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3 years ago

Students in grade6, 7 and 8 sold a total of 320 concert tickets.

Mathematics

1 answer:

Luba_88 [7]3 years ago

8 0

Answer:

x=320+t-s

Step-by-step explanation:

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g A manufacturer is making cylindrical cans that hold 300 cm3. The dimensions of the can are not mandated, so to save manufactur

sdas [7]

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 h:

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

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 h.

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

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.

7 0

3 years ago

15 dived by 6 2/3 A) 2 3/4 B) 100 1/4 C) 2 1/4 D) 100

Lady bird [3.3K]

15 divided by 6 2/3 is 2.25. Or 2 1/4. Pick C

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3 years ago

5x5 what is this answer let's see how smart you are probably everyone knows this but I am bored

vampirchik [111]

Answer:

Step-by-step explanation:

Cause math

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Answer:

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How can you describe the graph of the equation ax + by = c? Explain

scoundrel [369]

Answer:

When A and B are not both zero, the graph of Ax + By = C is always a line. The graph of Ax + By = C, where A and B are not both zero, is a line. Divide both sides by B. Because the form Ax + By = C can describe any line, it is called the standard form of an equation for a line.

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