A shipping container in the shape of a rectangular solid must have a volume of 84 cubic meters. The client tells the manufacturer that, because of the contents, the length of the container must be one meter longer than the width, and the height must be one meter greater than twice the width. What should the dimensions of the container be?
To find
$\text{\hspace{0.17em}}f(k),\text{\hspace{0.17em}}$ determine the remainder of the polynomial
$\text{\hspace{0.17em}}f(x)\text{\hspace{0.17em}}$ when it is divided by
$\text{\hspace{0.17em}}x-k.\text{\hspace{0.17em}}$ See
[link] .
$\text{\hspace{0.17em}}k\text{\hspace{0.17em}}$ is a zero of
$\text{\hspace{0.17em}}f(x)\text{\hspace{0.17em}}$ if and only if
$\text{\hspace{0.17em}}(x-k)\text{\hspace{0.17em}}$ is a factor of
$\text{\hspace{0.17em}}f(x).$ See
[link] .
Each rational zero of a polynomial function with integer coefficients will be equal to a factor of the constant term divided by a factor of the leading coefficient. See
[link] and
[link] .
When the leading coefficient is 1, the possible rational zeros are the factors of the constant term.
Synthetic division can be used to find the zeros of a polynomial function. See
[link] .
According to the Fundamental Theorem, every polynomial function has at least one complex zero. See
[link] .
Every polynomial function with degree greater than 0 has at least one complex zero.
Allowing for multiplicities, a polynomial function will have the same number of factors as its degree. Each factor will be in the form
$\text{\hspace{0.17em}}(x-c),\text{\hspace{0.17em}}$ where
$\text{\hspace{0.17em}}c\text{\hspace{0.17em}}$ is a complex number. See
[link] .
The number of positive real zeros of a polynomial function is either the number of sign changes of the function or less than the number of sign changes by an even integer.
The number of negative real zeros of a polynomial function is either the number of sign changes of
$\text{\hspace{0.17em}}f(-x)\text{\hspace{0.17em}}$ or less than the number of sign changes by an even integer. See
[link] .
Polynomial equations model many real-world scenarios. Solving the equations is easiest done by synthetic division. See
[link] .
a colony of bacteria is growing exponentially doubling in size every 100 minutes. how much minutes will it take for the colony of bacteria to triple in size
100•3=300
300=50•2^x
6=2^x
x=log_2(6)
=2.5849625
so, 300=50•2^2.5849625
and, so,
the # of bacteria will double every (100•2.5849625) =
258.49625 minutes
Thomas
what is the importance knowing the graph of circular functions?
The domain of a function is the set of all input on which the function is defined. For example all real numbers are the Domain of any Polynomial function.
Spiro
Spiro; thanks for putting it out there like that, 😁
Melissa
foci (–7,–17) and (–7,17), the absolute value of the differenceof the distances of any point from the foci is 24.