Answer:
(D^2 + 9)y = cos 2x….(1). The corresponding homogeneous equation is (D^2 +9)y= 0,…(2), whose auxiliary equation is m^2 + 9 = 0, which has (+/-)3i as roots. The general solution of (2) is y = A.cos(3x) + B.sin(3x). Now to get a general solution of (1) we have just to add to the above, a particular solution of (1). One such solution is [cos(2x)]/[-2^2 +9] = (1/5).cos 2x. Hence a general solution of the given equation is given by y = A.cos(3x) + B.sin(3x) + (1/5)cos(2x), where A and B are arbitrary constants. The above solution incorporates all the solutions of the given equation.
Step-by-step explanation:
Answer:
D.
hope this helps
have a good day :)
Step-by-step explanation:
Need help myself not sure sorry
Answer:
3x-4
Step-by-step explanation:
y=ax+b general type of the line
a is the slope
y=3x+b
put 5 instead of the x and put 11 instead of the y
11=15+b
b=(-4)
Equation is 3x-4
Answer:
the common ratio is either 2 or -2.
the sum of the first 7 terms is then either 765 or 255
Step-by-step explanation:
a geometric sequence or series of progression (these are the most common names for the same thing) means that every new term of the sequence is created by multiplying the previous term by a constant factor which is called the common ratio.
so,
a1
a2 = a1×f
a3 = a2×f = a1×f²
a4 = a3×f = a1×f³
the problem description here tells us
a3 = 4×a1
and from above we know a3 = a1×f².
so, f² = 4
and therefore the common ratio = f = 2 or -2 (we need to keep that in mind).
again, the problem description tells us
a2 + a4 = 30
a1×f + a1×f³ = 30
for f = 2
a1×2 + a1×2³ = 30
2a1 + 8a1 = 30
10a1 = 30
a1 = 3
for f = -2
a1×-2 + a1×(-2)³ = 30
-10a1 = 30
a1 = -3
the sum of the first n terms of a geometric sequence is
sn = a1×(1 - f^(n+1))/(1-f) for f <>1
so, for f = 2
s7 = 3×(1 - 2⁸)/(1-2) = 3×-255/-1 = 3×255 = 765
for f = -2
s7 = -3×(1 - (-2)⁸)/(1 - -2) = -3×(1-256)/3 = -3×-255/3 =
= -1×-255 = 255
