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3 years ago

14

What was the role of mankind during the renaissance?

Advanced Placement (AP)

2 answers:

Harlamova29_29 [7]3 years ago

6 0

To learn never stop and liberate as much as you can

larisa [96]3 years ago

6 0

To never stop and liberate

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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

7 0

2 years ago

Use implicit differentiation to find dy/dx if xy=ln (xcoty).

Assoli18 [71]

$\frac{1-xy}{x^2+x\csc{y}\sec{y}}$

8 0

2 years ago

Which is a MAIN purpose of a protective tariff?

Rzqust [24]

Answer:

D

Explanation:

to increase gov't reveneu

5 0

2 years ago

Read 2 more answers

Anyone in the FCCLA program? If so what should I expect when I go to an FCCLA event this Tuesday? I am really scared cause my sc

Tcecarenko [31]

Answer:

The work of FCCLA helps students and teachers focus on a variety of youth concerns, including parenting, family relationships, substance abuse, peer pressure, sustainability, nutrition and fitness, teen violence, and career preparation in four specific Career Pathways.

Explanation:

Do not let the age gap do discourage you from joining this activity. Just be you, and be smarter than everyone else in the room XD

7 0

2 years ago

Students were measuring distances and found one to be 2.04 m. When they asked the teacher if their measurement was correct, the

IgorLugansk [536]

Answer:

The percentage error is 5.56%

Explanation:

Given

$Measured (M) = 2.04m$

$Actual (A)= 2.16m$

Required

Determine the percentage error

Percentage error (P) is calculated as follows:

$P = \frac{|A - M|}{A} * 100\%$

$P = \frac{|2.16 - 2.04|}{2.16} * 100\%$

$P = \frac{|0.12|}{2.16} * 100\%$

$P = \frac{0.12}{2.16} * 100\%$

$P = \frac{12\%}{2.16}$

$P = 5.56\%$

Hence:

<em>The percentage error is 5.56%</em>

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2 years ago