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slega [8]
3 years ago
12

Convey 90 cubic feet into cubic yards

Mathematics
1 answer:
nignag [31]3 years ago
5 0
There are 3 feet in 1 yard, so 90/3 = x cubic yards

x = 30

30 cubic yards is your answer

hope this helps
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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 th
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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×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 ×x^{2} +b×+ 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
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