Given the function below, if h(x) =-1 find x

the length of a flag is 0.3 foot less than twice its width. if the perimeter is 14.4 feet longer than the width, find the dimens

forsale [732]

$x-\ length\\
y-\ width\\\\
x+0.3=2y\ \ \ \ \ | subtract\ 0.3\\x=2y-0.3\\
perimeter=2x+2y\\ 2x+2y-14.4=y\\\\
2*(2y-0.3)+2y-14.4=y\\
4y-0.6+2y-14.4=y\\
6y-15=y\ \ \ | add\ 15\\
6y=15+y\ \ | subtract\ y\\
5y=15\ \ \ | divide\ by\ 5\\
y=3\\
x=2y-0.3=2*3-0.3=6-0.3=5.7\\\\
Dimensions:\ length=5.7\ feet\, width=3\ feet.$

4 0

4 years ago

Find an equation with vertical asymptotes 1 and 4 and horizontal asymptote 1 please help

Brilliant_brown [7]

Answer:

y = 1 + 1/((x -1)(x -4))

Step-by-step explanation:

To get vertical asymptotes at 1 and 4, you need factors (x -1) and (x -4) in the denominator. As x approaches 1 or 4, one of these will approach zero, and the function value will approach infinity.

To get a horizontal asymptote of 1, the function must approach the value 1 when the value of x gets large (positive or negative). This can generally be accomplished by simply adding 1 to a fraction that approaches zero when x is large.

Here, we make the fraction be the one that gives the vertical asymptotes, and we simply add 1 to it.

... y = 1 + 1/((x -1)(x -4))

If you like, this can be "simplified" to ...

... y = (x² -5x +5)/(x² -5x +4)

_____

In this rational expression form, please note that the numerator and denominator have the same degree. That will be the case when there is a horizontal asymptote. (When a slant asymptote, the numerator degree is 1 higher than the denominator.) The ratio of the coefficients of the highest degree terms is the horizontal asymptote value (or the slope of a slant asymptote).