The image of the point (1, 2, 3) is (3, 7)
<h3>How to determine the image?</h3>
The given parameters are:
- Point = (1, 2, 3)
- Transformation rule = (3x, 2y + z)
In (1, 2, 3), we have:
x = 1; y = 2 and z = 3
When the rule is applied, we have:
Image = (3x, 2y + z)
Image = (3 * 1, 2 *2 + 3)
Evaluate
Image = (3, 7)
Hence, the image of the point (1, 2, 3) is (3, 7)
Read more about transformation at:
brainly.com/question/4289712
#SPJ1
I think 5,8 if not I’m srry
Answer:
Step-by-step explanation:
The first differences of the sequence are ...
- 5-2 = 3
- 10-5 = 5
- 17-10 = 7
- 26-17 = 9
- 37-26 = 11
Second differences are ...
- 5 -3 = 2
- 7 -5 = 2
- 9 -7 = 2
- 11 -9 = 2
The second differences are constant, so the sequence can be described by a second-degree polynomial.
We can write and solve three equations for the coefficients of the polynomial. Let's define the polynomial for the sequence as ...
f(n) = an^2 + bn + c
Then the first three terms of the sequence are ...
- f(1) = 2 = a·1^2 + b·1 + c
- f(2) = 5 = a·2^2 +b·2 + c
- f(3) = 10 = a·3^2 +b·3 +c
Subtracting the first equation from the other two gives ...
3a +b = 3
8a +2b = 8
Subtracting the first of these from half the second gives ...
(4a +b) -(3a +b) = (4) -(3)
a = 1 . . . . . simplify
Substituting into the first of the 2-term equations, we get ...
3·1 +b = 3
b = 0
And substituting the values for a and b into the equation for f(1), we have ...
1·1 + 0 + c = 2
c = 1
So, the formula for the sequence is ...
f(n) = n^2 + 1
__
The 20th term is f(20):
f(20) = 20^2 +1 = 401
_____
<em>Comment on the solution</em>
It looks like this matches the solution of the "worked example" on your problem page.
1st year= 18000 x 0.85 = 15300
2nd year= 15300 x 0.85 = 13005
3rd year= 13005 x 0.85= 11054.25
