A zero has a "multiplicity", which refers to the number of times that its associated factor appears in the polynomial. Since x=3 has an associated factor of (x−3) and appears 3 times in h(x), then the multiplicity of x=3 is 3.

Question

asked 2021-03-20

The graph of y = f(x) contains the point (0,2), \(\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}={\frac{{-{x}}}{{{y}{e}^{{{x}^{{2}}}}}}}\), and f(x) is greater than 0 for all x, then f(x)=

A) \(\displaystyle{3}+{e}^{{-{x}^{{2}}}}\)

B) \(\displaystyle\sqrt{{{3}}}+{e}^{{-{x}}}\)

C) \(\displaystyle{1}+{e}^{{-{x}}}\)

D) \(\displaystyle\sqrt{{{3}+{e}^{{-{x}^{{2}}}}}}\)

E) \(\displaystyle\sqrt{{{3}+{e}^{{{x}^{{2}}}}}}\)

A) \(\displaystyle{3}+{e}^{{-{x}^{{2}}}}\)

B) \(\displaystyle\sqrt{{{3}}}+{e}^{{-{x}}}\)

C) \(\displaystyle{1}+{e}^{{-{x}}}\)

D) \(\displaystyle\sqrt{{{3}+{e}^{{-{x}^{{2}}}}}}\)

E) \(\displaystyle\sqrt{{{3}+{e}^{{{x}^{{2}}}}}}\)

asked 2021-02-18

A given polynomial has a root of x = 3, an zero of x = -2, and an x-intercept of x = -1.

The equation of this polynomial in factored form would be f(x) =

The equation of this polynomial in standard form would be f(x) =

The equation of this polynomial in factored form would be f(x) =

The equation of this polynomial in standard form would be f(x) =

asked 2021-05-18

Find all zeros of the polynomial \(\displaystyle{P}{\left({x}\right)}={x}^{{{3}}}-{3}{x}^{{{2}}}-{10}{x}+{24}\) knowing that x = 2 is a zero of the polynomial.

asked 2021-05-07

Find f'(a)

\(\displaystyle{f{{\left({t}\right)}}}={\frac{{{3}{t}+{3}}}{{{t}+{2}}}}\)

\(\displaystyle{f{{\left({t}\right)}}}={\frac{{{3}{t}+{3}}}{{{t}+{2}}}}\)

asked 2021-02-27

Form a polynomial f(x) with real coefficients the given degree and zeros.
Degree 4, Zeros:, 4-4i, -5 multiplicity 2

asked 2021-02-02

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 2021-05-16

Consider the curves in the first quadrant that have equationsy=Aexp(7x), where A is a positive constant. Different valuesof A give different curves. The curves form a family,F. Let P=(6,6). Let C be the number of the family Fthat goes through P.

A. Let y=f(x) be the equation of C. Find f(x).

B. Find the slope at P of the tangent to C.

C. A curve D is a perpendicular to C at P. What is the slope of thetangent to D at the point P?

D. Give a formula g(y) for the slope at (x,y) of the member of Fthat goes through (x,y). The formula should not involve A orx.

E. A curve which at each of its points is perpendicular to themember of the family F that goes through that point is called anorthogonal trajectory of F. Each orthogonal trajectory to Fsatisfies the differential equation dy/dx = -1/g(y), where g(y) isthe answer to part D.

Find a function of h(y) such that x=h(y) is the equation of theorthogonal trajectory to F that passes through the point P.

A. Let y=f(x) be the equation of C. Find f(x).

B. Find the slope at P of the tangent to C.

C. A curve D is a perpendicular to C at P. What is the slope of thetangent to D at the point P?

D. Give a formula g(y) for the slope at (x,y) of the member of Fthat goes through (x,y). The formula should not involve A orx.

E. A curve which at each of its points is perpendicular to themember of the family F that goes through that point is called anorthogonal trajectory of F. Each orthogonal trajectory to Fsatisfies the differential equation dy/dx = -1/g(y), where g(y) isthe answer to part D.

Find a function of h(y) such that x=h(y) is the equation of theorthogonal trajectory to F that passes through the point P.

asked 2021-05-03

Consider the following system of linear equations:

4x+2y=25

4x-y=-5

If the value of y is 10 what is the value of X for this system:

1.1.25

2.11.25

3.1.45

4.5

4x+2y=25

4x-y=-5

If the value of y is 10 what is the value of X for this system:

1.1.25

2.11.25

3.1.45

4.5

asked 2020-11-01

Consider the following functions.

\(\displaystyle{f{{\left({x}\right)}}}={3}{x}^{{2}}+{x}+{2}\)

\(\displaystyle{g{{\left({x}\right)}}}={4}{x}^{{2}}+{2}{\left({3}{x}−{4}\right)}\)

h(x)=5(x2−1)

Find f(x)−g(x).

\(\displaystyle{f{{\left({x}\right)}}}={3}{x}^{{2}}+{x}+{2}\)

\(\displaystyle{g{{\left({x}\right)}}}={4}{x}^{{2}}+{2}{\left({3}{x}−{4}\right)}\)

h(x)=5(x2−1)

Find f(x)−g(x).