 Recent questions in Precalculus
Polynomials
ANSWERED ### Given $$\displaystyle{P}{\left({x}\right)}={3}{x}^{{2}}+{4}{y}^{{2}}$$ and $$\displaystyle{R}{\left({x}\right)}=-{7}{x}^{{2}}+{4}{x}{y}-{3}{y}^{{2}}$$, find $$P(x)-R(x)$$.

Polynomials
ANSWERED ### Find the roots of the quadratic polynomials: a) $$\displaystyle{f{{\left({x}\right)}}}={4}{x}^{{2}}-{3}{x}-{1}$$ b) $$\displaystyle{f{{\left({x}\right)}}}={x}^{{2}}-{2}{x}-{1}$$

Polynomials
ANSWERED ### Find the zeros ofcthe polynomials $$\displaystyle{f{{\left({x}\right)}}}={x}^{{3}}-{12}{x}^{{2}}+{39}{x}-{28}$$, if it's is given that the zeros in AP

Polynomials
ANSWERED ### Divide the polynomials $$\displaystyle-{13}{x}^{{2}}+{4}{x}^{{3}}+{2}{x}-{7}$$ and explain each step. State the answer in full sentence and ecxpress it as one expression. Check your solution.

Transformations of functions
ANSWERED ### Find the limit and discuss the continuity of the function. $$\displaystyle\lim_{{{x},{y}}}\rightarrow{\left({\frac{{\pi}}{{{4}}}},{2}\right)}{y}{\cos{{x}}}{y}$$

Transformations of functions
ANSWERED ### Describe the transformations that must be applied to y=x^2 to create the graph of each of the following functions. a) $$\displaystyle{y}=\frac{{1}}{{4}}{\left({x}-{3}\right)}^{{2}}+{9}$$ b) $$\displaystyle{y}={\left({\left(\frac{{1}}{{2}}\right)}{x}\right)}^{{2}}-{7}$$

Polynomials
ANSWERED ### $$(2x − 1)$$ is a factor of the polynomial $$\displaystyle{6}{x}^{{6}}+{x}^{{5}}-{92}{x}^{{4}}+{45}{x}^{{3}}+{184}{x}^{{2}}+{4}{x}-{48}$$. Determine whether the statement is true or false. Justify your answer.

Polynomials
ANSWERED ### Subtract the polynomials using the horizontal format. $$\displaystyle{2}{x}^{{3}}+{x}^{{2}}-{7}{x}-{2}$$ from $$\displaystyle{5}{x}^{{3}}+{2}{x}^{{2}}+{6}{x}-{13}$$

Polynomials
ANSWERED ### Add the polynomials. $$\displaystyle{\left({7}{x}^{{2}}-{6}{x}+{6}\right)}+{\left({3}{x}^{{3}}-{9}{x}\right)}$$

Polynomials
ANSWERED ### List all of the polynomials of degrees 2 and 3 in $$\displaystyle{\mathbb{{{Z}}}}_{{2}}{\left[{x}\right]}$$. Find all of the irreducible polynomials of degrees 2 and 3 in $$\displaystyle{\mathbb{{{Z}}}}_{{2}}{\left[{x}\right]}$$.

Polynomials
ANSWERED ### Do the polynomials $$\displaystyle{x}^{{3}}-{2}{x}^{{2}}+{1},{4}{x}^{{2}}-{x}+{3}$$, and $$3x-2$$ generate $$\displaystyle{P}_{{3}}{\left({R}\right)}$$? Justify your answer.

Polynomials
ANSWERED ### Find the roots of the quadratic polynomials: $$\displaystyle{f{{\left({x}\right)}}}={x}^{{2}}-{2}{x}-{1}$$

Trigonometry
ANSWERED ### Please, help to find a model for simple harmonic motion satisfying the specified conditions. Displacement (t = 0) 0, Amplitude 3 meters, Period 6 seconds.

Transformations of functions
ANSWERED ### Sketch the graph of the function f(x)=[x]]+[∣−x] $$\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{l}\right\rbrace}{\left\lbrace\ \text{ (a) Evaluate }\ {f{{\left({1}\right)}}},{f{{\left({0}\right)}}},{f}{\left({\frac{{{1}}}{{{2}}}}\right)},\ \text{ and }\ {f{{\left(-{2.7}\right)}}}\right\rbrace}\backslash{\left\lbrace\ \text{ (b) Evaluate the limits }\ \lim_{{{x}\rightarrow{1}^{{-}}}}{f{{\left({x}\right)}}},\lim_{{{x}\rightarrow{1}^{{+}}}}{f{{\left({x}\right)}}},\ \text{ and }\ \lim_{{{x}\rightarrow{1}&#{x}{2}{F}.{2}}}{f{{\left({x}\right)}}}\right\rbrace}\backslash{\left\lbrace\ \text{ (c) Discuss the continuity of the function. }\ \right\rbrace}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}$$

Exponential models
ANSWERED ### The exponential growth models describe the population of the indicated country, A, in millions, t years after 2006. Canada A=33.1e0.009t Uganda A=28.2e0.034t use this information to determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. By 2009, the models indicate that Canada's population will exceed Uganda's by approximately 2.8 million.

Polynomials
ANSWERED ### Determine whether the following polynomials u,v, w in P(t) are linearly dependent or independent: $$\displaystyle{u}={t}^{{3}}-{4}{t}^{{2}}+{3}{t}+{3},$$ $${v}={t}^{{3}}+{2}{t}^{{2}}+{4}{t}-{1},$$ $${w}={2}{t}^{{3}}-{t}^{{2}}-{3}{t}+{5}$$

Polynomials
ANSWERED ### Find the difference of the polynomials. $$\displaystyle{\left({3}{x}^{{2}}+{2}{x}-{1}\right)}-{\left(-{5}{x}^{{2}}+{8}{x}+{4}\right)}$$

Probability and combinatorics
ANSWERED ### A license plate is designed so that the first two characters are letters and the last four characters are digits. How many different license plates can be formed assuming that letters and numbers can be used more than once

Vectors
ANSWERED ### Find the vector, not with determinants, but by using properties of cross products. $$\displaystyle{\left({i}\times{j}\right)}\times{k}$$

Composite functions
ANSWERED 