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Yakvenalex [24]
3 years ago
12

Can some one help me ????????

Mathematics
2 answers:
Annette [7]3 years ago
7 0
-\frac{1}{7}=-\frac{1}{2}u+\frac{2}{3}|\cdot42\\
-6=-21u+28\\
21u=34\\
y=\frac{34}{21}

Murljashka [212]3 years ago
6 0
-\frac{1}{7}=-\frac{1}{2}u+\frac{2}{3}\ \ \ \ \ |multiply\ both\ sides\ by\ LCM(7;\ 2;\ 3)=42\\\\42\times(-\frac{1}{7})=42\times(-\frac{1}{2})u+42\times\frac{2}{3}\\\\-6=-21u+14\times2\ \ \ \ \ |add\ 21u\ to\ both\ sides\\\\21u-6=28\ \ \ \ \ \ |add\ 6\ to\ both\ sides\\\\21u=34\ \ \ \ \ |divide\ both\ sides\ by\ 21\\\\\boxed{u=\frac{34}{21}}

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Answer:

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.

Step-by-step explanation:

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.

Recall that the volume for a cylinder is given by:

\displaystyle V = \pi r^2h

Substitute:

\displaystyle (300) = \pi r^2 h

Solve for <em>h: </em>

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

Recall that the surface area of a cylinder is given by:

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

We want to minimize this equation. To do so, we can find its critical points, since extrema (minima and maxima) occur at critical points.

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

\displaystyle \begin{aligned} A &= 2\pi r^2 + 2\pi r\left(\frac{300}{\pi r^2}\right) \\ \\ &=2\pi r^2 + \frac{600}{ r}  \end{aligned}

Find its derivative:

\displaystyle A' = 4\pi r - \frac{600}{r^2}

Solve for its zero(s):

\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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3 years ago
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by using Pythagoras theorem we can find the distance between the points,

so...

distance between the points, which is the hypotenuse will be xy

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difference between the x coordinates will be dx

according to pythagoras theorem,

xy^{2} = dx^{2} +  dy^{2} \\xy^{2} = (-6-(-2))^{2} + (-5-5)^{2}\\xy^{2} =(-4)^{2} +(-10)^{2} \\xy^{2} =16+100\\xy^{2} =116\\xy =\sqrt{116} \\xy=10.77

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