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Anarel [89]
1 year ago
13

Four pounds of flour cost $2.60 how much flour do you get per dollar? round your answer to the nearest hundredth, if necessary.

Mathematics
1 answer:
gogolik [260]1 year ago
7 0

Since 4 pounds of flour costs $2.60, we have that:

\begin{gathered} 4\text{pounds}\to2.60 \\ x\to1 \end{gathered}

Where x is the amount of flour you get for 1 dollar.

We can rewrite the expression above as follows:

\begin{gathered} \frac{4\text{pounds}}{2.60}=\frac{x\text{ pounds}}{1} \\ \Rightarrow x\text{ pounds}=\frac{4pounds}{2.6}=1.53846\ldots \\ \Rightarrow x\approx1.54 \end{gathered}

Then, we get 1.54 pounds of flour per dollar

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The total surface area of a closed cylinder is
Degger [83]

The maximum volume of the cylinder is 27147.355 at the maximum point  r = \frac{50}{\sqrt{3} } .

<h3>How do you find the maximum volume of the cylinder?</h3>

The formula for the volume of the cylinder v = \pir^{2}h, To find the maximum volume of the cylinder we apply the condition of maxima  \frac{\mathrm{d} v}{\mathrm{d} r} = 0.

Let r cm be the radius and h cm be the height of the closed cylinder.

Then, Total surface area of the cylinder = 2\pi r(r+h)

                                                        5000 = 2\pi r^{2} +2\pi rh

                                                             h =   \frac{5000-2\pi r^{2} }{2\pi rh} .............(1)

Volume of the cylinder v = \pi r^{2} h

Substitute the value of h in the above equation

\Rightarrow                                       = \pi r^{2} × \left [ \frac{5000-2\pi  r^{2}}{2\pi r} \right ]

\Rightarrow                                      = \frac{r}{2} ×  (5000-2\pi r^{2} )

\Rightarrow                                    v = 2500r-\pi r^{3} ..............(2)

Now, for the maximum volume of the cylinder  \frac{\mathrm{d} v}{\mathrm{d} r} = 0

\Rightarrow                                                            \frac{\mathrm{d} (2500r-\pi r^{3})}{\mathrm{d} r} = 0

\Rightarrow                                                                      3\pi r^{2} = 2500

\Rightarrow                                                                          r^{2} = \frac{2500}{3\pi }

\Rightarrow                                                                          r = \frac{50}{\sqrt{3\pi } }

Volume is maximum for  r = \frac{50}{\sqrt{3\pi } }  

Then, v = 2500r-\pi r^{3}

\Rightarrow              =  2500 \frac{50}{\sqrt{3\pi } } -\pi (\frac{50}{\sqrt{3\pi } } )^{3}                              

\Rightarrow             = \frac{125000}{\sqrt{3\pi } } - \frac{125000}{3\sqrt{3\pi } }

\Rightarrow             = \frac{125000}{\sqrt{3\pi } }×\frac{2}{3}

\Rightarrow             = \frac{250000}{3\sqrt{3\pi } }                                                              

\Rightarrow          v = 27147.355

Hence, The maximum volume of the cylinder is 27147.355 at the maximum point  r = \frac{50}{\sqrt{3} } .                                                

To learn more about total surface area and volume of the cylinder from the given link

brainly.com/question/16095729

#SPJ4                                                                                   

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