if you dont help im literally going to faill!! i have to present how to do this question to my class tomorrow and have no idea how to do it!!
natasha is a marathon runner and she likes to train on a 2pi km stretch of rolling hills. The height, in kilometers, of the hills above sea level, relative to her home can be modeled by the funtion
h(d) = 4cos^2 d - 1 where d is the distance traveled in kilometers. At what intervals in the stretch of rolling hills is the height above sea level, relative to natashas home, less than zero?
if you show tell me how to do this i will give you 10 points, and i swear ill answer any of your questions!!
natasha is a marathon runner and she likes to train on a 2pi km stretch of rolling hills. The height, in kilometers, of the hills above sea level, relative to her home can be modeled by the funtion
h(d) = 4cos^2 d - 1 where d is the distance traveled in kilometers. At what intervals in the stretch of rolling hills is the height above sea level, relative to natashas home, less than zero?
if you show tell me how to do this i will give you 10 points, and i swear ill answer any of your questions!!
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The height of the hills is above sea level if h(d) > 0, less than 0 if h(d) < 0. Now h(d) > 0 if and only if
4 cos^2(d) - 1 > 0, or cos^2(d) > 1/4, or cos(d) < -1/2 or cos(d) > 1/2. Now you decide where on the interval [0,2pi] cos(d) is < -1/2 or > 1/2.
Then, h(d) < 0 Then -1/2 < cos(d) < 1/2. Finish it yourself.
4 cos^2(d) - 1 > 0, or cos^2(d) > 1/4, or cos(d) < -1/2 or cos(d) > 1/2. Now you decide where on the interval [0,2pi] cos(d) is < -1/2 or > 1/2.
Then, h(d) < 0 Then -1/2 < cos(d) < 1/2. Finish it yourself.