Question

The average daily high temperature in madrid peaks at 92°f in the summer and drops as low as 33°f in the winter. the temperature can be modeled by t (d) = 29.5 cosine (startfraction 2 pi over 365 endfraction (d minus 204) ) 62.5, where d represents the day number of the year (january 1 is 1, january 2 is 2, and so on). during which day is the high temperature expected to be closest to 75°f? 106 63 270 204

Answer 1

The day in Madrid at which the high temperature is expected to be closest to 75 degree Fahrenheit is 270.

What is linear function?

Linear function is the function in which the highest power of the unknown variable is one. Linear functions are used to model the real life problem in the mathematical expressions.

The average daily high temperature in Madrid peaks at 92°f in the summer and drops as low as 33°f in the winter.

The temperature can be modeled by the following function,

$t (d) = 29.5 \cos\left(\dfrac{2\pi}{365}(d-204)\right)+62.5$

Here, d represents the day number of the year (january 1 is 1, january 2 is 2, and so on).

The day has to be find out when the temperature is at 75 degree Fahrenheit. Put the value of temperature 75 in the above equation as,

$75 = 29.5 \cos\left(\dfrac{2\pi}{365}(d-204)\right)+62.5$

On solving the above equation for cosine function, we get the two values of d as,

$d\approx 138\\d\approx 270$

From the given options, 270 is the correct one.

Thus, the day at which the high temperature is expected to be closest to 75 degree Fahrenheit is 270.

Learn more about the linear function here;

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