1. The value of the digit 8 in the number 850.74 is *

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

HELP PLEASEE:(((((( THANk YOU

alina1380 [7]

Answer:

(C). g(x) = ( $\frac{1}{4}$ x )²

Step-by-step explanation:

The correct answer is (C). g(x) = (  $\frac{1}{4}$  x )²

7 0

2 years ago

A city has a population of 34000. the value k is 0.0305. what is the population of the city after 9 years

sesenic [268]

Answer:

6

Step-by-step explanation: 6 9 0

3 0

2 years ago

(c) When organisms die, their bodies become food for decomposers.

Korvikt [17]

Answer

An example of a decomposer is a fungus. They are important because they recycle energy from consumers so it can be used again by producers to continue the cycle.

3 0

3 years ago

The product of two rational numbers is 6 If one of them is 8 find the other numbers

gtnhenbr [62]

Answer:

3/4

Step-by-step explanation:

8x = 6

x = other number = 6/8 = 3/4

4 0

2 years ago