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Nitella [24]
3 years ago
5

I need help in partial fraction!! With simple explaination would be nice!

Mathematics
1 answer:
WITCHER [35]3 years ago
3 0
\dfrac{x^4-7x^2+17x-10}{x(x^2-3)}

The degree of the numerator (4) is larger than the degree of the denominator (3), so first you need to divide. (Added screenshot of long division procedure.)

\dfrac{x^4-7x^2+17x-10}{x(x^2-3)}=x-\dfrac{4x^2-17x+10}{x(x^2-3)}

Now the second term can be decomposed into partial fractions.

\dfrac{4x^2-17x+10}{x(x^2-3)}=\dfrac{r_1}x+\dfrac{r_2x+r_3}{x^2-3}
\dfrac{4x^2-17x+10}{x(x^2-3)}=\dfrac{r_1(x^2-3)+x(r_2x+r_3)}{x(x^2-3)}
4x^2-17x+10=r_1(x^2-3)+x(r_2x+r_3)
4x^2-17x+10=(r_1+r_2)x^2+r_3x-3r_1
\implies\begin{cases}r_1+r_2=4\\r_3=-17\\-3r_1=10\end{cases}\implies r_1=-\dfrac{10}3,r_2=\dfrac{22}3,r_3=-17=-\dfrac{51}3
\implies\dfrac{4x^2-17x+10}{x(x^2-3)}=-\dfrac{10}{3x}+\dfrac{22x-51}{x^2-3}

So

\dfrac{x^4-7x^2+17x-10}{x(x^2-3)}=x+\dfrac{10}{3x}-\dfrac{22x-51}{x^2-3}

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laiz [17]
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We take out 7 as a constant focus on secant (x^3)
To take the derivative, we use the chain rule, taking the derivative of the inside, bringing it out, and then the derivative of the original function. For example:
The derivative of x^3 is 3x^2, and the derivative of secant is tan(x) and sec(x).
Knowing this: secant (x^3) becomes tan(x^3) * sec(x^3) * 3x^2. We transform tan(x^3) into sin(x^3)/cos(x^3) since tan(x) = sin(x)/cos(x). Then secant(x^3) becomes 1/cos(x^3) since the secant is the reciprocal of the cosine.

We then multiply everything together to simplify:

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our derivative is 21x^2 * sin(x^3)/(cos(x^3))^2


6 0
3 years ago
Maria tenia 6.500kg de patatas. Las envaso en sacos de 25kg y los puso a la venta a 30$ cada uno. Vendio la mitad de los sacos a
mojhsa [17]

Responder:

$ 7540

Explicación paso a paso:

Dado que:

Kilogramos totales de papa = 6500

Número de kilogramos por paquete = 25

Precio por paquete = $ 30

La mitad se vendió a $ 30

El resto se vende a ($ 30 - $ 2)

Número total de paquetes de 25 kg:

6500 kg / 25 kg = 260 paquetes

Por lo tanto, paquete total = 260 paquetes

La mitad se vende a $ 30:

(260/2) * 30

130 * $ 30 = $ 3900

Resto vendido a $ 28:

(260 - 130) * $ 28

130 * $ 28 = $ 3640

Cantidad total realizada:

$ (3640 + 3900) = $ 7540

8 0
3 years ago
The ratio of girls to boys in a lunchroom is 3 to 4. There are 48 boys. How many girls are there?
BabaBlast [244]

Answer:

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Step-by-step explanation:

ratio is 3 to 4

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allsm [11]

Answer:

Step-by-step explanation:

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0.88 = 0.70 + 0.60 -  P(a and b)

P(a and b) = 1.30 - 0.88 = 0.42.

So the events a and b are not mutually exclusive.

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Find the value of c(5)<br>c(n)=10+2n​
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Answer:

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Step-by-step explanation:

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