Word problem (infinite amount of answers)

Question

x f(x)

0 0.55

25 0.325

50 0.1

75 0.325

100 0.55

125 0.325

150 0.1

175 0.325

200 0.55

f(x)=0.225 sin(π/50(x-75))+ 0.325

f(x)= 0.255 cos(π/50(x))+0.325

Using one of these equations, how much time in the first minute is the valve of the tire above 0.15 m (should result in infinite amount of answers). Include at least 4 or more answers.

x=time (seconds) f(x)= height (meters) (all heights measured from the tip of the valve of the bicycle wheel all the way to the ground)

Answer 1

I'm assuming your cosine function has a typo and should be 0.225 instead of 0.255.

Let's find the "x" value where f(x) = 0.15

0.15 = 0.225 sin(π/50(x - 75)) + 0.325

-0.175 = 0.225 sin(π/50(x - 75))

-7/40 = 9/40sin(π/50(x - 75))

-7/9 = sin(π/50(x - 75))

arcsin(-7/9) = π/50(x - 75)

The angle is 0.8911225079 past π so 0.8911225079 + 3.1415926535 = 4.032715161

4.032715161 = π/50(x - 75)

50/π(4.032715161) = (x - 75)

64.1826552 = x - 75

x = 139.1826552

However, the period is 100 seconds, so to get the first time after zero, we need to subtract 100 seconds from this.

x = 139.1826552 - 100 = 39.1826552 seconds

So the height is above 0.15 m for the first 39.18 seconds.

I fail to see how there could be an infinite number of answers between 0 and 60 seconds. Perhaps there is something else in the question that clarifies this.