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2 years ago

Please answer this quickly!

Mathematics

2 answers:

hjlf2 years ago

6 0

Answer:20,000⋅(1.08)^t/3≤50,000

olchik [2.2K]2 years ago

4 0

1)Take the problem go to your y= button on your graphing calculator.

2)Then clear out all information within.

3) Type in 20,00020000(1+.08)t (raise the 't' like you would using numbers ex: 2 squared. 't' is the same as 'x').

4) Hit the 2nd button then Graph button which will bring you to the table. Scroll down until you get your answer.

Hope that helps :)

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A cylindrical can holds 300 cubic centimeters, and we want to find the dimensions that minimize the cost for materials: that is, the dimensions that minimize the surface area.

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$\displaystyle V = \pi r^2h$

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$\displaystyle \frac{300}{\pi r^2} = h$

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$\displaystyle A = 2\pi r^2 + 2\pi rh$

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First, substitute for <em>h</em>.

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$\displaystyle \begin{aligned} (0) &= 4\pi r - \frac{600}{r^2} \\ \\ 4\pi r - \frac{600}{r^2} &= 0 \\ \\ 4\pi r^3 - 600 &= 0 \\ \\ \pi r^3 &= 150 \\ \\ r &= \sqrt[3]{\frac{150}{\pi}} \approx 3.628\text{ cm}\end{aligned}$

Hence, the radius that minimizes the surface area will be about 3.628 centimeters.

Then the height will be:

$\displaystyle \begin{aligned} h&= \frac{300}{\pi\left( \sqrt[3]{\dfrac{150}{\pi}}\right)^2} \\ \\ &= \frac{60}{\pi \sqrt[3]{\dfrac{180}{\pi^2}}}\approx 7.25 6\text{ cm} \end{aligned}$

In conclusion, the dimensions that minimize the cost of materials for the cylinders have radii of about 3.628 cm and heights of about 7.256 cm.

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