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Natalka [10]
3 years ago
14

If c (x) = 4x – 2 and d(x) = x2 + 5x, what is (cd) (x)

Mathematics
1 answer:
jolli1 [7]3 years ago
3 0

c(x) = 4x - 2

d(x) = x^2 + 5x

4x - 2(x^2 + 5x)

<em><u>Using FOIL, distribute each term appropriately. </u></em>

4x^3 + 20x^2 - 2x^2 - 10x

<em><u>Combine like terms.</u></em>

4x^3 + 18x^2 - 10x is the simplified polynomials achieved when c(x) and d(x) are multiplied.

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Answer:

To this question; we want to show that if two antipodal points on a sphere were A and B, for any random point C on the sphere, AC is perpendicular to BC?

Step-by-step explanation:

I would proceed by imagining the sphere in a three dimensional Cartesian coordinate system. For example, use a sphere of diameter 2 and let it sit at the origin. Then (0, 0, 1) and (0, 0, -1) are the vector locations of the “north and south poles” of the sphere.

Now choose the vector location of any point on the surface of the sphere. It will have a vector location - we’ll call it (x, y, z). Now the vectors from your point to the two poles are (-x, -y, 1-z) and (-x, -y, -1-z).

Now just form the dot product of those two vectors:

(-x, -y, 1-z) . (-x, -y, -1-z) = x^2 +y^2 + (1-z)*(-1-z)

Now the truth of your claim will be embodied in that dot product being zero:

x^2 + y^2 - (1+z)(1-z) = 0

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But that last line is just the definition of points on the surface of a sphere of radius 1, so the claim is proven.

Since R>0 and AC is perpendicular to BC, the <ACB is at right angle.

Please, find attached a simple image to show antipodal points (Two points that makes a diameter) and a point C on the sphere.

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3 years ago
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BigorU [14]

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Step-by-step explanation:

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The sin function is an odd function
Llana [10]

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yes, idk if thats the answer you are looking for though

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