1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
KonstantinChe [14]
2 years ago
12

Write out the form of the partial fraction decomposition of the fraction. Do not determine the numerical values of the coefficie

nts.
\frac{x^4}{(x^3+x)(x^2-x+7)}
Mathematics
1 answer:
anyanavicka [17]2 years ago
7 0

Factorizing the denominator gives

\dfrac{x^4}{(x^3+x)(x^2-x+7)} = \dfrac{x^4}{x(x^2+1)(x^2-x+7)} = \dfrac{x^3}{(x^2+1)(x^2-x+7)}

Then the partial fraction decomposition would take the form

\dfrac{x^4}{(x^3+x)(x^2-x+7)} = \dfrac{a_0x + b_0}{x^2+1} + \dfrac{a_1x + b_1}{x^2-x+7}

You might be interested in
Jason and Karina have matching gardens Jason plants 2/3 of his garden with roses Karina's garden is divided into ninths how much
olganol [36]

Answer:

6/9

Step-by-step explanation:

5 0
3 years ago
If middle school and senior school are winning football games in the ratio 3:9 . If the Middle school won 17 games, calculate ho
Helen [10]
The Middle school won 17 games so the senior school won 51 games

4 0
3 years ago
one x-intercept for a parabola is at the point (2, 0). use the quadratic formula to find the other x-intercept for the parabola
omeli [17]

Answer:

Step-by-step explanation:

There are 3 ways to find the other x intercept.

1) Polynomial Long Division.

Divide x^2 - 3x + 2 by the binomial x - 2, because by the Factor Theorem if a is a root of a polynomial then x - a is a factor of said polynomial.

2) Just solving for x when y = 0, by using the quadratic formula.

x^2 - 3x + 2 = 0\\x_{12} = \frac{3 \pm \sqrt{9 - 4(1)(2)}}{2} = \frac{3 \pm 1}{2} = 2, 1.

So the other x - intercept is at (1, 0)

3) Using Vietta's Theorem regarding the solutions of a quadratic

Namely, the sum of the solutions of a quadratic equation is equal to the quotient between the negative coefficient of the linear term divided by the coefficient of the quadratic term.

x_1 + x_2 = \frac{-b}{a}

And the product between the solutions of a quadratic equation is just the quotient between the constant term and the coefficient of the quadratic term.

x_1 \cdot x_2 = \frac{c}{a}

These relations between the solutions give us a brief idea of what the solutions should be like.

6 0
3 years ago
An animal shelter relies on
mote1985 [20]

Answer:

Step-by-step explanation:

x ≥ 2800

12*75=900

900< x

8 0
3 years ago
PLEAES HELP ME I SUCK AT MATH!!
ehidna [41]

Answer:

its 5

Step-by-step explanation:

4 0
3 years ago
Other questions:
  • the moon is 240,000 from earth what is the distance written as a whole number multiplied by a power of ten
    12·1 answer
  • Plz help me with 2,3,4,5,6,7,8,9,10,11
    6·1 answer
  • Which property would you use to simplify the following expression? 5(y+7)
    14·2 answers
  • Which of the following represents the zeros of f(x) = x3 − 12x2 + 47x − 60?
    10·2 answers
  • The difference of twice a number and 6 is at most 20 use the variable c for t he unknown number.
    10·1 answer
  • Live fund is selling their holdings
    13·1 answer
  • Help me
    14·1 answer
  • Lena walks 2.5km every day. How far does she walk in 7 days? Write your answer in meters.
    7·1 answer
  • Ratio of 20 to24 is ​
    15·1 answer
  • Enter the number in scientific notation.<br> 8,400,000,000,000 =<br> PLEASE HELP
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!