Answer:
90
Step-by-step explanation:
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
Answer:
khanya pays higher
Step-by-step explanation:
You have to find the $/hr ratios:
khanya's is 480/8->$60/hr
rex's is 660/12->%55/hr
Khanya pays the higher rate
X = bessie and y = betty
x + y = 1464
y = 2x - 375
x + 2x - 375 = 1464
3x - 375 = 1464
3x = 1464 + 375
3x = 1839
x = 1839/3
x = 613 <== Bessie gave 613 gallons
y = 2x - 375
y = 2(613) - 375
y = 1226 - 375
y = 851 <== Betty gave 851 gallons
Answer:
See below in bold.
Step-by-step explanation:
cos 150 = - cos(180 - 150)
= - cos 30
= -√3/2.
sin 150
= sin (180 - 150
= sin 30
= 1/2.
