By letting
we get derivatives
a) Substitute these into the differential equation. After a lot of simplification, the equation reduces to
Examine the lowest degree term 
, which gives rise to the indicial equation,
with roots at r = 0 and r = 4/5.
b) The recurrence for the coefficients 
is
so that with r = 4/5, the coefficients are governed by
c) Starting with 
, we find
so that the first three terms of the solution are
Answer:
$ 3820
Step-by-step explanation:
When the car is new, it is 0 year old. It means, t = 0
Initial value = 26,000 (0.84)^0 = 26,000(1)
Initial value = $ 26000
Similarly, when car is 11 year old, t = 11
=> 26000(0.84)¹¹ = 26000(0.14691)
≈ $ 3819.842
≈ $ 3820 (round to near ten)
1) let both have x ,
so putting in eqn ;
4x+0.50 = 9x-3
5x=2.50
x=0.50
therefore both have 50 p in the beginning !!
2) let the number be x
so in eqn;
(x+18)/2=5x
x+18=10x
9x=18
x=2
so the number must be 2 !!
if you have still any problem, comment !!
Answer:
Step-by-step explanation:
Let s represent the son's age now. Then s+32 is the father's age. In 4 years, we have ...
5(s+4) = (s+32)+4
5s +20 = s +36 . . . . . eliminate parentheses
4s = 16 . . . . . . . . . . . . subtract s+20
s = 4
The son is now 4 years old; the father, 36.
_____
<em>Alternate solution</em>
In 4 years, the ratio of ages is ...
father : son = 5 : 1
The difference of their ages at that time is 5-1 = 4 "ratio units". Since the difference in ages is 32 years, each ratio unit must stand for 32/4 = 8 years. That is, the future age ratio is ...
father : son = 40 : 8
So, now (4 years earlier), the ages must be ...
father: 36; son: 4.
