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antoniya [11.8K]

2 years ago

7

Describe 7 non-experimental methodologies and a precaution??

Advanced Placement (AP)

1 answer:

Tamiku [17]2 years ago

3 0

Non-experimental research does not mean nonscientific. Non-experimental research means there is a predictor variable or group of subjects that cannot be manipulated by the experimenter. Typically, this means that other routes must be used to draw conclusions, such as correlation, survey or case study.
There are three broad types of nonexperimental research. Single-variable research focuses on a single variable rather than a relationship between variables. Correlational and quasi-experimentalresearch focus on a statistical relationship but lack manipulation or random assignment.

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Surface Area of a can is 517.8 cm^2. Maximize the volume of this can using the measured surface area.

mafiozo [28]

Answer:

$r = 5.24$ --- Radius

$h = 10.48$ --- Height

Explanation:

Given

Object: Can (Cylinder)

$Surface\ Area = 517.8cm^2$

Required

Maximize the volume

The surface area is:

$S.A = 2\pi r^2 + 2\pi rh$

Substitute 517.8 for S.A

$517.8 = 2\pi r^2 + 2\pi rh$

Divide through by 2

$258.9 = \pi r^2 + \pi rh$

Factorize:

$258.9 = \pi r(r + h)$

Divide through by $\pi r$

$\frac{258.9}{\pi r} = r + h$

Make h the subject

$h = \frac{258.9}{\pi r} - r$ --- (1)

Volume (V) is calculated as:

$V = \pi r^2h$

Substitute (1) for h

$V = \pi r^2(\frac{258.9}{\pi r} - r)$

Open Bracket

$V = 258.9r - \pi r^3$

Differentiate V

$V' = 258.9 - 3\pi r^2$

Set V' to 0

$0 = 258.9 - 3\pi r^2$

Collect Like Terms

$3\pi r^2 = 258.9$

Divide through by 3

$\pi r^2 = 86.3$

Divide through by $\pi$

$r^2 = \frac{86.3}{\pi}$

$r^2 = \frac{86.3*7}{22}$

$r^2 = \frac{604.1}{22}$

Take square root of both sides

$r = \sqrt{\frac{604.1}{22}$

$r = 5.24$

Recall that:

$h = \frac{258.9}{\pi r} - r$

Substitute 5.24 for r

$h = \frac{258.9}{\pi * 5.24} - 5.24$

$h = \frac{258.9*7}{22 * 5.24} - 5.24$

$h = \frac{1812.3}{115.28} - 5.24$

$h = 15.72 - 5.24$

$h = 10.48$

Hence, the dimension that maximize the volume is:

$r = 5.24$ --- Radius

$h = 10.48$ --- Height

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