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Triss [41]
2 years ago
14

Helppppppppppppppppp

Mathematics
1 answer:
monitta2 years ago
6 0
Domain: (-infinity, +infinity)
Range: [4,-infinity)
Vertex: (0,4)
Zeros: (0,2) and (0,-2)
Axis of symmetry: y=0
Y intercept: (0,4)
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A long jumper lifts off 3 m after starting his run, and lands 6 m later. When he is 8 m from the start line, he is 5 cm above an
slega [8]

Answer:

The equation of the parabola that models the path of the long jumper through the air is y = -x^{2}+12\cdot x -27.

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:

y = a\cdot x^{2}+b\cdot x + c

Where:

x - Horizontal distance from the start line, measured in meters.

y - Height of the long jumper, measured in meters.

a, b, c - Polynomial constants, measured in \frac{1}{m}, dimensionless and meters, respectively.

If we know that (x_{1},y_{1}) = (3\,m, 0\,m), (x_{2},y_{2}) = (8\,m, 0.05\,m) and (x_{3}, y_{3}) = (9\,m, 0\,m), this system of linear equations is presented below:

9\cdot a + 3\cdot b + c = 0 (Eq. 1)

81\cdot a + 9\cdot b + c = 0 (Eq. 2)

64\cdot a + 8\cdot b + c = 0.05 (Eq. 3)

The coefficients of the polynomial are, respectively:

a = -\frac{1}{100}, b = \frac{3}{25}, c = -\frac{27}{100}

The equation of the parabola that models the path of the long jumper through the air is y' = -\frac{1}{100}\cdot x^{2}+\frac{3}{25}\cdot x -\frac{27}{100}.

But we need y measured in centimeters, then, we use the following conversion:

y = 100\cdot y'

Then, we get that:

y = -x^{2}+12\cdot x -27

Where x and y are measured in meters and centimeters, respectively.

The equation of the parabola that models the path of the long jumper through the air is y = -x^{2}+12\cdot x -27.

4 0
3 years ago
More, less or equal to: <br> Absolute 4 or Absolute 1
Sloan [31]

|4| > |1|

Absolute value of 4 is just 4, and the abosulute valvue of 1 is just 1.

So , since 4 is greater than 1 , that would be your answer.

4 > 1


7 0
3 years ago
What is the mathematical expression for the sum of 2 times 2 and 5 times 6
expeople1 [14]
2x2=4, 5x6=30
Not sure if they’re one expression, of so it’s (2x2)+(5x6)=34
7 0
3 years ago
A triangle has sides of length 3 cm and 3 cm. What can be concluded about the length of the third side?
mrs_skeptik [129]

Answer:

that its 3cm

Step-by-step explanation:

7 0
2 years ago
JKLM is a rhombus. KM is 6 and JL is 8. Find the perimeter of the rhombus. image of rhombus JKLM with diagonals JL and KM inters
VLD [36.1K]
If a quadrilateral is a rhombus then:

i) all its sides have equal length,

and

ii) the 2 diagonals are perpendicular and bisect each other.


The 2 diagonals of rhombus JKLM intersect at N.

Then m(MNJ)=90°,  |JN|=4 and |NM|=3 units

thus, by the Pythagorean theorem, 

|MJ|= \sqrt{ 3^{2} + 4^{2} }= \sqrt{9+16}= \sqrt{25}=5

The perimeter of the rhombus is 4*5 units=20 units.


Answer: 20 units 

4 0
3 years ago
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