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2 years ago

Simplify 3x + 6x 2 - 5x - x 2. 6x 2 + 2x 6x 2 - 2x 5x 2 - 2x 5x 2 + 2x

Mathematics

2 answers:

Damm [24]2 years ago

6 0

Answer:

5x 2 - 2x

Step-by-step explanation:

Firlakuza [10]2 years ago

3 0

Answer:

$5x^2-2x$

Step-by-step explanation:

5x 2 - 2x

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Explain how you could write a quadratic function in factored form that would have a vertex with an x-coordinate of 3 and two dis

skad [1K]

The definition of quadratic function is given by:

 $(1) \ f(x)=ax^{2}+bx+c \\ \\ where \ a, b, c \ are \ real \ values$ 

So the problem asks for two conditions:

1. Write the quadratic function in factored form. 
2. The vertex has an x-coordinate of 3.

Then the equation (1) must be written as follows:

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To satisfy the two conditions:

$\frac{m+n}{2}=3$

So we are free to choose the value of one root, say:

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Thus:

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Finally, the answer is:

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The graph of this function is shown in the figure below.

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3 years ago

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3 years ago

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In the question, we are asked to show that x.cosec²x = cot x - d/dx x.cot x.

To prove, we go by the right-hand side of the equation:

cot x - d/dx x.cot x.

We solve the differential d/dx using the product rule, according to which, d/dx uv = u. d/dx(v) + v. d/dx(u), where u and v are functions of x.

cot x - {x. d/dx(cot x) + cot x. d/dx(x)}

= cot x - {x. (-cosec²x) + cot x} {Since, d/dx(cot x) = -cosec²x, and d/dx(x) = 1}

= cot x + x. cosec²x - cot x

= x. cosec²x

= The left-hand side of the equation.

Thus, the given equation, x.cosec²x = cot x - d/dx x.cot x, is proved using the product rule of differentials.

Learn more about differentials at

brainly.com/question/14830750

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