mathmath333
  • mathmath333
Prove
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
mathmath333
  • mathmath333
\(\large \color{black}{\begin{align} & \normalsize \text{Prove the area of the region enclosed by the graph }\hspace{.33em}\\~\\ & y=-|x\pm k|+5,y=0\hspace{.33em}\\~\\ & \normalsize \text{ is constant for} \ \ k,\ k\in \mathbb{R}\ \hspace{.33em}\\~\\ \end{align}}\)
ganeshie8
  • ganeshie8
I'm finding it hard to visualize... could you show the area in graph ?
mathmath333
  • mathmath333
https://www.desmos.com/calculator/ylkcvfm5ss

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ganeshie8
  • ganeshie8
Ahh that should be easy
ganeshie8
  • ganeshie8
First of all, we acknowledge that the the absolute value gives the distance between two points on number line: |dw:1434119749216:dw|
perl
  • perl
You can prove it using calculus. The integral of that is constant.
ganeshie8
  • ganeshie8
In light that of above thing, \(|x-k|\) represents the distance between \(x\) and \(k\).
ganeshie8
  • ganeshie8
Set the given function equal to \(0\) and solve \(x\) intercepts : \[-|x-k|+5=0 \implies |x-k|=5\]
mathmath333
  • mathmath333
x=5+k.-5+k
ganeshie8
  • ganeshie8
Yes, subtract them to get the base of triangle
mathmath333
  • mathmath333
base->10
ganeshie8
  • ganeshie8
|dw:1434120100063:dw|
mathmath333
  • mathmath333
ok thnx

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