Question

question 2 (1 point)
the height, h, in centimetres, of a piston moving up and down in an engine cylinder can be modelled by the function h(t) = 18 sin(50πt) + 18, where t is the time, in seconds.
what is the pistons minimum height?
a) 18 cm
b) 0 cm
c) 9 cm
d) -18 cm

Explanation:

Step1: Determine the range of the sine function

The range of \(y = \sin(x)\) is \([- 1,1]\). So for \(y=\sin(50\pi t)\), \(-1\leqslant\sin(50\pi t)\leqslant1\).

Step2: Find the minimum value of \(h(t)\)

Multiply the inequality by \(18\): \(-18\leqslant18\sin(50\pi t)\leqslant18\). Then add \(18\) to each part of the inequality: \(-18 + 18\leqslant18\sin(50\pi t)+18\leqslant18 + 18\). So \(0\leqslant h(t)\leqslant36\).

Answer:

B. \(0\) cm