Clifland

2021-08-17

Whether the given function is an appropriate model for extended years and explain the reason.

Given: The polynomial function is$f\left(x\right)=-0.87{x}^{3}+0.35{x}^{2}+81.62x+7684.94$

Here, x represents the number of years after 1987 and f(x) represents the number of thefts in that respective year.

Given: The polynomial function is

Here, x represents the number of years after 1987 and f(x) represents the number of thefts in that respective year.

Latisha Oneil

Skilled2021-08-18Added 100 answers

Procedure used:

Leading Coefficient Test:

As x increases or decreases without bound, the graph of the polynomial function.

$f\left(x\right)={a}_{n}{x}^{n}+{a}_{n-1}{x}^{n-1}+\cdots +{a}_{2}{x}^{2}+{a}_{1}x+{a}_{0}({a}_{n}\ne q0)$ eventually rises or falls. In particular,

(1) For n odd:

If the leading coefficient is positive, the graph falls to the left and rises to the right.

If the leading coefficient is negative, the graph rises to the left and falls to the right.

(2) For n even:

If the leading coefficient is positive, the graph rises to the left and rises to the right.

If the leading coefficient is negative, the graph falls to the left and falls to the right.

Description:

The degree of the given function is observed to be 3, which is odd.

The odd polynomial function have opposite behavior at each end.

The number$a}_{n$ , which is the coefficient of the variable with highest power is called the leading coefficient.

The coefficient$x}^{3$ is noticed to be -0.87. That is, the leading coefficient is negative.

Thus, by above procedure, the graph of$f\left(x\right)=-0.87{x}^{3}+0.35{x}^{2}+81.62x+7684.94$ rises to the left and falls to the right.

This implies that the number of thefts in x years after 1987 will be negative as the number the years increases.

This is impossible. So, it is not capable for modeling the number of thefts in United States for the extended years.

Leading Coefficient Test:

As x increases or decreases without bound, the graph of the polynomial function.

(1) For n odd:

If the leading coefficient is positive, the graph falls to the left and rises to the right.

If the leading coefficient is negative, the graph rises to the left and falls to the right.

(2) For n even:

If the leading coefficient is positive, the graph rises to the left and rises to the right.

If the leading coefficient is negative, the graph falls to the left and falls to the right.

Description:

The degree of the given function is observed to be 3, which is odd.

The odd polynomial function have opposite behavior at each end.

The number

The coefficient

Thus, by above procedure, the graph of

This implies that the number of thefts in x years after 1987 will be negative as the number the years increases.

This is impossible. So, it is not capable for modeling the number of thefts in United States for the extended years.

$\frac{20b}{{\left(4{b}^{3}\right)}^{3}}$

Which operation could we perform in order to find the number of milliseconds in a year??

$60\cdot 60\cdot 24\cdot 7\cdot 365$ $1000\cdot 60\cdot 60\cdot 24\cdot 365$ $24\cdot 60\cdot 100\cdot 7\cdot 52$ $1000\cdot 60\cdot 24\cdot 7\cdot 52?$ Tell about the meaning of Sxx and Sxy in simple linear regression,, especially the meaning of those formulas

Is the number 7356 divisible by 12? Also find the remainder.

A) No

B) 0

C) Yes

D) 6What is a positive integer?

Determine the value of k if the remainder is 3 given $({x}^{3}+k{x}^{2}+x+5)\xf7(x+2)$

Is $41$ a prime number?

What is the square root of $98$?

Is the sum of two prime numbers is always even?

149600000000 is equal to

A)$1.496\times {10}^{11}$

B)$1.496\times {10}^{10}$

C)$1.496\times {10}^{12}$

D)$1.496\times {10}^{8}$Find the value of$\mathrm{log}1$ to the base $3$ ?

What is the square root of 3 divided by 2 .

write $\sqrt[5]{{\left(7x\right)}^{4}}$ as an equivalent expression using a fractional exponent.

simplify $\sqrt{125n}$

What is the square root of $\frac{144}{169}$