Answer:
The sum of the coefficients of the terms in (-1.5·x² + 0.5·x + 4)¹⁶ that have even degree is -4273411167.501
Step-by-step explanation:
The parameters given are;
f(-4) = -22
f(-1) = 2
f(2) = -1
g(x) = f(x)¹⁶
The function f(x) is presented as follows;
f(x) = a·x² + b·x +c
We have;
-22 = a·(-4)² + b·(-4) +c
-22 = a·16 - 4·b +c ..............(1)
2 = a·(-1)² + b·(-1) +c
2 = a - b +c...........................(2)
-1 = a·(2)² + b·(2) +c
-1 = 4·a + 2·b +c...................(3)
Solving the equations (1), (2), and (3) by using an online linear systems solver, we get;
a = -1.5, b = 0.5, c = 4
Therefore, f(x) = -1.5·x² + 0.5·x + 4
f(x)¹⁶ = (-1.5·x² + 0.5·x + 4)¹⁶ which gives the coefficients of the even terms as follows;
656.841 - 19267.331 + 248302.054 - 1772904.419 + 6735603.932 - 2868054.635 - 119602865.901 + 750783340.827 + -2542435585.611 + 5338903756.992 - 6048065910.25 -1031335136 + 17223697920 - 32238338048 + 32107397120 - 17716740096 = -4273411167.501.
12% and 0.12 are the percentages and deciamls
Short leg = 18 Long leg= 24 Hypotenuse= 30
My calculations were simple trial and error. I started with a trial of 10 for the short leg to begin with, averaging and estimating the appropriate proportions based off 6 additional increments. Sorry I don't have an algebraic method for you. Hope this has helped somewhat :)
