I cant figure this one out..
1 answer:
Answer: y=-4/3x-(34/3)
Step-by-step explanation:
Since we want to find the equation of a parallel line, we know the slope is going to stay the same. If the slope is changed, the lines will intersect at one point. All we need to do is to find the y-intercept. We can do that by using the point provided.
Now that we know the y-intercept, we can complete the equation.
y=-4/3x-(34/3)
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Answer:
a) initial height = 0 m
b) 8 s
c) vertex = (4, 32)
maximum height = 32 m
Step-by-step explanation:
<u>Given equation</u>:
where:
- h is the height of the arrow about the ground (in metres)
- t is the time (in seconds)
The initial height of the arrow will be at the beginning of its journey, so when t = 0
Substitute t = 0 into the equation and solve for h:
Therefore, the initial height of the arrow is 0 m.
<h3><u>Part (b)</u></h3>The arrow will hit the ground when the height is 0 m.
Substitute h = 0 into the given equation:
Factor out -2t:
Therefore:
And:
Therefore, the arrow will hit the ground at 8 seconds.
<h3><u>Part (c)</u></h3>The vertex is the <u>turning point</u> of a parabola - it's minimum or maximum point.
As the leading coefficient for the given equation is <u>negative</u>, the parabola <u>opens downwards</u> and so its <u>vertex</u> is its <u>maximum point</u>.
There are different ways to find the vertex of a parabola. The easiest way to find the x-coordinate is by calculating the midpoint of the x-intercepts.
We have determined that the arrow has a height of 0 m at 0 seconds and 8 seconds. Therefore, t = 0 and t = 8 are the x-intercepts. The midpoint is halfway between zero and 8, so the midpoint is t = 4
To find the y-coordinate, substitute t = 4 into the equation and solve for h:
Therefore, the coordinates of the vertex are (4, 32)
The maximum height is the y-coordinate of the vertex.
Therefore, the maximum height is 32 m