You attend a baseball game with friends and visit the snack stand between innings. Soda costs $2 a can, and a box of popcorn cos
1 answer:
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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 .
Answer:
Part a) The solution is the ordered pair (6,10)
Part b) The solutions are the ordered pairs (7,3) and (15,1.4)
Step-by-step explanation:
Part a) we have
----> equation A
----> equation B
Multiply equation A by 10 both sides to remove the fractions
----> equation C
isolate the variable y in equation B
----> equation D
we have the system of equations
----> equation C
----> equation D
Solve the system by substitution
substitute equation D in equation C
solve for x
Multiply by 3 both sides
Combine like terms
<em>Find the value of y</em>
The solution is the ordered pair (6,10)
Part b) we have
---> equation A
----> equation B
isolate the variable x in the equation B
----> equation C
substitute equation C in equation A
solve for y
Solve the quadratic equation by graphing
The solutions are y=1.4, y=3
see the attached figure
<em>Find the values of x</em>
For y=1.4
For y=3
therefore
The solutions are the ordered pairs (7,3) and (15,1.4)
