Correct Answer: D. \(x^{2} + y^{2} - 8x - 10y + 21 = 0\)

Explanation

On the y-intercept, x=0. At this point, y = 5(0) - 2y = -6; y = 3, so the y- intercept has coordinates (0,3).

The equation of the circle is given as \((x-a)^{2} + (y-b)^{2} = r^{2}\), where (a,b) is the centre and r is the radius.

The radius of the circle through the y- intercept = \(\sqrt{(4-0)^{2} + (5-3)^{2}} = \sqrt{20}\)

The equation of the circle is \((x-4)^{2} + (y-5)^{2} = 20\); expanding, we have

\(x^{2} + y^{2} + 8x - 10y + 21 = 0\)

Correct Answer: C. Central Buying

Correct Answer: C. sales

Correct Answer: B. 0

Explanation

To find the maximum value, we can use the second derivative test where, given \(f(x)\), the second derivative < 0, makes it a maximum value.

\(x(x + 1)^{2} = x(x^{2} + 2x + 1) = x^{3} + 2x^{2} + x\)

\(\frac{\mathrm d y}{\mathrm d x} = 3x^{2} + 4x + 1 = 0\)

Solving, we have \( x = \frac{-1}{3}\) or \(-1\).

\(\frac{\mathrm d^{2} y}{\mathrm d x^{2}} = 6x + 4\)

When \(x = \frac{-1}{3}, \frac{\mathrm d^{2} y}{\mathrm d x^{2}} = 2 > 0\)

When \(x = -1, \frac{\mathrm d^{2} y}{\mathrm d x^{2}} = -2 < 0\)

At maximum value of x being -1, \(y = -1(-1 + 1)^{2} = 0\)

Correct Answer: B. reconcile his book of accounts

Correct Answer: D) chromatography

Explanation

A brand of ink containing cobalt (II) and copper (II) ions can be separated into its various components usingchromatography, which is the correct option in this question.

Chromatography is a technique used to separate mixtures based on the differences in the movement of their components through a stationary phase. In the case of ink, the components are often dyes or pigments, which can be separated using paper or thin-layer chromatography.

Let's briefly discuss why the other options are not suitable for separating the components of the ink:

Fractional crystallization: This technique is used to separate components of a mixture based on their solubility. It involves dissolving the mixture in a solvent and then cooling it to form crystals of different components. However, this method is not suitable for separating components of the ink, as both cobalt (II) and copper (II) ions are likely to have similar solubilities in a solvent.

Fractional distillation: This method is used to separate components of a mixture based on their boiling points. It is commonly used for separating components of liquid mixtures, like petroleum. Since ink is a mixture of solid components in a liquid medium, fractional distillation is not an appropriate method for separating its components.

Sublimation: Sublimation is a process in which a solid directly transforms into a gas without going through the liquid phase. This method is used to separate components of a mixture that have different sublimation temperatures. However, sublimation is not suitable for separating ink components, as both cobalt (II) and copper (II) ions do not undergo sublimation.

In conclusion,chromatography is the most appropriate technique for separating the components of an ink containing cobalt (II) and copper (II) ions, as it relies on the differences in their movement through a stationary phase, allowing the separation of the components based on their interactions with the stationary phase and mobile phase.

Correct Answer: C. -1

Explanation

9^2x = \(\frac{1}{3}\)(27^x)

(2²)^2x = \(\frac{(3^{3x})}{3}\)

(3^4x) = 3^{3x - 1}

4x = 3x - 1

4x - 3x = -1

x = -1

Correct Answer: C. auxin

Correct Answer: B. F

Correct Answer: B. prevents arbitrary law making

Explanation

A bicameral system is a reference to a government with two legislative houses or chambers. A practical reason for a bicameral system is to prevent the legislative branch from having too much power and making arbitrary laws.

An arbitrary law refers to law imposed by the mere will of the legislature