Question

Prove

Answer 1

\(\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}}\)

Answer 2

I'm finding it hard to visualize... could you show the area in graph ?

Answer 3

https://www.desmos.com/calculator/ylkcvfm5ss

Answer 4

Ahh that should be easy

Answer 5

First of all, we acknowledge that the the absolute value gives the distance between two points on number line:

Answer 6

You can prove it using calculus. The integral of that is constant.

Answer 7

In light that of above thing, \(|x-k|\) represents the distance between \(x\) and \(k\).

Answer 8

Set the given function equal to \(0\) and solve \(x\) intercepts :
\[-|x-k|+5=0 \implies |x-k|=5\]

Answer 9

x=5+k.-5+k

Answer 10

Yes, subtract them to get the base of triangle

Answer 11

base->10