Answer:
Linear
Step-by-step explanation:
It is just a never ending straight line. no complications in that.
If y = cos(kt), then its first two derivatives are
y' = -k sin(kt)
y'' = -k² cos(kt)
Substituting y and y'' into 49y'' = -16y gives
-49k² cos(kt) = -15 cos(kt)
⇒ 49k² = 15
⇒ k² = 15/49
⇒ k = ±√15/7
Note that both values of k give the same solution y = cos(√15/7 t) since cosine is even.
Answer:
We have to prove
sin(α+β)-sin(α-β)=2 cos α sin β
We will take the left hand side to prove it equal to right hand side
So,
=sin(α+β)-sin(α-β) Eqn 1
We will use the following identities:
sin(α+β)=sin α cos β+cos α sin β
and
sin(α-β)=sin α cos β-cos α sin β
Putting the identities in eqn 1
=sin(α+β)-sin(α-β)
=[ sin α cos β+cos α sin β ]-[sin α cos β-cos α sin β ]
=sin α cos β+cos α sin β- sinα cos β+cos α sin β
sinα cosβ will be cancelled.
=cos α sin β+ cos α sin β
=2 cos α sin β
Hence,
sin(α+β)-sin(α-β)=2 cos α sin β
Answer:
14 miles
added with the miles she warmed up is 17 miles
