Answer:
A. .
Step-by-step explanation:
We have been given an inequality . We are asked to solve the given inequality for x.
Using distributive property, we will get:
Subtract 2 from both sides:
Divide both sides by 7:
Therefore, option A is the correct choice.
Answer:
Step-by-step explanation:
Each successive year, he
earned a 5% raise. It means that the salary is increasing in geometric progression. The formula for determining the nth term of a geometric progression is expressed as
Tn = ar^(n - 1)
Where
a represents the first term of the sequence(amount earned in the first year).
r represents the common ratio.
n represents the number of terms(years).
From the information given,
a = $32,000
r = 1 + 5/100 = 1.05
n = 20 years
The amount earned in his 20th year, T20 is
T20 = 32000 × 1.05^(20 - 1)
T20 = 32000 × 1.05^(19)
T20 = $80862.4
To determine the his total
earnings over the 20-year period, we would apply the formula for determining the sum of n terms, Sn of a geometric sequence which is expressed as
Sn = (ar^n - 1)/(r - 1)
Therefore, the sum of the first 20 terms, S20 is
S20 = (32000 × 1.05^(20) - 1)/1.05 - 1
S20 = (32000 × 1.653)/0.05
S20 = $1057920
I don't know what method is referred to in "section 4.3", but I'll suppose it's reduction of order and use that to find the exact solution. Take
, so that
and we're left with the ODE linear in
:
Now suppose
has a power series expansion
Then the ODE can be written as
All the coefficients of the series vanish, and setting
in the power series forms for
and
tell us that
and
, so we get the recurrence
We can solve explicitly for
quite easily:
and so on. Continuing in this way we end up with
so that the solution to the ODE is
We also require the solution to satisfy
, which we can do easily by adding and subtracting a constant as needed:
Answer:A
Step-by-step explanation: