Carl's bead order includes 3 boxes of 100 beads. Which could be the number of beads in Carl's order?
1 answer:
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Answer:
Step-by-step explanation:
We can solve this system of equations by using elimination.
In this case, we can eliminate x by adding the two equations:
Then, substitute 7 for y to solve for x:
Substitute both these values into the system to check our answer:
Therefore the ordered pair is:
<em>x</em> ^2 + <em>y</em> ^2 = 9 => <em>y</em> = <em>y(x)</em> = ± √(9 - <em>x</em> ^2)
Each cross section would be a square with side length equal to the vertical distance between the upper and lower semicircles defined by <em>y(x)</em>, which is
√(9 - <em>x</em> ^2) - (- √(9 - <em>x</em> ^2)) = 2 √(9 - <em>x</em> ^2)
The area of each square section is the square of this length,
(2 √(9 - <em>x</em> ^2)) = 4 (9 - <em>x</em> ^2) = 36 - 4<em>x</em> ^2
We get the whole solid for -3 ≤ <em>x</em> ≤ 3, so integrating gives a volume of