$\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \textit{we also know that }~~ \begin{cases} y=-4\\ x=8 \end{cases}\implies -4=k(8)\implies \cfrac{-4}{8}=k\implies -\cfrac{1}{2}=k \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y=-\cfrac{1}{2}x~\hfill$

8 0

3 years ago

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A cylinder’s radius is reduced to 2004-06-01-04-00_files/i0480001.jpg its original size and the height is quadrupled. How has th

asambeis [7]

I can't answer this question if we don't know by what scale the cylinder's radius was reduced. Luckily, I found the same problem that says the radius was reduced to 2/5. So, we find the ratio of both volumes.

V₁ = πr₁²h₁
V₂ = πr₂²h₂

where r₂ = 2/5*r₁ and h₂ = 4h₁

V₂/V₁ = π(2/5*r₁ )²(4h₁)/πr₁²h₁= 8/5 or 1.6

<em>Thus, the volume has increased more by 60%.</em>

6 0

3 years ago

140 fluid ounces increased by 45%

Radda [10]

$100\%\ increased\ by\ 45\%=100\%+45\%=145\%\\\\method\ \#1\\\\p\%=\frac{p}{100}\to145\%=\frac{145}{100}=\frac{145:5}{100:5}=\frac{29}{20}\\\\145\%\ of\ 140=\frac{29}{20}\cdot140=29\cdot7=\boxed{203\ (ounces)}\leftarrow answer$

$method\ \#2\\\\\begin{array}{ccc}140&-&100\%\\x&-&145\%\end{array}\ \ \ cross\ multiply\\\\\\100\cdot x=140\cdot145\ \ \ \ |divide\ both\ sides\ by\ 100\\\\x=\frac{140\cdot145}{100}\\\\\boxed{x=203\ (ounces)}$

4 0

3 years ago