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python， A dartboard of radius 10 and the wall it is hanging on are represented using...

python， A dartboard of radius 10 and the wall it is hanging on are represented using the two-dimensional coordinate system, with the board’s center at coordinate (0, 0). Variables x and y store x- and y-coordinate of a dart hit. Write an expression using variables x and y that evaluates to True if the dart hits (is within) the dartboard, and evaluate the expression for these dart coordinates:
a) (0, 0)
b) (10, 10)
c) (6, -6)
d) (-7, 8)
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Answer #1

The dartboard is a circle with its centre at the (0, 0) coordinates => it satisfies the equation

For the inside of the dartbaoard, the sum of and is less than or equal to the sqaure of radius. The following graph represents the dartboard with the equation .

=>

a) (0, 0)

0 + 0 <= 100

0 <= 100 - True

=> (0, 0) lies within the dartboard

b) (10, 10)

100 + 100 <= 100

200 <= 100 - False

=> (10, 10) does not lie within the dartboard

c) (6, -6)

36 + 36 <= 100

72 <= 100 - True

=> (6, -6) lies within the dartboard

d) (-7, 8)

49 + 64 <= 100

113 <= 100 - False

=> (7, -8) does not lie within the dartboard

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