Ummm don’t click the link
I think
It’s a virus
Answer:
The number is 3.
Step-by-step explanation:
5x - 4 = 11
5x = 15
x = 3
Answer:
a = 5.5, d = 11/3
Step-by-step explanation:
An arithmetic progression is a sequence of number such that the difference between consecutive numbers is a constant. It is given by:
The sum of fifth and sixth terms is 44
Therefore:
a + 4d + a + 5d = 44
2a + 9d = 44 (1)
The sum of the first n terms is:
Since the sum of the first eighteen terms is thrice the sum of the first ten terms:
18a + 153d = 3(10a + 45d)
18 a + 153d = 30a + 135d
18a - 30a + 153d - 135d = 0
-12a + 18d = 0 (2)
Multiply equation 1 by 6 and add to equation 2:
72d = 264
d = 11/3
Putting d = 11/3 in eqn 2
-12a + 18(11/3) = 0
-12a + 66 = 0
12a = 66
a = 5.5
If you make yourself a monthly expense chart:
Months
<u> 1 2 3 4 5 6 7 8 9 10</u>
Opt 1 -80 -30 -30 -30 -30 -30 -30 -30 -30 -30
Opt 2 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40
By month 5 the total amount spent for Opt 1 is $200 and Opt 2 is $200
For part two add up the values for each all the way up to month 9.
Option 1: 80 + 30(8) = 80 + 240 = 320 spent
Option 2: 40(9) = 360 spent
So option 1 is cheaper by month 9
In matrix form, the system is
First find the eigenvalues of the coefficient matrix (call it ).
Find the corresponding eigenvector for each eigenvalue:
Then the system has general solution
or
Given that and , we have
so that the system has particular solution