at a certain location, the number of hours of sunlight is modeled by ( y = 6.4cosleft(\frac{pi}{26}x\right)+1…

at a certain location, the number of hours of sunlight is modeled by ( y = 6.4cosleft(\frac{pi}{26}x\right)+12 ), where ( x ) represents the number of weeks after the summer solstice. based on the model, what is the minimum number of hours of sunlight at this location? 3.2 5.6 6.4 13.0

at a certain location, the number of hours of sunlight is modeled by ( y = 6.4cosleft(\frac{pi}{26}x\right)+12 ), where ( x ) represents the number of weeks after the summer solstice. based on the model, what is the minimum number of hours of sunlight at this location? 3.2 5.6 6.4 13.0

Answer

Explanation:

Step1: Determine the range of the cosine function

The range of the cosine function ( \cos(\theta) ) is ( - 1\leqslant\cos(\theta)\leqslant1 ).

Step2: Find the minimum value of ( y = 6.4\cos\left(\frac{\pi}{26}x\right)+12 )

When ( \cos\left(\frac{\pi}{26}x\right)=-1 ), we substitute this into the equation. [ \begin{align*} y&=6.4\times(- 1)+12\ &=-6.4 + 12\ &=5.6 \end{align*} ]

Answer:

5.6