Complex zeroes are always in conjugate pairs: so 4-6i is paired with 4+6i, and -2+11i is paired with -2-11i.

Question

asked 2021-04-21

Polynomial calculations Find a polynomial f that satisfies the following properties. Determine the degree of f. then substitute a polynomial of that degree and solve for its coefficients.

\(\displaystyle{f{{\left({f{{\left({x}\right)}}}\right)}}}={9}{x}-{8}\)

\(\displaystyle{f{{\left({f{{\left({x}\right)}}}\right)}}}={x}^{{{4}}}-{12}{x}^{{{2}}}+{30}\)

\(\displaystyle{f{{\left({f{{\left({x}\right)}}}\right)}}}={9}{x}-{8}\)

\(\displaystyle{f{{\left({f{{\left({x}\right)}}}\right)}}}={x}^{{{4}}}-{12}{x}^{{{2}}}+{30}\)

asked 2021-03-23

Identify the degree of each term of the polynomial and the degree of the polynomial.

\(\displaystyle-{5}{x}^{{{3}}}+{5}{x}^{{{2}}}+{\frac{{{6}}}{{{7}{x}}}}+{4}\)

\(\displaystyle-{5}{x}^{{{3}}}+{5}{x}^{{{2}}}+{\frac{{{6}}}{{{7}{x}}}}+{4}\)

asked 2021-03-15

Three long wires (wire 1, wire 2,and wire 3) are coplanar and hang vertically. The distance betweenwire 1 and wire 2 is 16.0 cm. On theleft, wire 1 carries an upward current of 1.50 A. To the right,wire 2 carries a downward current of 3.40 A. Wire 3 is located such that when itcarries a certain current, no net force acts upon any of the wires.

(a) Find the position of wire 3, relative to wire 1.

(b) Find the magnitude and direction of the current in wire 3.

(a) Find the position of wire 3, relative to wire 1.

(b) Find the magnitude and direction of the current in wire 3.

asked 2021-05-17

Find the fifth derivative of the function \(\displaystyle{y}={\left({x}^{{{3}}}+{2}{x}^{{{2}}}+{3}{x}\right)}{e}^{{{x}}}\).

asked 2021-05-13

A major information system has 1140 modules.There are 96 modules that perform control and coordinationfunctions and 490 modules who function depends on prior processing.The system processes approximately 220 data objects that each havean average of three attributes. There are 140 unique data baseitems and 90 different database segments. Finally, 600 modules havesingle entry and exit points. Compute the DSQI for this system

asked 2021-02-14

Mg reacts with H+ (aq) according to

\(\displaystyle{M}{g{{\left({s}\right)}}}+{2}{H}+{\left({a}{q}\right)}\to{M}{g}_{{2}}+{\left({a}{q}\right)}+{H}_{{2}}{\left({g}\right)}\)

Suppose that 0.524 g of Mg is reacted with 60.o ml of 1.0 M H+(aq). Assume that the density of the H+ (aq) solution os 1.00 g/ml,and that its specific heat capacity equals that of water. Theinitial and final temperatures are 22.0 degree celsius and 65.8degree celsius.

a) Is the reaction endothermic or exothermic?

b) Calculate \(\displaystyle\triangle{H}\) of of th reaction. Use correct sigs andgive units.

c) Calculate the \(\displaystyle\triangle{H}\) of the reaction per mole of magnesium.

\(\displaystyle{M}{g{{\left({s}\right)}}}+{2}{H}+{\left({a}{q}\right)}\to{M}{g}_{{2}}+{\left({a}{q}\right)}+{H}_{{2}}{\left({g}\right)}\)

Suppose that 0.524 g of Mg is reacted with 60.o ml of 1.0 M H+(aq). Assume that the density of the H+ (aq) solution os 1.00 g/ml,and that its specific heat capacity equals that of water. Theinitial and final temperatures are 22.0 degree celsius and 65.8degree celsius.

a) Is the reaction endothermic or exothermic?

b) Calculate \(\displaystyle\triangle{H}\) of of th reaction. Use correct sigs andgive units.

c) Calculate the \(\displaystyle\triangle{H}\) of the reaction per mole of magnesium.

asked 2021-02-10

An electron enters a uniform magnetic field B= 0.23T at a 45 degree angle to B. Determine the pitch p (distance between loops) of the electron's helical path assuming its speed to be \(\displaystyle{3.0}\cdot{10}^{{6}}\) m/s.

asked 2021-05-10

Hypothetical potential energy curve for aparticle of mass m

If the particle is released from rest at position r0, its speed atposition 2r0, is most nearly

a) \(\displaystyle{\left({\frac{{{8}{U}{o}}}{{{m}}}}\right)}^{{1}}{\left\lbrace/{2}\right\rbrace}\)

b) \(\displaystyle{\left({\frac{{{6}{U}{o}}}{{{m}}}}\right)}^{{\frac{{1}}{{2}}}}\)

c) \(\displaystyle{\left({\frac{{{4}{U}{o}}}{{{m}}}}\right)}^{{\frac{{1}}{{2}}}}\)

d) \(\displaystyle{\left({\frac{{{2}{U}{o}}}{{{m}}}}\right)}^{{\frac{{1}}{{2}}}}\)

e) \(\displaystyle{\left({\frac{{{U}{o}}}{{{m}}}}\right)}^{{\frac{{1}}{{2}}}}\)

if the potential energy function is given by

\(\displaystyle{U}{\left({r}\right)}={b}{r}^{{P}}-\frac{{3}}{{2}}\rbrace+{c}\)

where b and c are constants

which of the following is an edxpression of the force on theparticle?

1) \(\displaystyle{\frac{{{3}{b}}}{{{2}}}}{\left({r}^{{-\frac{{5}}{{2}}}}\right)}\)

2) \(\displaystyle{\frac{{{3}{b}}}{{{2}}}}{\left\lbrace{3}{b}\right\rbrace}{\left\lbrace{2}\right\rbrace}{\left({r}^{{-\frac{{1}}{{2}}}}\right)}\)

3) \(\displaystyle{\frac{{{3}{b}}}{{{2}}}}{\left\lbrace{3}\right\rbrace}{\left\lbrace{2}\right\rbrace}{\left({r}^{{-\frac{{1}}{{2}}}}\right)}\)

4) \(\displaystyle{2}{b}{\left({r}^{{-\frac{{1}}{{2}}}}\right)}+{c}{r}\)

5) \(\displaystyle{\frac{{{3}{b}}}{{{2}}}}{\left\lbrace{2}{b}\right\rbrace}{\left\lbrace{5}\right\rbrace}{\left({r}^{{-\frac{{5}}{{2}}}}\right)}+{c}{r}\)

If the particle is released from rest at position r0, its speed atposition 2r0, is most nearly

a) \(\displaystyle{\left({\frac{{{8}{U}{o}}}{{{m}}}}\right)}^{{1}}{\left\lbrace/{2}\right\rbrace}\)

b) \(\displaystyle{\left({\frac{{{6}{U}{o}}}{{{m}}}}\right)}^{{\frac{{1}}{{2}}}}\)

c) \(\displaystyle{\left({\frac{{{4}{U}{o}}}{{{m}}}}\right)}^{{\frac{{1}}{{2}}}}\)

d) \(\displaystyle{\left({\frac{{{2}{U}{o}}}{{{m}}}}\right)}^{{\frac{{1}}{{2}}}}\)

e) \(\displaystyle{\left({\frac{{{U}{o}}}{{{m}}}}\right)}^{{\frac{{1}}{{2}}}}\)

if the potential energy function is given by

\(\displaystyle{U}{\left({r}\right)}={b}{r}^{{P}}-\frac{{3}}{{2}}\rbrace+{c}\)

where b and c are constants

which of the following is an edxpression of the force on theparticle?

1) \(\displaystyle{\frac{{{3}{b}}}{{{2}}}}{\left({r}^{{-\frac{{5}}{{2}}}}\right)}\)

2) \(\displaystyle{\frac{{{3}{b}}}{{{2}}}}{\left\lbrace{3}{b}\right\rbrace}{\left\lbrace{2}\right\rbrace}{\left({r}^{{-\frac{{1}}{{2}}}}\right)}\)

3) \(\displaystyle{\frac{{{3}{b}}}{{{2}}}}{\left\lbrace{3}\right\rbrace}{\left\lbrace{2}\right\rbrace}{\left({r}^{{-\frac{{1}}{{2}}}}\right)}\)

4) \(\displaystyle{2}{b}{\left({r}^{{-\frac{{1}}{{2}}}}\right)}+{c}{r}\)

5) \(\displaystyle{\frac{{{3}{b}}}{{{2}}}}{\left\lbrace{2}{b}\right\rbrace}{\left\lbrace{5}\right\rbrace}{\left({r}^{{-\frac{{5}}{{2}}}}\right)}+{c}{r}\)

asked 2020-11-03

Find a quadratic polynomial whose sum and product respectively of the zeroes are as given .Also find the zeroes of these polynomials by factorization

\(\displaystyle{\left(\frac{{-{3}}}{{{2}\sqrt{{5}}}}\right)},{\left(-\frac{{1}}{{2}}\right)}\)

\(\displaystyle{\left(\frac{{-{3}}}{{{2}\sqrt{{5}}}}\right)},{\left(-\frac{{1}}{{2}}\right)}\)

asked 2021-02-21

Form a polynomial function whose real zeros and degree are given. Answers will vary depending on the choice of a leading coefficient. Zeros: -1, multiplicity 1, 3, multiplicity 2, degree 3