The height, in meters, of a machine piston can be modeled by the regression equation y is equal to 4 point 4 sine open paren 0 point 4 x minus 1 point 7 close paren plus 2 point 3 , where x represents time, in seconds. To the nearest tenth of a meter, what is the height of the piston after 10 seconds?
Substitute x = 10 into the equation: y = 4.4 sin(0.4(10) − 1.7) + 2.3 = 4.4 sin(2.3) + 2.3. Using sin(2.3) ≈ 0.746 gives y ≈ 5.58 meters, which rounds to 5.6 meters. The correct choice is 5.6 m.
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