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

  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

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x

step-by-step explanation:

last month maria hiked the 5-mile mountain trail a number of times and she hiked the 10-mile canal trail several times. let x represent the number of times she hiked the 5-mile trail, and let y represent the number of times she hiked the 10-mile trail. if she hiked a total of 90 miles, which equation can be used to find the number of times maria hiked each trail? x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x