3 years ago

Find an equation for the line which is parallel to y= 1/4x + 5/3 and passes through the point (5,6)

Mathematics

1 answer:

amm18123 years ago

6 0

the answer is:

y=1/4x+19/4

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Simplify using trigonometric identities<br> 2sinθ - sin2θ cosθ

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Double angle identity for sine:

$\sin(2x) = 2 \sin(x) \cos(x)$

$\implies 2 \sin(\theta) - \sin(2\theta) \cos(\theta) = 2 \sin(\theta) - 2 \sin(\theta) \cos^2(\theta)$

Factorize the left side.

$2 \sin(\theta) - 2 \sin(\theta) \cos^2(\theta) = 2 \sin(\theta) \left(1 - \cos^2(\theta)\right)$

Pythagorean identity:

$\cos^2(x) + \sin^2(x) = 1$

$\implies 2 \sin(\theta) \left(1 - \cos^2(\theta)\right) = 2 \sin^3(\theta)$

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Add the following polynomials, then place the answer in the proper location on the grid. Write answer in descending powers of x.

CaHeK987 [17]

Answer:

$-x^5+3x^4+16x^3+7x^2-3x+6$

Step-by-step explanation:

Given polynomials are:

$x^5-4x^4+7x^3+8$ , $9x^3+7x^2-10$ and $-2x^5+7x^4-3x+8$

Now we need to add the given polynomials, then place the answer in the proper location on the grid. Also we need to write answer in descending powers of x.

So let's add them by combining like terms:

$x^5-4x^4+7x^3+8+9x^3+7x^2-10-2x^5+7x^4-3x+8$

$-x^5+3x^4+16x^3+7x^2-3x+6$

Hence final answer in descending order is $-x^5+3x^4+16x^3+7x^2-3x+6$

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