A wrestling mat used for high school competition is shown. The wrestling circle has a diameter of 28 feet. The inner circle has
a diameter of 10 feet. What is the approximate area of the large wrestling circle (not including the inner circle)? Round your answer to the
nearest tenths place.
nearest tenths place.
1 answer:
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<h2>Answer/Step-by-step explanation:</h2>
Direct variation occurs when a variable varies directly with another variable. That is, as the x-variable increases, the y-variable also increases.
The ratio of between y-variable and x-variable would be constant.
Direct variation can be represented by the equation, , where k is a constant. Thus,
From the table given, it seems, as x increases, y also increases. Let's find out if there is a constant of proportionality (k).
Thus, ratio of y to x,
k = 0.5.
If the given table of values has a direct variation relationship, then, plugging in the values of any (x, y), into , should give us the same constant if proportionality.
Let's check:
When x = 2, and y = 1:
,
,
When x = 3, y = 1.5:
,
When x = 5, y = 2.50:
,
The constant of proportionality is the same. Therefore, the relationship forms a direct variation.
Let's start by visualising this concept.
Number of grains on square:
1 2 4 8 16 ...
We can see that it starts to form a geometric sequence, with the common ratio being 2.
For the first question, we simply want the fifteenth term, so we just use the nth term geometric form:
Thus, there are 16, 384 grains on the fifteenth square.
The second question begs the same process, only this time, it's a summation. Using our sum to n terms of geometric sequence, we get:
Thus, there are 32, 767 total grains on the first 15 squares, and you should be able to work the rest from here.
Number of grains on square:
1 2 4 8 16 ...
We can see that it starts to form a geometric sequence, with the common ratio being 2.
For the first question, we simply want the fifteenth term, so we just use the nth term geometric form:
Thus, there are 16, 384 grains on the fifteenth square.
The second question begs the same process, only this time, it's a summation. Using our sum to n terms of geometric sequence, we get:
Thus, there are 32, 767 total grains on the first 15 squares, and you should be able to work the rest from here.