Answer: 54 cubic units
Step-by-step explanation:
I did it on khan academy and I got it right
Cut the shape into shapes you know the area of and do the formula this helps
The train is travelling at 80 miles per hour, this can be represented by 80mi/h
As the symbol suggests, you find the value of speed by dividing the amount of miles by the amount of hours.
Let S be speed, D be distance and T be time
we get S=D/T so we have also T=D/S
as such, the time to go 288 miles is simply:
1.
has a horizontal asymptote at ![y=-4](https://tex.z-dn.net/?f=y%3D-4)
This means that
![\displaystyle\lim_{x\to\pm\infty}f(x)-(-4)=0](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Clim_%7Bx%5Cto%5Cpm%5Cinfty%7Df%28x%29-%28-4%29%3D0)
(for at least one of these limits)
2.
has a vertical asymptote at ![x=3](https://tex.z-dn.net/?f=x%3D3)
This means that
has a non-removable discontinuity at
. Since
is some rational function, there must be a factor of
in its denominator.
3.
has an
-intercept at (1, 0)
This means
.
(a) With
![f(x)=\dfrac{ax+b}{x+c}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdfrac%7Bax%2Bb%7D%7Bx%2Bc%7D)
the second point above suggests
. The first point tells us that
![\displaystyle\lim_{x\to\pm\infty}\frac{ax+b}{x-3}+4=0=\lim_{x\to\pm\infty}\frac{ax+b+4x-3}{x-3}=0](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Clim_%7Bx%5Cto%5Cpm%5Cinfty%7D%5Cfrac%7Bax%2Bb%7D%7Bx-3%7D%2B4%3D0%3D%5Clim_%7Bx%5Cto%5Cpm%5Cinfty%7D%5Cfrac%7Bax%2Bb%2B4x-3%7D%7Bx-3%7D%3D0)
In order for the limit to be 0, the denominator's degree should exceed the numerator's degree; the only way for this to happen is if
so that the linear terms vanish.
The third point tells us that
![f(1)=\dfrac{a+b}{1-3}=0\implies a=-b\implies b=4](https://tex.z-dn.net/?f=f%281%29%3D%5Cdfrac%7Ba%2Bb%7D%7B1-3%7D%3D0%5Cimplies%20a%3D-b%5Cimplies%20b%3D4)
So
![f(x)=\dfrac{-4x+4}{x-3}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdfrac%7B-4x%2B4%7D%7Bx-3%7D)
(b) Since
![f(x)=\dfrac{rx+s}{2x+t}=\dfrac12\dfrac{rx+s}{x+\frac t2}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdfrac%7Brx%2Bs%7D%7B2x%2Bt%7D%3D%5Cdfrac12%5Cdfrac%7Brx%2Bs%7D%7Bx%2B%5Cfrac%20t2%7D)
we find that
, and
and
.
Answer: Option 'B' is correct.
Step-by-step explanation:
Since we have given that
In case of Alpha:
Number of oranges = 18
Number of apples = 9
In case of Beta :
Number of oranges = 16
Number of apples = 4
We need to find the opportunity cost of producing 1 orange for Alpha and Beta.
Opportunity cost for Alpha is given by
![\dfrac{\text{number of sacrificing units}}{\text{Number of gaining units}}\\\\=\dfrac{18}{9}=2](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Ctext%7Bnumber%20of%20sacrificing%20units%7D%7D%7B%5Ctext%7BNumber%20of%20gaining%20units%7D%7D%5C%5C%5C%5C%3D%5Cdfrac%7B18%7D%7B9%7D%3D2)
Opportunity cost for Beta is given by
![\dfrac{16}{4}=4](https://tex.z-dn.net/?f=%5Cdfrac%7B16%7D%7B4%7D%3D4)
Hence, Opportunity cost for producing 1 orange for Alpha and Beta are 9 apples and 4 apples respectively.
Hence, Option 'B' is correct.