The daily low temperature in Guangzhou, China Varies over time in a periodic way that can be modeled by a trigonometric function
. The period of change is exactly one year. the temperature peaks around July 26 at 78°F and has its minimum half a year later at 49°F. assuming a year is exactly 365 days July 26 is 206/365 of a year after January 1. Find the formula of the trigonometric function that models the daily low temperature T in Guangzhou t years after January 1, 2015 defined the function using radians
1 answer:
Answer:
T(t) = 14.5cos(2π(t -206/365)) +63.5
Step-by-step explanation:
The function can be written as ...
T = A·cos(2π(t -206/365)) +B
where A is half the difference of the high and low temperature values, and B is the average of the high and low temperature values.
A = (78-49)/2 = 29/2 = 14.5
B = (78 +49)/2 = 127/2 = 63.5
The value 206/365 is the horizontal right shift of the peak of the function. That makes the peak occur on July 26, as required.
Filling in these values gives us the function ...
T(t) = 14.5cos(2π(t -206/365)) +63.5
You might be interested in
Answer:
Step-by-step explanation:
Let be "x" the time in minutes that will take him to mow the entire park.
You know that he can mow 13 square feet in 1 minute and he has to mow 14,623 square feet.
Then, you can write the following proportion:
Solving for "x", you get:
To write that improper fraction as a mixed number:
- The quotient when you divide the numerator by the denominator of the fraction obtained, is (This will be the whole number).
- The remainder of that division is (This will be the numerator of the fraction).
- The denominator does not change.
Then: