Number 5? Pre Cal- A small airplane is cruising at an airspeed of 235 kph heading in a direction of 45° (measured from the posit
ive z-axis). The wind is blowing at 60kph in a direction of 120°. Find the resulting direction and groundspeed of the airplane to the nearest whole number.
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<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