The average daily maximum temperature for Laura’s hometown can be modeled by the function f(x)=4.5sin(πx6)+11.8 , where f(x) is the temperature in °C and x is the month.
x = 0 corresponds to January.
What is the average daily maximum temperature in May?
Round to the nearest tenth of a degree if needed.
Use 3.14 for π .
1.45?? confused!!
May is the 5th month. So,
f(4)=4.5sin(4π/6)+11.8 = 4.6*√3/2 + 11.8 = 15.784
and it must be a strange location, since the minimum temperature occurs in October . . .
To find the average daily maximum temperature in May, we need to substitute the value for x corresponding to May into the function f(x).
Since x = 0 corresponds to January, we need to determine the value of x for May. May is the fifth month of the year, so x will be 5.
Now let's substitute x = 5 into the function:
f(5) = 4.5sin(π * 5/6) + 11.8
Since we are given to use 3.14 for π, let's use that:
f(5) = 4.5sin(3.14 * 5/6) + 11.8
Calculating the expression inside the sine function:
3.14 * 5/6 = 2.6167
Now we can substitute this value into the function:
f(5) = 4.5sin(2.6167) + 11.8
Using a calculator or a mathematical software, we can calculate the sine of 2.6167:
sin(2.6167) ≈ 0.5272
Now let's substitute this value into the function:
f(5) = 4.5 * 0.5272 + 11.8
Calculating the expression:
4.5 * 0.5272 = 2.3724
f(5) = 2.3724 + 11.8
Adding the values together:
2.3724 + 11.8 = 14.1724
Finally, we round the answer to the nearest tenth of a degree:
f(5) ≈ 14.2
Therefore, the average daily maximum temperature in Laura's hometown for May is approximately 14.2°C.
To find the average daily maximum temperature in May, we need to substitute the corresponding value of x into the function f(x) = 4.5sin(πx/6) + 11.8 and evaluate it.
Given:
x = 0 corresponds to January.
May is the 5th month of the year, so x = 5.
Substituting x = 5 into the function:
f(5) = 4.5sin(π(5)/6) + 11.8
Now, let's calculate:
f(5) = 4.5sin(5π/6) + 11.8
Using the value of π as 3.14:
f(5) = 4.5sin(3.14(5)/6) + 11.8
Simplifying further:
f(5) = 4.5sin(15.7/6) + 11.8
Using a calculator or a math software, we can evaluate the sine of 15.7/6, which is approximately 0.95682:
f(5) ≈ 4.5(0.95682) + 11.8
Calculating the above expression:
f(5) ≈ 4.30569 + 11.8
Adding:
f(5) ≈ 16.10569
Rounding to the nearest tenth of a degree, the average daily maximum temperature in May is approximately 16.1°C.