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:
1st ∡ = 15.5°
2nd ∡ = 77.25°
3rd ∡ = 87.25°
Step-by-step explanation:
1st ∡: x
2nd ∡: y
3rd ∡: z
Equations we can create from data given in problem:
y + z = 5x
z = 5x + 10
We have enough expressions to create an equation:
x + 5x + 5x + 10 = 180
11x = 170
x = 15.5
y = 5(15.5) = 77.25
z = y + 10 = 87.25
Answer:
<u>Equation</u>: 
<u>The balance after 5 years is: $1742.43</u>
<u></u>
Step-by-step explanation:
This is a compound growth problem . THe formula is:
Where
F is future amount
P is present amount
r is rate of interest, annually
n is the number of compounding per year
t is the time in years
Given:
P = 1500
r = 0.03
n = 12 (compounded monthly means 12 times a year)
The compound interest formula modelled by the variables is:
Now, we want balance after 5 years, so t = 5, substituting, we get:
<u>The balance after 5 years is: $1742.43</u>
I would use the pythagorean theorem to find the lengths of each side. a² + b² = c².
Side AB is one we're looking for. If you make other right triangle with that same side you can see that one length is 4 and the other is 3. So, 4² + 3² = c² → 25 = c² → 5 = c. Side AB is length 5.
Side AC is another. Do the same with that side and you get that one length is 4 and the other is 3. (This is the same one as above) so side AC is length 5.
Side BC is the last one. One of the lengths is 1 and the other is 1 → 1² + 1² = c² → 2 = c² → 1.414213562 = c so side BC is approximately length 1.41.
Add each length up and you get a perimeter of roughly 11.4
