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Sever21 [200]
3 years ago
11

Find the partial fraction decomposition of x-3/x(x^2+3)

Mathematics
1 answer:
Setler [38]3 years ago
3 0

Answer:

-1 / x + (x + 1) / (x² + 3)

Step-by-step explanation:

(x − 3) / (x (x² + 3))

There are two factors in the denominator, so split this into two fractions with unknown numerators:

A / x + (Bx + C) / (x² + 3)

Combine back into one fraction:

(A (x² + 3) + (Bx + C) x) / (x (x² + 3))

Now equate this numerator with the original:

A (x² + 3) + (Bx + C) x = x − 3

Ax² + 3A + Bx² + Cx = x − 3

(A + B) x² + Cx + 3A = x − 3

Match the coefficients:

A + B = 0

C = 1

3A = -3

Solve:

A = -1

B = 1

C = 1

Therefore, the partial fraction decomposition is:

-1 / x + (x + 1) / (x² + 3)

Here's a graph showing that the two are the same:

desmos.com/calculator/hrxfnijewh

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I just wanted to see if this was 8 or negative 8 :)​
nirvana33 [79]

Answer:

It's a positive 8.

Step-by-step explanation:

You can't have a negative amount of money.

4 0
3 years ago
5. Use any method to solve the equation. If necessary, round to the nearest hundredth.
DanielleElmas [232]

Answer:

2.45, -2.45

Step-by-step explanation:

Since the equation has only one term in the unknown "x", we can solve for it isolating "x" on one side of the equal sign:

8x^2-48=0\\8x^2=48\\x^2=\frac{48}{8} \\x^2=6\\x=+/-\sqrt{6} \\x=+/- 2.449

Which we can round to: x = - 2.45 and x = 2.45

7 0
3 years ago
A-attached earlobes a-unattached earlobes if a is the allele for having attached earlobes, what percentage of offspring will hav
Scorpion4ik [409]

The percentage of the offspring that will have atatched earlobes as the dominant trait, is: 50%.

What is a Dominant Trait?

A dominant trait surpresses a recessive trait, and expresses itself. The allele of a dominant trait is usally denoted using capital letters.

Given the following traits:

A - attached earlobes (dominant allele)

a - unattached earlobes (recessive allele)

A cross between Aa and aa is shown in the image attached below.

The offspring having attached earlobes = 2 Aa = 50%.

50% of the osspring will have attached earlobes.

Learn more about dominant trait on:

brainly.com/question/16616523

4 0
2 years ago
Ariane borrows $300 on a 5−year loan. She is charged 5% simple interest per year. How much interest is she charged for 5 years?
AnnyKZ [126]

Answer:

Interest = $75

Total to pay back = $375

Step-by-step explanation:

The total amount she will have to pay back is found by the formula:

= Amount borrowed * (1 + rate * years)

= 300 * ( 1 + 5% * 5)

= $375

The interest is therefore:

= Amount to be paid back - Amount borrowed

= 375 - 300

= $75

6 0
3 years ago
Calculate the stroke of a slider-crank where the crank radius is 4.13 inches and the coupler is 5 inches.
scoray [572]

Answer:

x=8.268 inches

Step-by-step explanation:

From the question we are told that:

Radius r=4.13

Coupler C= 5 inches.

Generally the equation for Stroke in a slider-crank Mechanism x is mathematically given by

 x=2* Radius

 x=2*4.13

 x=8.268 inches

5 0
3 years ago
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