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josephmarvens1666
14.08.2020 •
Mathematics
On a distant planet, a ball is thrown upwards from ground level , reaching a maximum height of 12m and hitting the ground again in eight seconds. Determine a quadratic equation in the form a * x ^ 2 + bx + + c =0 that could be used to calculate when the ball is a height of 3m. Do not solve the equation
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Ответ:
(-3 ÷ 4)x^2 + 6x
Step-by-step explanation:
Data provided in the question
Maximum height = 12m
Number of seconds = 8
Height = 3m
Based on the above information, the quadratic equation is as follows
Since it took 8 seconds for reaching the maximum height and then it returned to the ground level so here the highest point is done after 4 seconds also this graph represents the motion in parabola so the a should be negative
Now it is mentioned that
a × x ^ 2 + bx + c =0
We can assume that
x = 0
x = 8
As these {0.8} are intercepts of x
When x = 0, then it would be
a × 0 ^ 2 + b(0) + c = 0 (i)
Therefore 0 = 0
Now x = 8, it would be
a × 8 ^ 2 + b(8) + c = 0
Therefore a(8)^2 + b(8) + c = 0 (ii)
As we can see that in the first equation c should be zero
While the second equation would be
64a + 8b = 0
i.e.
8a = -b or a = -b ÷ 8
Now as per the quadratic function, it appears
(-b ÷8)x^2 + bx + 0
Now the parabola vertex is (4, 12)
Now put this in the place of a
(-b ÷ 8)(4)^2 + b(4) = 12
Now for solving this b, all terms should be multiplied by 8
That comes
-b(16) + 32b = 96
16b = 96
So, b = 6.
As a = -b ÷8
a = -6 ÷ 8
a = -3 ÷4
Now the equation is
= (-3 ÷ 4)x^2 + 6x
Hence, this is the equation
Ответ:
The
Might be 300, im not sure. Hopefully it's right.