Inequalities question
Can someone help me with this? I know how to draw all the graphs but I'm not sure how to actually calculate the area...
Calculate the exact area satisfied by the inequalities
x^2+y^2≥25
x ≤5
y ≤5
I HAVE THE ANSWER AND WORKINGS OUT BUT I DON'T UNDERSTAND WHERE THE NUMBERS COME FROM...
Any help would be much appreciated
ANSWER:
5.37 TO 2DP
Calculate the exact area satisfied by the inequalities
x^2+y^2≥25
x ≤5
y ≤5
I HAVE THE ANSWER AND WORKINGS OUT BUT I DON'T UNDERSTAND WHERE THE NUMBERS COME FROM...
Any help would be much appreciated
ANSWER:
5.37 TO 2DP
Graph them all and you get the image below.
The area that satisfies all the inequalities is the little square from 0-5 on the x axis and 0-5 on the y axis, minus that quarter of the circle.
To work out the area:
Square = 5 * 5 = 25
Circle = 1/4 * pi * 5^2
Square - Circle = 5.36504591506
To 2 d.p you get 5.37
The area that satisfies all the inequalities is the little square from 0-5 on the x axis and 0-5 on the y axis, minus that quarter of the circle.
To work out the area:
Square = 5 * 5 = 25
Circle = 1/4 * pi * 5^2
Square - Circle = 5.36504591506
To 2 d.p you get 5.37
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