your first constant of propotionality is 10
The second constant of propotionality 5
No (random words to reach 20 characters lol)
Answer: OPTION A
Step-by-step explanation:
We need to remember that Product of powers property, which states that:
Let's check the options:
A. For 
you can apply the property mentioned before. Then:
(It is the equivalent expression)
B. Add the exponents:
(It is not the equivalent expression)
C. For 
you can apply the property mentioned before. Then:
(It is not the equivalent expression)
D. We know that 
and we maje the addition indicated in this option, we get:
(It is not the equivalent expression)
Answer: f(x) = -0.016x² + 1.6x
Step-by-step explanation:
If the lenght of the road over the arch is 100m, we can consider a coordinate plane and say that the road starts at point (0,0) and finishes at (100,0). The vertice of the parabola is at point (50,40), because the maximum height is 40 and it is always in the middle point of the roots.
So, we have
(0,0) (50,40) (100,0)
A quadratic function is always on the form: f(x) = ax² + bx + c
0 = a0² + b0 + c
40 = a50² + b50 + c
0 = a100² + b100 + c
0 = a0² + b0 + c → c = 0 ∴
40 = a50² + b50
0 = a100² + b100
_________________________
2500a + 50b = 40 (*2)
10000a + 100b = 0
_________________________
5000a + 100b = 80
10000a + 100b = 0 (-)
__________________________
-5000a = 80
-a=80/5000
a=-0.016
∴
2500a + 50b = 40
2500.(-0.016) + 50b = 40
-40 + 50b = 40
50b = 80
b = 80/50
b = 1.6
This way f(x) = -0.016x² + 1.6x
C because the x's repeat with the 3 and 3. If the x's repeat it is not a function.
Hope that helps.
