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3 years ago

Need help with number 12. Thanks

Mathematics

1 answer:

Licemer1 [7]3 years ago

6 0

7x - 7 = 3x + 45
4x = 52
x = 13

7x - 7 = 7(13) - 7 = 84

y - 6 = 180 - (84 + 63)
y - 6 = 180 - 147
y - 6 = 33
y = 39

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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.

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3 years ago

Please help, please

Kisachek [45]

Answer:

Total amount of fencing needed as an algebraic expression in terms of x is: 10x + 3 .

Step-by-step explanation:

As it is given that each rectangle has the same dimensions, the dimensions of each rectangle must be: x units by 2x + 1 units.

Based on this, we can calculate the total amount of fencing needed.

Let width of each rectangle = x

Let length of each rectangle = 2x + 1

There are 4 widths and 3 lengths in total of fencing.

Therefore:

= 4 ( x ) + 3 ( 2x + 1 )

Expand:

= 4x + 6x + 3

Group like-terms:

= 10x + 3

7 0

2 years ago