Chesley
2020-11-27
Answered

the constant differences of an 8 degree polynomial is 241920.What is the leading coefficient?

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Arham Warner

Answered 2020-11-28
Author has **102** answers

The relationship between the constant difference, d, the leading coefficient, c, and the degree, n, of a polynomial is

If the polynomial has a degree of

The definition of a factorial is

Using this definition gives

Using a calculator to evaluate the product then gives

We then have

Dividing both sides by 40,320 then gives a leading coefficient of

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Find the point on the line

asked 2021-05-13

5)The graph of f is given. State the numbers at which f is not differentiable.

x=?(smaller value)

x=?(larger value)

6)The graph of f is given. State the numbers at which f is not differentiable.

x=?(smaller value)

x=?(larger value)

asked 2022-04-14

Discriminant Problems

We all know that the discriminant is the part${b}^{2}-4ac$ of the equation

$x=\frac{-b\pm \sqrt{{b}^{2}-4ac}}{2a}$

that we use to find the roots of a quadratic equation eg:

$a{x}^{2}+bx+c=0$ or the part in a trinomial expression like $a{x}^{2}+bx+c$ .

What I want to know is what kind of ideas we can conclude for a given inequality of a discriminant. We know that in quadratic formulas the number of real roots depends on the case whether the discriminant is <0, 0, or >0. But if given only the discriminant and the inequality of it, for examples like this:

${b}^{2}-4ac=0$

${b}^{2}-4ac>0$

${b}^{2}-4ac<0$

What can we conclude by the given information for each case? How can it help to reveal certain problems involving trinomial expressions?

We all know that the discriminant is the part

that we use to find the roots of a quadratic equation eg:

What I want to know is what kind of ideas we can conclude for a given inequality of a discriminant. We know that in quadratic formulas the number of real roots depends on the case whether the discriminant is <0, 0, or >0. But if given only the discriminant and the inequality of it, for examples like this:

What can we conclude by the given information for each case? How can it help to reveal certain problems involving trinomial expressions?

asked 2022-06-21

Let $X(t),A,B,C$ be matrices and $A,B,C$ are constant matrices. Does the following linear differential equation have a closed form solution?

$\frac{dX(t)}{dt}=A+BXC.$

$\frac{dX(t)}{dt}=A+BXC.$

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What is the value of $x-y$ , if $xy=144$ , $x+y=30$ , and $x>y$ ?

asked 2022-05-29

For an irrational number

$x=\sum _{n\in \mathbb{Z}}{a}_{n}{10}^{n}$

Does ${a}_{n}$ takes all the numbers between $0$ and $9$ ?

$x=\sum _{n\in \mathbb{Z}}{a}_{n}{10}^{n}$

Does ${a}_{n}$ takes all the numbers between $0$ and $9$ ?

asked 2022-05-28

Given a system of inequalities $Ax\le b$ , how can I derive the upper and lower bound on $x$?

I have the following system of inequalities $Ax\le b$, where ${x}_{1}$ and ${x}_{2}$ are unknown, and the $a$'s and $\u0438$'s are constants.

$\left[\begin{array}{cc}{a}_{11}& {a}_{12}\\ {a}_{21}& {a}_{22}\end{array}\right]\left[\begin{array}{c}{x}_{1}\\ {x}_{2}\end{array}\right]\le \left[\begin{array}{c}{b}_{1}\\ {b}_{2}\end{array}\right]$

I have the following system of inequalities $Ax\le b$, where ${x}_{1}$ and ${x}_{2}$ are unknown, and the $a$'s and $\u0438$'s are constants.

$\left[\begin{array}{cc}{a}_{11}& {a}_{12}\\ {a}_{21}& {a}_{22}\end{array}\right]\left[\begin{array}{c}{x}_{1}\\ {x}_{2}\end{array}\right]\le \left[\begin{array}{c}{b}_{1}\\ {b}_{2}\end{array}\right]$