A triangle has sides with lengths of 6 meters, 12 meters, and 16 meters. Is it a right triangle?
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Answer:
The equation of the parabola that models the path of the long jumper through the air is .
Step-by-step explanation:
Mathematically, we know that parabolas are second-order polynomials and every second-order polynomials, also known as quadratic functions, can be constructed by knowing three different points of the curve. The standard form of the parabola is:
Where:
- Horizontal distance from the start line, measured in meters.
- Height of the long jumper, measured in meters.
,
,
- Polynomial constants, measured in
, dimensionless and meters, respectively.
If we know that ,
and
, this system of linear equations is presented below:
(Eq. 1)
(Eq. 2)
(Eq. 3)
The coefficients of the polynomial are, respectively:
,
,
The equation of the parabola that models the path of the long jumper through the air is .
But we need measured in centimeters, then, we use the following conversion:
Then, we get that:
Where and
are measured in meters and centimeters, respectively.
The equation of the parabola that models the path of the long jumper through the air is .