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3 years ago

Can someone please help me with this? Let f(x) = x^3 + x + 1. Which expression

Advanced Placement (AP)

1 answer:

Tatiana [17]3 years ago

8 0

Answer:

Last Option

Explanation:

I'm not sure about this one so I had to google the equation real quick.

The equation for the derivative of an inverse is:

$[f^{-1}(x)]'=\frac{1}{f'(f^{-1}(x))}$

From my understanding of the format, it might look like a hard equation to understand but its pretty simple.

The inverse derivative is 1 divided by the derivative of f(x), except you plug in f⁻¹(x) into that derivative.

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Which of the following principles is reflected in Article V?

Aleksandr-060686 [28]

Answer:

The answer is B: federalism

Explanation

I did it and got it right

6 0

3 years ago

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

3 years ago

1) Calcula la diagonales de un poligono n lados. Heptágono: 2 puntos

ahrayia [7]

Answer:

El número de diagonales de un polígono de n lados se calcula mediante la siguiente fórmula:

$d = \frac{n\cdot (n-3)}{2}$ (1)

Donde:

$d$ - Cantidad de diagonales del polígono.

$n$ - Cantidad de lados del polígono.

Bajo esta fórmula, tenemos los siguientes resultados:

a) El heptágono tiene 14 diagonales.

b) El octágono tiene 20 diagonales.

c) El eneágono tiene 27 diagonales.

d) El decágono tiene 35 diagonales.

e) El pentadecágono tiene 90 diagonales.

Explanation:

La cantidad de diagonales de un polígono se puede determinar mediante la siguiente ecuación:

$d = \frac{n\cdot (n-3)}{2}$ (1)

Donde:

$d$ - Cantidad de diagonales del polígono.

$n$ - Cantidad de lados del polígono.

A continuación, calculamos la cantidad de diagonales de los siguientes polígonos:

Heptágono ( $n = 7$ )

$d = \frac{7\cdot (7-3)}{2}$

$d = 14$

El heptágono tiene 14 diagonales.

Octágono ( $n = 8$ )

$d = \frac{8\cdot (8-3)}{2}$

$d = 20$

El octágono tiene 20 diagonales.

Eneágono ( $n = 9$ )

$d = \frac{9\cdot (9-3)}{2}$

$d = 27$

El eneágono tiene 27 diagonales.

Decágono ( $n = 10$ )

$d = \frac{10\cdot (10-3)}{2}$

$d = 35$

El decágono tiene 35 diagonales.

Pentadecágono ( $n = 15$ )

$d = \frac{15\cdot (15-3)}{2}$

$d = 90$

El pentadecágono tiene 90 diagonales.

8 0

3 years ago

What evidence suggests that China’s society was highly patriarchal?

Lostsunrise [7]

Answer:

Answer: In China, society was patriarchy where there was a presence of male dominance. Explanation: Women role in ancient China was to look after the household, men, and raise the children.

Explanation:

4 0

3 years ago

Comparison: How did the patterns of settlement differ among the Spanish, English, French, and Dutch immigrants?

SashulF [63]

Spanish settlement began in the early 16th century and was a massive and intensive enterprise organized, subsidized and overseen by the Spanish Crown, whereas English, Dutch and French settlement of the New World began about a hundred years after the Spanish effort and was a more timid and tentative affair; for instance, when the first successful English settlement in North America was founded —Jamestown colony in present-day Virginia in 1607— the Spanish colony of Puerto Rico had had governors and organized governments for a hundred years and when the Pilgrims landed in Plymouth rock in present-day Massachusetts in 1620, Puerto Rico’s capital city of San Juan was celebrating its first century of existence. English settlement patterns changed substantially later on and the Thirteen Colonies were very successful enterprises but in other parts of the New World the English —or British— built upon Spanish success. Jamaica was founded as a SPANISH colony and remained one until the British conquered it in the late 17th century; Trinidad was founded as a SPANISH colony until the British conquered it in 1797 during the French Revolutionary Wars. Florida also started out as a Spanish colony, was taken over by the British at the end of the Seven years War (1756–1763), was returned to Spain at the end of the American Revolution —in payment for Spain’s assistance to the Americans— and was purchased by the US from Spain in 1819. Belize —British Honduras— was founded on marginal land that the Spanish Crown didn’t really care for in Central America. The Dutch concerned themselves with much smaller settlements in the Lesser Antilles and Dutch Guiana —present day Suriname— and the French, even though they settled over a much larger area, comprising Canada and the Louisiana territory, did not treat human settlement over such a large area with the same energy and dedication that the British did, such that by the time of the Seven Years War —known in the US and Canada as the “French and Indian War”— the entire European population of ALL of French Canada —not counting Native Americans— was only 80,000 and that for the Louisiana territory —again, not counting Native Americans— was perhaps another 20,000 AT MOST—at a time when the Thirteen (British) colonies in North America had a total population of two and a half million.

3 0

3 years ago