Tangent Line h(t) = sec t / t @ (Pi, 1/pi)
1 answer:
Take derivitive
note
the derivitive of sec(x)=sec(x)tan(x)
so
remember the quotient rule
the derivitive of
so
the derivitive of
so now evaluate when t=pi
we get
sec(pi)=-1
tan(pi)=0
we get
slope=1/pi
use slope point form
for
slope=m and point is (x1,y1)
equation is
y-y1=m(x-x1)
slope is 1/pi
point is (pi,1/pi)
y-1/π=1/π(x-π)
times both sides by π
πy-1=x-π
πy=x-π+1
y=(1/π)x-1+(1/π)
or, alternately
-(1/π)x+y=(1/π)-1
x-πy=π-1
note
the derivitive of sec(x)=sec(x)tan(x)
so
remember the quotient rule
the derivitive of
so
the derivitive of
so now evaluate when t=pi
we get
sec(pi)=-1
tan(pi)=0
we get
slope=1/pi
use slope point form
for
slope=m and point is (x1,y1)
equation is
y-y1=m(x-x1)
slope is 1/pi
point is (pi,1/pi)
y-1/π=1/π(x-π)
times both sides by π
πy-1=x-π
πy=x-π+1
y=(1/π)x-1+(1/π)
or, alternately
-(1/π)x+y=(1/π)-1
x-πy=π-1
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Answer:
Step-by-step explanation:
After travelling two hours, the two cruise ships form a triangle. One of the legs of this triangle will be the distance Cruise A travelled, and another will be the distance Cruise B travelled. We can find the distance they travel using:
Cruise A is travelling at 18 miles per hour for 2 hours. Therefore, Cruise A has travelled:
Cruise B is travelling at 15 miles per hour for 2 hours. Therefore, Cruise B has travelled:
Because we are given the angle between these legs, we can use the Law of Cosines to find the third leg. The Law of Cosines is given by:
, where
,
, and
are interchangeable. Let
represent the distance between the two cruises. We have:
(one significant figure).