$\bf \textit{volume of a cone}\\\\
V=\cfrac{\pi r^2 h}{3}\quad 
\begin{cases}
r=radius\\
h=height\\
----------\\
diameter=2\\
r=\frac{diameter}{2}\\
\quad = 1\\
h=6
\end{cases}\implies V=\cfrac{\pi\cdot 1^2\cdot 6}{3}
\\\\\\
V=2\pi \\\\
-------------------------------$

$\bf \cfrac{\stackrel{vanilla}{volume}}{\stackrel{chocolate}{volume}}\qquad 2:1\qquad \cfrac{2}{1}\implies \cfrac{2\cdot \frac{V}{2+1}}{1\cdot \frac{V}{2+1}}\implies \cfrac{2\cdot \frac{2\pi }{2+1}}{1\cdot \frac{2\pi }{2+1}}
\\\\\\
\cfrac{2\cdot \frac{2\pi }{3}}{1\cdot \frac{2\pi }{3}}\implies \cfrac{\quad \frac{4\pi }{3}\quad }{\frac{2\pi }{3}}$

3 0

3 years ago

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Juan wants to change the shape of his vegetable garden from a square to a rectangle, but keep the same area so he can grow the s

irina [24]

The value of x that makes sense in this context is; 32.

The dimensions of the new garden is; 64 by 16.

<h3>How to find the real dimensions of the rectangle?</h3>

The expression that represents the problem statement is;

x² = (2x)(x – 16)

Expanding the bracket gives us;

x² = 2x² – 32x

x² - 32x = 0

x(x - 32) = 0

Thus; x = 0 or x = 32

x can't be 0 and as such the value of x is 32.

Thus;

The length of the new garden is; l = 2x = 64.

The width of the new garden is; w = x - 16 = 32 - 16 = 16

The dimensions of the new garden are therefore; 64 by 16

Read more about Rectangle Dimensions at; brainly.com/question/17297081

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4 0

2 years ago