Hi, can anyone help with b) and c)?
1 answer:
Answer:
steps below
Step-by-step explanation:
From the graph: parabola pass (0,4) (3,4) (1,2)
equation: y = ax² + bx + c
(0,4): c = 4
(3,4): 9a + 3b + 4 = 4 9a+3b = 0 3a + b = 0 ... (1)
(1,2): a + b + 4 = 2 a+b = -2 ... (2)
(1)-(2): 2a = 2 a = 1
(2): b = -3
parabola equation: f(x) = x² - 3x +4
(a) <u>f(3) = 3² - 3*3 + 4 = 4</u>
(b) normal line: parallel to tangent line y = 3x -5 at (3,4)
slope of line N: -1/3 pass (3,4)
equation of N: (y-4)/(x-3) = -1/3 y-4 = -1/3 x + 1
<u>line N: 1/3 x + y - 5 = 0</u>
(c) picture attached
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Answer:
Length = 150 yards
Width = 100 yards
Step-by-step explanation:
We want 600 yards of fencing that will result in the largest 2 fenced corrals, sharing a common border.
It will take the shape of a rectangle, with a dividing fence down the center.
Let W and L, Width and Length of the larger enclosure.
See attachment.
W= Area of the larger enclosure.
The perimeter is 2W + 2L.
The dividing fence is 1W
We know that we only have 600 yards of fence, so:
2W + 2L + 1W = 600 yards
Area = W x L
---
3W + 2L = 600 (yards)
2L = 600 -3W
L = (600-3W)/2
L = 300 -(3/2)W
---
Use this expression in the Area calculation:
Area = W x L
Area = W x (300 -(3/2)W)
Area = 300W -(3/2)W^2)
To find the maximum area, take the first derivative and set to zero to find the value of W that results in the greatest area.
Area' = 300 -2(3/2)W)
0 = 300 - 3W
3W = 300
W = 100 yards
Since 3W + 2L = 600
L = (600 - 3W)/2
L = (600 - 3(100))/2
L = 150 yards
Area = 150*100 = 15,000 yards^2
