sinusoidal function h(t) was used to predict a certain citys high and low tides for january. the prediction…

sinusoidal function h(t) was used to predict a certain citys high and low tides for january. the prediction was a high of 8.738 ft and a low of 1.149 ft. in february, the data was analyzed. the verified high was 12.257 ft, and the low was 0.735 ft. what was the change in amplitude from the predicted values to the verified values for january? the amplitude increased from 4.944 ft to 6.496 ft. the amplitude increased from 3.795 ft to 5.761 ft. the amplitude decreased from 5.761 ft to 3.795 ft. the amplitude decreased from 6.496 ft to 4.944 ft.

sinusoidal function h(t) was used to predict a certain citys high and low tides for january. the prediction was a high of 8.738 ft and a low of 1.149 ft. in february, the data was analyzed. the verified high was 12.257 ft, and the low was 0.735 ft. what was the change in amplitude from the predicted values to the verified values for january? the amplitude increased from 4.944 ft to 6.496 ft. the amplitude increased from 3.795 ft to 5.761 ft. the amplitude decreased from 5.761 ft to 3.795 ft. the amplitude decreased from 6.496 ft to 4.944 ft.

Answer

Answer:

The amplitude increased from 3.795 ft to 5.761 ft.

Explanation:

Step1: Calculate predicted amplitude

The formula for the amplitude of a sinusoidal - function given high ($H$) and low ($L$) values is $A=\frac{H - L}{2}$. For the predicted values in January, $H = 8.738$ ft and $L = 1.149$ ft. So, $A_{predicted}=\frac{8.738 - 1.149}{2}=\frac{7.589}{2}=3.7945\approx3.795$ ft.

Step2: Calculate verified amplitude

For the verified values in January (using February's verified high and low as the new reference for January's verification), $H = 12.257$ ft and $L = 0.735$ ft. So, $A_{verified}=\frac{12.257 - 0.735}{2}=\frac{11.522}{2}=5.761$ ft.

Step3: Determine the change

Since $5.761>3.795$, the amplitude increased from 3.795 ft to 5.761 ft.