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3 years ago

I need help please???!

Mathematics

1 answer:

Usimov [2.4K]3 years ago

3 0

Answer:

6x-12

Step-by-step explanation:

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Find the partial fraction decomposition of the rational expression with prime quadratic factors in the denominator

SpyIntel [72]

$\dfrac{5x^4-7x^3-12x^2+6x+21}{(x-3)(x^2-2)^2}=\dfrac{a_1}{x-3}+\dfrac{a_2x+a_3}{x^2-2}+\dfrac{a_4x+a_5}{(x^2-2)^2}$
$\implies 5x^4-7x^3-12x^2+6x+21=a_1(x^2-2)^2+(a_2x+a_3)(x-3)(x^2-2)+(a_4x+a_5)(x-3)$

When $x=3$ , you're left with

$147=49a_1\implies a_1=\dfrac{147}{49}=3$

When $x=\sqrt2$ or $x=-\sqrt2$ , you're left with

$\begin{cases}17-8\sqrt2=(\sqrt2a_4+a_5)(\sqrt2-3)&\text{for }x=\sqrt2\\17+8\sqrt2=(-\sqrt2a_4+a_5)(-\sqrt2-3)\end{cases}\implies\begin{cases}-5+\sqrt2=\sqrt2a_4+a_5\\-5-\sqrt2=-\sqrt2a_4+a_5\end{cases}$

Adding the two equations together gives $-10=2a_5$ , or $a_5=-5$ . Subtracting them gives $2\sqrt2=2\sqrt2a_4$ , $a_4=1$ .

Now, you have

$5x^4-7x^3-12x^2+6x+21=3(x^2-2)^2+(a_2x+a_3)(x-3)(x^2-2)+(x-5)(x-3)$
$5x^4-7x^3-12x^2+6x+21=3x^4-11x^2-8x+27+(a_2x+a_3)(x-3)(x^2-2)$
$2x^4-7x^3-x^2+14x-6=(a_2x+a_3)(x-3)(x^2-2)$

By just examining the leading and lagging (first and last) terms that would be obtained by expanding the right side, and matching these with the terms on the left side, you would see that $a_2x^4=2x^4$ and $a_3(-3)(-2)=6a_3=-6$ . These alone tell you that you must have $a_2=2$ and $a_3=-1$ .

So the partial fraction decomposition is

$\dfrac3{x-3}+\dfrac{2x-1}{x^2-2}+\dfrac{x-5}{(x^2-2)^2}$

7 0

3 years ago

Can someone with knowledge see what I did wrong on number 4 also see if number 3 is right

Yakvenalex [24]

Answer:

#4. m=0;

#3. m = $\frac{-1}{2}$

Step-by-step explanation:

It seems right.

#4.

Maybe your teacher wants you to write m=0; because when a fraction has a numerator equal to zero then the fraction is zero.

#3.

Maybe your teachers want you to simplify the fraction and write m = $\frac{-1}{2}$

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3 years ago

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Explain what is wrong with the figure below.

Georgia [21]

Answer:

The diagonal side length shouldn't be 14. Or one of the side lengths shouldn't be what it is.

Step-by-step explanation:

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3 years ago

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If tan e = 1.3, what is the value of cot (90° - 9)?

ella [17]

Answer:

Step-by-step explanation:

We are given that:

$\tan(\theta)=1.3$

And we want to find:

$\cot(90^\circ -\theta)$

Remember that tangent and cotangent are co-functions. In other words, they follow the cofunction identities:

$\tan(\theta)=\cot(90^\circ-\theta)\text{ and } \cot(90^\circ-\theta)=\tan(\theta)$

Therefore, since tan(θ) = 1.3 and cot(90° - θ) = tan(θ), then cot(90° - θ) must also be 1.3.

Our answer is A.

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