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charle [14.2K]
3 years ago
10

Find the missing coefficient (4d—4)(3d—2)=12d^2+ []d+8

Mathematics
1 answer:
sergij07 [2.7K]3 years ago
8 0
<span>(4d-4)(3d-2)=12d^2 + []d + 8

Using FOIL method:
4d x 3d = 12d^2
4d x  -2 = -8d
-4 x 3d = -12d
-4 x -2 = 8

Adding common terms, we have:
-8d + -12d = -20 d

The missing coefficient is -20.</span>
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A cylindrical tin can for cookies has a height of 6 inches and a radius of 2 inches. What is the volume of the tin can? Use 3.14
Anna007 [38]

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Step-by-step explanation:

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2 years ago
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
In the right triangle shown, A= 30° and AB = 8.
zloy xaker [14]

Answer:

BC=4\ units

Step-by-step explanation:

The picture of the question in the attached figure

we know that

sin(30^o)=\frac{BC}{AB} ----> by SOH (opposite side divided by the hypotenuse)

we have

AB=8\ units\\\\sin(30^o)=\frac{1}{2}

solve for BC

BC=sin(30^o)(AB)

substitute the values

BC=(\frac{1}{2})(8)

BC=4\ units

4 0
3 years ago
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