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NARA [144]
3 years ago
12

Drag the tiles to the correct boxes to complete the pairs.Not all tiles will be used match the equations representing parabolas

with their directrixes

Mathematics
1 answer:
IceJOKER [234]3 years ago
4 0

Answer:

y=-8.08 -------> y+8=3(x+2)^{2}

y=14.25 -------> y-14=-(x-3)^{2}

y=-7.625 -----> y+7.5=2(x+2.5)^{2}

y=17.25 -------> y-17=-(x-3)^{2}

y=-7.25 -------> y+7=(x-4)^{2}

y=6.25 -------> y-6=-(x-1)^{2}

Step-by-step explanation:  

we know that

The standard form of a vertical parabola is equal to

(x-h)^{2}=4p(y- k)

where

(h,k) is the vertex

the focus is (h, k + p)

and

the directrix is y = k - p

Part 1) we have

y+8=3(x+2)^{2}

Convert to standard form

(x+2)^{2}=(1/3)(y+8)

The vertex is the point (-2,-8)

h=-2,k=-8

4p=1/3

p=1/12

the directrix is equal to

y = k-p -----> y=-8-(1/12)=-8.08

Part 2) we have

y-14=-(x-3)^{2}

Convert to standard form

(x-3)^{2}=-(y-14)

The vertex is the point (3,14)

h=3,k=14

4p=-1

p=-1/4

the directrix is equal to

y = k-p -----> y = 14-(-1/4)=14.25

Part 3) we have

y+7.5=2(x+2.5)^{2}

Convert to standard form

(x+2.5)^{2}=(1/2)(y+7.5)

The vertex is the point (-2.5,-7.5)

h=-2.5,k=-7.5

4p=1/2

p=1/8

the directrix is equal to

y = k-p -----> y=-7.5-(1/8)=-7.625

Part 4) we have

y-17=-(x-3)^{2}

Convert to standard form

(x-3)^{2}=-(y-17)

The vertex is the point (3,17)

h=3,k=17

4p=-1

p=-1/4

the directrix is equal to

y = k-p -----> y = 17-(-1/4)=17.25

Part 5) we have

y+7=(x-4)^{2}

Convert to standard form

(x-4)^{2}=(y+7)

The vertex is the point (4,-7)

h=4,k=-7

4p=1

p=1/4

the directrix is equal to

y = k-p -----> y=-7-(1/4)=-7.25

Part 6) we have

y-6=-(x-1)^{2}

Convert to standard form

(x-1)^{2}=-(y-6)

The vertex is the point (1,6)

h=1,k=6

4p=-1

p=-1/4

the directrix is equal to

y = k-p -----> y=6-(-1/4)=6.25

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Hope this helps you.

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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.

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Answer:

Step-by-step explanation:

15% = 15/100 = .15

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5 0
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lisabon 2012 [21]

Answer:

16

Step-by-step explanation:

According to the given description, PS is the mid segment of the \triangle TQR

Therefore by Mid-segment Theorem:

PS = \frac{1}{2}  QR \\  \\ PS = \frac{1}{2}   \times 32 \\  \\ PS =16 \:

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