Answer:
Below in bold
Step-by-step explanation:
The sequence is:
3, x, y, 18
If this is an A P then
x - 3 = y - x
2x - y = 3 (A) and
y - x = 18 - y
2y - x = 18 (B)
Multiply (A) by 2:
4x - 2y = 6 (C)
Adding B and C:
3x = 24
x = 8.
and
2y - 8 = 18
2y = 26
y = 13.
So x = 8 and y = 13.
b) ar + ar^2 = 6ar^3 where a = first term and r = common ratio
Divide by a:
r + r^2 = 6r^3
6r^3 - r^2 - r = 0
r(6r^2 - r - 1) = 0
r(3r + 1)(2r - 1) = 0
So the 2 possible values of r
= -1/3 and 1/2.
i) The common ratio is positive so it must be 1/2.
Second term ar = 8
1/2 a = 8
a = 16.
So the first 6 terms are:
16, 8, 4, 2, 1, 1/2.
Comment
There are 12 months in a year. He plans on visiting 8 times each month.
Step One
Find the number of visits per year.
<em>Givens</em>
Number of visits per month = 8
Number of months per year = 12
Visits = # visits / month * number of months
Visitis = 8 * 12
Visits = 96 visits in total.
Step Two
<em>Calculate the cost / visit</em>
Total Cost = 414 visits.
Total Visits = 96
Cost / Visit = Total Cost / Total visits.
Cost / Visit = 414 / 96
Cost / Visit = 4.31 roughly.
The most helpful form to find the coordinates of the minimum is the vertex form.
<h3>Which form is better to find the minimum?</h3>
Remember that for a quadratic equation with a positive leading coefficient, the minimum is at the vertex.
So the better form to determinate the coordinates of the minimum value will be the vertex form, where if the vertex is (h, k), we get:
y = a*(x - h)^2 + k
In this case, the first option is in that form:
y = (x + 1)^2 - 25
so:
h = -1
k = -25
This means that the coordinates of the minimum are (-1, -25)
If you want to learn more about quadratic equations, you can read:
brainly.com/question/1214333
27x^3 - 45x^2 - 39x - 7
To find this, you can use either the FOIL method or the box method.
In this case, I used the FOIL method where I multiples 9x^2 by 3x + 1 and continued my way down on the first equation.
After multiplying, I combined like terms to receive my final answer:
Hope this helps!
