Exercise 44 Page 673

With a circular dartboard, the probability is the ratio between the area of entire circular board to the area of the desired target, the inner yellow circle. P(Hitting Yellow)=A_(Yellow Circle)/A_(Entire Board) Since our answers need to be in centimeters, recall that 1 meter is the same as 100 centimeters. Let's use this to find the area of the whole circular board. Now, let's put this area in our probability equation. Since we are interested in the radius of the yellow circle, we can use the formula for the area of the yellow circle. P(Hitting Yellow)&=A_(Yellow Circle)/A_(Board) &=A_(Yellow Circle)/10 000 We are interested in finding the radius of the yellow circle. Therefore, let us also substitute the formula for the area of a circle for the area of the yellow circle. P(Hitting Yellow)&=A_(Yellow Circle)/10 000 &=π r_(Yellow Circle)^2/10 000 Now, we can solve this equation for the radius of the yellow circle. We can disregard the negative root since we are working with positive distances. Let's input our equation into our calculator. We can press Y= and enter our function.

Now let's look at the table of values. Make sure to change the table setup, so that the Δ Tbl=0.1. We can press 2nd then GRAPH to see the table of values.

From here, we can see all the probabilities between 0.2 and 0.8 on one screen. We can scroll down to get our last value of y when x=1.

Now, we can express our radius y that would generate all six answers x for the probability of a dart landing in the yellow circle. We can round each answer to the nearest centimeter.

P(Hitting Yellow)	Radius of Yellow Region (cm)
a. 0.2	45
b. 0.4	63
c. 0.5	71
d. 0.6	77
e. 0.8	89
f. 1.0	100