What will be the answer?

Question

Mathematics

Hello.
Tell me the formula, how can you find out X?
if 2.3 = 0 and 40.6 = 400, how much will 11.6 be proportional to ?

2.3 = 0
11.6 = X
40.6 = 400

Answer 1

If it is considered that the dependence of the output on the input is linear, then it can be composed as follows:
y = k*x+b
And you are given 2 values ​​for x and y:

0 = k*2.3+b
400 = k*40.6+b

You need to find k*11.6+b.
A system of two linear equations is simply solved analytically, without specific values:

y1 = k*x1+b
y2 = k*x2+b

y1-y2 = k*(x1-x2) +(b-b)
k = (y1-y2)/(x1-x2)
b = y1 - k*x1 = y1 - (y1-y2)/(x1-x2)*x1

y = (y1-y2)/(x1-x2)*(x-x1) + y1

Substitute your values ​​there for x = :

y = (0-400)/(2.3-40.6)(11.6-2.3) + 0 = 400/38.3*9.3 = 43.81

Answer 2

1) "Shift" all y by 2.3

11.6 - 2.3 = X
40.6 - 2.3 = 400

2) Proportion from class 2:

X = (11.6 - 2.3 * 400) / (40.6 - 2.3)