![f_{X,Y}(x,y)=\begin{cases}cx(1+y)&\text{for }0\le x\le1,0\le y\le2\\0&\text{otherwise}\end{cases}](https://tex.z-dn.net/?f=f_%7BX%2CY%7D%28x%2Cy%29%3D%5Cbegin%7Bcases%7Dcx%281%2By%29%26%5Ctext%7Bfor%20%7D0%5Cle%20x%5Cle1%2C0%5Cle%20y%5Cle2%5C%5C0%26%5Ctext%7Botherwise%7D%5Cend%7Bcases%7D)
For
![f](https://tex.z-dn.net/?f=f)
to be a proper density function, we need to have the integral over its support
![\mathcal S](https://tex.z-dn.net/?f=%5Cmathcal%20S)
to equal 1.
![\displaystyle\iint_{\mathcal S}f_{X,Y}(x,y)\,\mathrm dx\,\mathrm dy=\int_{y=0}^{y=2}\int_{x=0}^{x=1}cx(1+y)\,\mathrm dx\,\mathrm dy=2c=1](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Ciint_%7B%5Cmathcal%20S%7Df_%7BX%2CY%7D%28x%2Cy%29%5C%2C%5Cmathrm%20dx%5C%2C%5Cmathrm%20dy%3D%5Cint_%7By%3D0%7D%5E%7By%3D2%7D%5Cint_%7Bx%3D0%7D%5E%7Bx%3D1%7Dcx%281%2By%29%5C%2C%5Cmathrm%20dx%5C%2C%5Cmathrm%20dy%3D2c%3D1)
![\implies c=\dfrac12](https://tex.z-dn.net/?f=%5Cimplies%20c%3D%5Cdfrac12)
Now,
Answer:
time taken=1800 seconds
Step-by-step explanation:
velocity=v=10m/s
distance=S=18km=18×10³m=18000m
t=?
as we know that
velocity=![\frac{distance covered}{time taken}](https://tex.z-dn.net/?f=%5Cfrac%7Bdistance%20covered%7D%7Btime%20taken%7D)
velocity×time taken=distance covered
now here we have to find time
time taken=![\frac{distance covered}{velocity}](https://tex.z-dn.net/?f=%5Cfrac%7Bdistance%20covered%7D%7Bvelocity%7D)
time taken=![\frac{18000m}{10m/s}](https://tex.z-dn.net/?f=%5Cfrac%7B18000m%7D%7B10m%2Fs%7D)
time taken=1800seconds
Answer:
the last one I think, sorry if it is roung.
Your answer should be 57 .7 I think its right
The domain is the set of allowed x inputs, or x coordinates of a function. In this case, any point on the curve has an x coordinate that is 4 or smaller.
Therefore, the domain is the set of numbers x such that
To write this in interval notation, we would write
This interval starts at negative infinity and stops at 4. We exclude infinity with the curved parenthesis and include 4 with the square bracket.
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The range is the set of possible y outputs. Every point on this curve has a y coordinate that is either 0 or it is larger than 0.
The range is the set of y values such that ![y \ge 0](https://tex.z-dn.net/?f=y%20%5Cge%200)
In interval notation, it would be written as
This time we start at 0 (including this endpoint) and "stop" at infinity
note: we always use curved parenthesis at positive or negative infinity because we cannot reach either infinity