We Make Solving Algebra 2 Problems and Answers Easy!

High School
Algebra
Algebra II

I 'm trying to solve this exercise of Fulton Algebraic Curves:
Let $D = \sum n_{P} P$ be an effective divisor, $S = {P \in X : n_{P} > 0}$ , $U = X ∖ S$ . Show that $L (r D) \subset Γ (U, O_{X})$ . Where $L (E) = {f \in K : {ord}_{P} (f) > - n_{P}, \forall P \in X}$ (The linear vectorial space of the rational functions with pole multiplicity worst at $n_{P}$ ).
But I have no idea

Cara Duke 2022-05-25

Evaluate:
$\int \frac{x}{x^{3} - x^{2} + 1} d x$
None of the regular methods to integrate rational functions (substitution, partial fractions, etc.) seems to work.

Keely Johnson2022-05-24

Find a polynomial f(x) of degree 5 that has the following zeros

-5, 3, -2( multiplicity 2),9

Eliaszowyr1 2022-05-24

Q is a rational function with $x \cdot Q (x + 2018) = (x - 2018) Q (x), \forall x \notin 2018 and 0$ . If $Q (1) = 1$ . what is Q(2017)?
I tried substituting values in for Q(x) but there is no way to have both Q(1) and Q(2017) in the same equation, perhaps im missing a property of a rational function since i haven't used it yet.

Antoine Hill 2022-05-24

If I have two algebraic numbers $α$ and $β$ and a rational function $w$ with rational coefficients (a function that's the ratio of two rational polynomials) that relates the two $α = w (β)$ if I were to substitute $β$ with one of it's algebraic cojugates $β^{^{'}}$ in the rational function will I get a conjugate of $α$ or rather is $w (β^{^{'}})$ an algebraic conjugate of alpha? I feel like there is a very obvious counter example but I've been struggling to find one.

Erick Clay 2022-05-24

Solve for: $2 \log_{3} (x^{2} - 4) + 3 \sqrt{\log_{3} {(x + 2)}^{2}} - \log_{3} {(x - 2)}^{2} \leq 4$
My try:
$2 \log_{3} (x^{2} - 4) + 3 \sqrt{\log_{3} {(x + 2)}^{2}} - \log_{3} {(x - 2)}^{2} \leq 4 \Leftrightarrow \log_{3} {(x^{2} - 4)}^{2} + 3 \sqrt{\log_{3} {(x + 2)}^{2}} - \log_{3} {(x - 2)}^{2} \leq 4 \Leftrightarrow \log_{3} [{(x - 2)}^{2} \times {(x + 2)}^{2}] + 3 \sqrt{\log_{3} {(x + 2)}^{2}} - \log_{3} {(x - 2)}^{2} \leq 4 \Leftrightarrow \log_{3} {(x - 2)}^{2} + \log_{3} {(x + 2)}^{2} + 3 \sqrt{\log_{3} {(x + 2)}^{2}} - \log_{3} {(x - 2)}^{2} \leq 4 \Leftrightarrow \log_{3} {(x + 2)}^{2} + 3 \sqrt{\log_{3} {(x + 2)}^{2}} - 4 \leq 0 ()$
Put: $t = \sqrt{\log_{3} {(x + 2)}^{2}} \Rightarrow () \Leftrightarrow t^{2} + 3 t - 4 \leq 0$
But I don't know Conditions defined for this math? Could help me?

dglennuo 2022-05-24

Question that can not be solve analytically .
You can know that the solution of this non-linear simultaneous equations is y=2 and x=3; but the question is : How can mathematically ( algebraically ) find this.
$\begin{array}{lcl} x^{y} & = & 9 \\ y^{x} & = & 8 \end{array}$

Denisse Valdez 2022-05-24

If $K$ is an infinite field, and $K (x)$ is the field of rational function (in the indeterminate $x$ ), is it true that the extension $K (x) / K$ is a Galois extension?

seiyakou2005n1 2022-05-24

Prove that $a b c$ is a cube of some integer.
Given three integers $a$ , $b$ , and $c$ such that $\frac{a}{b} + \frac{b}{c} + \frac{c}{a}$ is an integer too, prove that the product $a b c$ is a cube.

aniawnua 2022-05-24

Let $f$ be a meromorphic (equivalently, rational) function on the Riemann sphere with $k$ prescribed poles. What is the number of critical points (or critical values) of such function $f$ ? I believe the answer is $2 k - 2$ , but why?

Qamoos zahra2022-05-23

TsSun Gaming2022-05-23

Find a least-squares solution 𝑥̂ of Ax=b and the least-squares error :𝑨 =
[ 1 3
1 −1
1 1 ]
𝒃 =
[ 5
1
0 ]

Keekee Pall2022-05-23

Erick Clay 2022-05-23

Use a graph to estimate the time at which the number was increasing most rapidly
For the period from 2000 to 2008, the percentage of households in a certain country with at least one DVD player has been modeled by the function
$f (t) = \frac{87.5}{1 + 17.1 e^{- 0.91 t}}$
where the time t is measured in years since midyear 2000, so $0 \leq t \leq 8$ . Use a graph to estimate the time at which the number of households with DVD players was increasing most rapidly. Then use derivatives to give a more accurate estimate. (Round your answer to two decimal places.) $t = ?$

Davin Fields 2022-05-23

Let $L = C (X, Y, Z)$ be the rational function field over the complex field and σ be automorphism of $L$ over $C$ ,
$σ (X) = Y, σ (Y) = Z, σ (Z) = X$
Moreover let $M$ be the intermediate field of the extension $L / C$ fixed by the group $< σ >$ . I think the degree of filed extension $L / M$ is 3 since the order of group $< σ >$ is 3. But is it true? I know this is true if the extension $L / C$ is finite degree Galois extension. But now the extension $L / C$ is infinite degree extension. So I don't know it is true.
Please give me some advice.

brendijadq 2022-05-23

Let
$f (z) = \frac{z - a}{z - b}, z \neq b \neq a$
be a complex valued rational function.
How can I show that, if $| a |, | b | < 1,$ , then there is a complex number $z_{0}$ satisfying $| z_{0} | = 1$ and $f (z_{0}) \in R$ ?
I have tried in many ways, but on success. Basically I tried to show that there is a unimodular complex number such that
$\frac{a - b}{z - b} = \frac{\bar{a} - \bar{b}}{\bar{z} - \bar{b}} .$
I could make a quadratic equation by using the fact that $\bar{z} = \frac{1}{z}, \forall z \in \partial D .$ Unfortunately I could not solve this question using that. So, I would like to see different (and somewhat general) approach.
Also, I would like to know that what happen if (both or atleast one) $a, b \notin D .$ Any comment or hint will be welcome. Thank you.

Kaeden Woodard 2022-05-23

Let $f : C - A \to C$ be analytic and proper, where A is a finite point set in $C$ .
I.e. $f^{- 1} (C)$ is compact for all compact sets $C \subset C$ .
Is it true that f is a rational function, i.e. $f (z) = \frac{p (z)}{q (z)}$ for complex polynomials p(z) and q(z), such that f has poles at A and $\infty$ ?
Does the converse hold as well? I.e. if f is a rational function with poles at A and ∞, then f is proper.
I am pretty sure this is true, but am new with the concept of poles and am not sure where to start. I would appreciate any hints/help if possible.

Waylon Ruiz 2022-05-23

Simple Log Question
Fairly new to logs, stuck here:
The equation $y = 4^{3 x}$ can be written in terms of $x$ :
$y = 4^{3 x}$
$\log (y) = \log (4^{3 x})$
$0 = 3 x \log (4) - \log (y)$
$0 = 3 x \log (\frac{4}{y})$
At this point I am totally stumped. I must be missing something obvious here.

Kellen Perkins 2022-05-23

Prove that $\log_{9} 15$ is irrational
Im having trouble with the following proof... Ill post what I have completed so far..
Ill attempt by contradiction assuming $\log_{9} 15$ is rational.
So,
$\log_{9} 15 = \frac{a}{b}$
$15 = 9^{\frac{a}{b}}$
$15^{b} = 9^{a}$ (This is where I'm getting stuck)
Any hints/tips/advice would be great. Thanks

The majority of Algebra 2 homework will be almost the same for college students these days since the only changes will relate to a practical application like business solutions, financial challenges, and certain problems where formulas and concepts are applicable. Looking for Algebra 2 answers, you will find some solutions below that are most likely to answer your Algebra 2 problems and answers. If you’re a high-school learner, there are Algebra 2 questions for you as well with provided solutions. The most important is to share your instructions and read through examples that address various Algebra 2 questions and answers.

Algebra II

Expert Answers to Algebra 2 Problems