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
So for this problem you know that 15 is 1/4 of an hour so to get the amount of papers each individual could deliver by themselves in an hour you would multiply the amount they can deliver in 15 minutes by 4. Denny delivers 6 so multiplying that by 4 is 24. Next Brendan delivers 5 in 15 minutes so multiplying that by 4 you get 20. The final step is to add 20 and 24 to get the total amount of papers between the two of them that gets delivered in an hour. This will result in your answer of 44.
Answer:
y = -10x + 6
Step-by-step explanation:
If the diameter of the circle is 17.4 cm, the approximate circumference of the circle would be 54.636. If the radius of the circle is 17.4 cm, the approximate circumference would be 109.272.
Explanation:
Circumference of a circle = Pi (3.14) x diameter
In this case, the diameter (I am assuming) is 17.4, so in order to solve the circumference you must multiply Pi by 17.4.
(If 17.4 is the radius, simple multiply 17.4 by 2 and then solve for the circumference like you normally would. You must multiply the radius by two because the radius is half of the circles circumference.
Hope that helps. Happy learning!
A. 2x+y=25; x+y=20
x represents cheese wafers and y represents chocolate wafers.
B. I will choose elimination since there is y and y. I can multiply one equation by -1 to get y and -y, which cancels out.
2x+y=25
-x-y=-20
Add equations
x=5
Plug x in
5+y=20
y=15
Final answer: 5 cheese wafers, 15 chocolate wafers