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:
a) In other words, the equation 3x4−8x3+2=0 has a root in [2,3]
b) x≈2.630020
Step-by-step explanation:
Answer:
The length of x in #1 is 15.57
Step-by-step explanation:
Let's use #1 as an example to teach show you how to do this. In a right triangle we can solve these using trig. In this particular one, we have the measure adjacent to the angle and we are looking for the one opposite of the angle. So we look at all the trig functions and select the one that uses both of those two terms.
Sinα = Opp/Hyp
Tanα = Opp/Adj
Cosα = Adj/Hyp
As you can see, Tan is the function we are looking for. So we plug in all known information into that equation.
Tanα = Opp/Adj -----> Plug in known values
Tan(60) = x/9 ----->Calculate out the trig function
1.73 = x/9 -----> Multiply by the denominator to solve
15.57 = x
9514 1404 393
Answer:
see attached
Step-by-step explanation:
The scaling shown in the attachment is about as close as I can get using an on-line graphing program. You may fare better with graph paper. The vertex and x-intercepts are shown. The values at x=-3 and x=2 are y=11.
Answer:
33%
Step-by-step explanation:
311-208=103 ponds lost
103/311=33%
