Helloo
Use the quadratic formula to find the solutions.<span><span><span>−b±<span>√<span><span>b2</span>−4<span>(ac)</span></span></span></span><span>2a</span></span><span><span>-b±<span><span>b2</span>-4<span>(ac)</span></span></span><span>2a</span></span></span>Substitute the values <span><span>a=−1</span><span>a=-1</span></span>, <span><span>b=0</span><span>b=0</span></span>, and <span><span>c=50</span><span>c=50</span></span> into the quadratic formula and solve for <span>xx</span>.<span><span><span>0±<span>√<span><span>02</span>−4⋅<span>(−1⋅50)</span></span></span></span><span>2⋅−1</span></span><span><span>0±<span><span>02</span>-4⋅<span>(-1⋅50)</span></span></span><span>2⋅-1</span></span></span>Simplify.<span><span>x=±5<span>√2</span></span><span>x=±52</span></span>The result can be shown in both exact and approximate form.<span><span>x=±5<span>√2</span></span><span>x=±52</span></span><span>x≈7.07106781,−<span>7.07106781
Have a nice day</span></span>
so, we know both the rectangular prism and the cylinder got filled up to a certain height each, the same height say "h" cm.
we know the combined volume of both is 80 cm³, so let's get the volume of each, sum them up to get 80 then.
![\bf \stackrel{\stackrel{\textit{volume of a}}{\textit{rectangular prism}}}{V=Lwh}~~ \begin{cases} L=length\\ w=width\\ h=height\\[-0.5em] \hrulefill\\ L=4\\ w=2\\ \end{cases}~\hspace{2em}\stackrel{\textit{volume of a cylinder}}{V=\pi r^2 h}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=1 \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7B%5Cstackrel%7B%5Ctextit%7Bvolume%20of%20a%7D%7D%7B%5Ctextit%7Brectangular%20prism%7D%7D%7D%7BV%3DLwh%7D~~%20%5Cbegin%7Bcases%7D%20L%3Dlength%5C%5C%20w%3Dwidth%5C%5C%20h%3Dheight%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20L%3D4%5C%5C%20w%3D2%5C%5C%20%5Cend%7Bcases%7D~%5Chspace%7B2em%7D%5Cstackrel%7B%5Ctextit%7Bvolume%20of%20a%20cylinder%7D%7D%7BV%3D%5Cpi%20r%5E2%20h%7D~~%20%5Cbegin%7Bcases%7D%20r%3Dradius%5C%5C%20h%3Dheight%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20r%3D1%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D)
In order to get g(x) you would multiply the equation of f(x) by -1/2.
4x(-1/2)=-2x and -2(-1/2)=1.
