius of 41 inches</em>
Step-by-step explanation:
<u>Circles</u>
There are certain relations in a circle that help us to identify and calculate some of its characteristics.
The figure shows a circle with three parameters which will lead us to determine its radius. First, we have a chord that measures 80 inches. Since it doesn't go through the center of the circle, it's not the diameter.
But we also have the distance from the center to the chord, making a right angle with it. This makes the chord be divided into two equal parts of 40 inches each.
Now we form a right triangle joining the center to one of the extremes of the chord. The hypotenuse of this triangle is the required radius of the circle. Like every right triangle, this must comply with Pithagora's theorem:
where r is the hypotenuse and x, y are the legs or the smaller sides of the triangle. We have determined that x=9, y=40 (or vice-versa, it doesn't matter). Therefore
Solving for r
The circle has a radius of 41 inches
The mean weight of the packages is 2.5, so the total weight of the packages is found by multiplying 2.5 pounds by 4 which is equal to 10 pounds. That is the tial weight of the four books. To find the weight of the fourth book, the three other weights are subtracted from 10 pounds:
