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
determine the remainder of the polynomial
when it is divided by
See
[link] .
is a zero of
if and only if
is a factor of
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
where
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
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] .
For the following exercises, use the Factor Theorem to find all real zeros for the given polynomial function and one factor.
Questions & Answers
for the "hiking" mix, there are 1,000 pieces in the mix, containing 390.8 g of fat, and 165 g of protein. if there is the same amount of almonds as cashews, how many of each item is in the trail mix?
an object is traveling around a circle with a radius of 13 meters .if in 20 seconds a central angle of 1/7 Radian is swept out what are the linear and angular speed of the object
like this: (2)/(2-x)
the aim is to see what will not be compatible with this rational expression. If x= 0 then the fraction is undefined since we cannot divide by zero. Therefore, the domain consist of all real numbers except 2.
functions can be understood without a lot of difficulty.
Observe the following:
f(2) 2x - x
2(2)-2= 2
now observe this:
(2,f(2)) ( 2, -2)
2(-x)+2 = -2
-4+2=-2
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
158.5
This number can be developed by using algebra and logarithms.
Begin by moving log(2) to the right hand side of the equation like this:
t/100 log(2)= log(3)
step 1: divide each side by log(2)
t/100=1.58496250072
step 2: multiply each side by 100 to isolate t.
t=158.49
Dan
what is the importance knowing the graph of circular functions?
yeah, it does. why do we attempt to gain all of them one side or the other?
Melissa
how to find x:
12x = 144
notice how 12 is being multiplied by x. Therefore division is needed to isolate x
and whatever we do to one side of the equation we must do to the other.
That develops this:
x= 144/12
divide 144 by 12 to get x.
addition:
12+x= 14
subtract 12 by each side. x =2
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.
