Mathematics, 31.08.2019 14:50 devontemiles1174
Aregion r is enclosed by the coordinate axes and the graph of y=k(x-5)^2, k> 0. when this region is revolved around the x-axis, the solid formed has a volume of 2500pi cubic units. what is the value of k?k=2
Answers: 2
touches the x-axis at 
and has a y-intercept when 
at
![\bf \displaystyle \int\limits_{0}^{5}\ \pi [k(x-5)^2]^2dx\impliedby \textit{using the disk method} \\\\\\ \pi \displaystyle \int\limits_{0}^{5}\ k^2(x-5)^4dx\implies k^2\pi \int\limits_{0}^5 \ (x-5)^4dx \\\\\\ \displaystyle k^2\pi \int\limits_{0}^{5}\ (x^4-20x^3+150x^2-500x+625)dx](/tpl/images/0215/1984/8941c.png)
![\bf \\\\\\ k^2\pi \left[ \cfrac{x^5}{5}-5x^4+50x^3-250x^2+625x \right]_0^5 \\\\\\ k^2\pi [625-3125+6250-6250+3125]-k^2\pi [0] \\\\\\ \boxed{625k^2\pi =2500\pi }\implies k^2=\cfrac{2500\pi }{625\pi } \\\\\\ k^2=4\implies k=\pm \sqrt{4}\implies k=\pm 2](/tpl/images/0215/1984/41797.png)
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Aregion r is enclosed by the coordinate axes and the graph of y=k(x-5)^2, k> 0. when this region...
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