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3 years ago

If the price of an apple is $0.50, the marginal utility per dollar spent for the fifth apple is:

Advanced Placement (AP)

1 answer:

lakkis [162]3 years ago

3 0

Complete question :

If the price of an apple is $0.50, the marginal utility per dollar spent for the fifth apple is:

Number of apples ____total utility

2__________________130

3__________________180

4__________________220

5__________________250

6__________________270

7__________________280

Answer:

Explanation:

The marginal utility simply refers to the change or extra satisfaction derived with change in consumption.

Hence, the marginal utility of the fifth apple equals :

Difference /change or extra satisfaction derived by consuming one more than 4 apples = (total utility of 5th apple - total utility of 4th apple)

= (250 - 220) = 30

Hence, marginal utility per dollar :

Marginal utility / price per apple

Price per apple = $0.5

Marginal utility of 5th apple = 30

Therefore,

30 / 0.5

= 60

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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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3 years ago

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nirvana33 [79]

Answer:

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ZanzabumX [31]

Answer:

C. Double Jeopardy Clause.

Explanation:

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In the case of Matthew, the Double Jeopardy Clause bars the prosecution from carrying out another trial on Matthew's case for the second time. This clause states that <em>"No person shall . . . be subject for the same offense to be twice put in jeopardy of life or limb . . . . "</em> This means that a person cannot be tried more than once for the same crime.

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Sliva [168]

3 regions/countries of Europe in which Indo-European languages do NOT predominate are :

Uralic languages are spoken in:

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Finland: Finnish and Swedish

Hungary: Hungarian

Explanation :

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The most demographically important Uralic language is Hungarian, the official language of Hungary.
Two other Uralic languages, Estonian and Finnish are also spoken by millions.
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Finnish, Hungarian and Estonian belong to the Uralicfamily, and Basque has no genetic relation to any other language.

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