Advanced Placement (AP), 29.01.2021 14:00 antoinewill05

9. (07.02 MC) A new state has formed and chosen a unitary form
government. Based on the state's choice of government, which of the following are likely characteristics of the state? (4 points)

Answers: 1

Show answers

Answers

Unitary state, a system of political organization in which most or all of the governing power resides in a centralized government, in contrast to a federal state. A brief treatment of the unitary state follows. For additional discussion, see Political system: Unitary nation-states.

Unitary state

QUICK FACTS

READ MORE ON THIS TOPIC

political system: Unitary nation-states

…all the world’s nation-states are unitary systems, including Bulgaria, France, Great Britain, the Netherlands,...

The Editors of Encyclopaedia Britannica

This article was most recently revised and updated by Brian Duignan, Senior Editor.

LEARN MORE in these related Britannica articles:

League of Nations

political system: Unitary nation-states

…all the world’s nation-states are unitary systems, including Bulgaria, France, Great Britain, the Netherlands,...…

voting in the 2012 U.S. presidential election

democracy: Unitary and federal systems

In most older European and English-speaking democracies, political authority inheres in the central government,...…

constitutional law: The distinction between unitary and federal states

…said to possess either a unitary or a federal system (see also federalism). In a unitary...…

newsletter icon

HISTORY AT YOUR FINGERTIPS

Email address

By signing up, you agree to our Privacy Notice.

Answer from: Quest

Answerboth technicians a and b are correct;

Answer from: Quest

Answer: the interval on which the curve is concave up is (-∞, -1/2)====== $\displaystyle y = \int_{0}^x \frac{1}{1 + t + t^2} \; dt$ we find the interval where this curve is concave up by finding the interval in which the 2nd derivative is positive.differentiate the curve equation with respect to x $\begin{aligned} \frac{dy}{dx} & = \frac{d}{dx} \int_{0}^x \frac{1}{1 + t + t^2} \; dt \end{aligned}$ let the function f denote be the anti-derivative of the inside expression, i.e. a function such that $(d/dx)f(x) = 1/(1 + t + t^2)$ .then use the fundamental theorem of calculus: $\begin{aligned} \frac{dy}{dx} & = \frac{d}{dx} \int_{0}^x \frac{1}{1 + t + t^2} \; dt \\& = \frac{d}{dx} \big[ f(x) - f(0) \big] & & \text{\footnotesize apply ftc} \\ & = \frac{d}{dx}f(x) - 0 \\ & = \frac{1}{x + x + x^2} & & \text{\footnotesize since $\frac{d}{dx}f(x) = \frac{1}{1 + x + x^2}$ } \end{aligned}$ differentiate again to get second derivative. we can use chain rule with 1/x as the outside function and 1 + x + x² as the inside function $\begin{aligned} \frac{d}{dx} \left( \frac{dy}{dx} \right) & = \frac{d}{dx}\left(\frac{1}{1 + x + x^2} \right) \\ \frac{d^2y}{dx^2} & = \frac{-1}{\left(1 + x + x^2\right)^2} \cdot \tfrac{d}{dx}(1 + x + x^2) \\ & = \frac{-1}{\left(1 + x + x^2\right)^2} \cdot (1 + 2x) \\ & = \frac{-(1 + 2x)}{\left(1 + x + x^2\right)^2} \end{aligned}$ find critical numbers of the second derivative. these numbers are where the 2nd deriv. is undefined or zero.where the 2nd derivative is zero: set (d²y/dx²) to equal 0 and solve for x $\begin{aligned} 0 & = \frac{-(1 + 2x)}{\left(1 + x + x^2\right)^2} \\ 0 & = -(1+2x) \\ -1 & = 2x \\ x & = -1/2 \end{aligned}$ where the 2nd derivative is undefined: if the denominator is equal to zero, the derivative will be undefeined. attempting to solve the equation 1 + x + x² = 0results in a discriminant of $b^2 - 4ac = 1^2 - 4(1)(1) = -3$ meaning that the equal 1 + x + x² = 0 has no real solutions and therefore will never equal zero.======our only critical number is x = -1/2.this forms two intervals to test the sign for: (-∞, -1/2) and (-1/2, ∞)test values into the 2nd derivative for (-∞, -1/2)if we try x = -1, we get $\begin{aligned} \left.\frac{d^2y}{dx^2}\right|_{x = -1} & = \frac{-(1+2(-1))}{\left(1+(-1)+(-1)^2\right)^2} \\ & = \frac{-(1-2)}{1} \\ & = 1 \end{aligned}$ so the since the 2nd derivative of the curve is positive on the interval (-∞, -1/2), the curve is concave up on (-∞, -1/2)test values into the 2nd derivative for (-1/2, ∞)if we try x = 0, we get $\begin{aligned} \left.\frac{d^2y}{dx^2}\right|_{x = 0} & = \frac{-(1+2(0))}{\left(1+(0)+(0)^2\right)^2} \\ & = \frac{-(1)}{1} \\ & = -1 \end{aligned}$ so the since the 2nd derivative of the curve is positive on the interval (-∞, -1/2), the curve is concave down on (-∞, -1/2).the interval on which the curve is concave up is (-∞, -1/2)

Another question on Advanced Placement (AP)

Advanced Placement (AP), 25.06.2019 08:00

Which of the following would be paid for with a state’s capital budget? a) lawmakers’ salaries b) a new bridge c) the salaries of state troopers d) education

Answers: 1

Answer

Advanced Placement (AP), 25.06.2019 21:30

Which of the following is a unit of volume measure? a. bunch b. tablespoon c. gram d. dozen

Answers: 1

Answer

Advanced Placement (AP), 26.06.2019 10:00

Which of the following ideas would not lead to lower amounts of waste? a) the extension of a product’s lifetime b) the elimination of unnecessary packaging c) flexible construction for simple repair d) built-in obsolescence e) the introduction of new design technology

Answers: 1

Answer

Advanced Placement (AP), 27.06.2019 05:30

The law of inertia states objects that are moving continue to move, and alternatively objects that are static remain static, unless in both instances the objects are acted upon by another force

Answers: 1

Answer

You know the right answer?

9. (07.02 MC) A new state has formed and chosen a unitary form
government. Based on the state...

Questions