Sam went to the hardware store and bought two identical wooden planks. When Sam placed the planks end to end, the total length w
2 answers:
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Answer: 1. y = 2(x + 4)² - 3
<u>Step-by-step explanation:</u>
Notes: The vertex form of a parabola is y = a(x - h)² + k
- (h, k) is the vertex
- p is the distance from the vertex to the focus
1)
Now input a = 2 and (h, k) = (-4, -3) into the equation y = a(x - h)² + k
y = 2(x + 4)² - 3
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2)
Now input a = -1/3 and (h, k) = (-8, -7) into the equation y = a(x - h)² + k
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3)
The midpoint of the focus and directrix is the y-coordinate of the vertex:
The x-coordinate of the vertex is given in the focus as 7
(h, k) = (7, 1)
Now let's find the a-value:
Now input a = -1/2 and (h, k) = (7, 1) into the equation y = a(x - h)² + k
Answer:
Step-by-step explanation:
I see you're in college math, so we'll solve this with calculus, since it's the easiest way anyway.
The position equation is
That equation will give us the height of the rock at ANY TIME during its travels. I could find the height at 2 seconds by plugging in a 2 for t; I could find the height at 12 seconds by plugging in a 12 for t, etc.
The first derivative of position is velocity:
v(t) = -3.72t + 15 and you stated that the rock will be at its max height when the velocity is 0, so we plug in a 0 for v(t):
0 = -3.72t + 15 and solve for t:\
-15 = -3.72t so
t = 4.03 seconds. This is how long it takes to get to its max height. Knowing that, we can plug 4.03 seconds into the position equation to find the height at 4.03 seconds:
s(4.03) = -1.86(4.03)² + 15(4.03) so
s(4.03) = 30.2 meters.
Calculus is amazing. Much easier than most methods to solve problems like this.