Correct Answer: D. \(100\pi\) cm\(^2\)

Explanation

Volume of a cone = \(\frac{1}{3}\pi r^2 h\)

r = 5 cm

l = 13 cm

Using Pythagoras theorem

⇒ \(13^2 = 5^2 + h^2\)

⇒ \(169 = 25 + h^2\)

⇒ \(169 - 25 = h^2\)

⇒ \(h^2 = 144\)

⇒ \(h = \sqrt144 = 12 cm\)

∴ Volume of the cone = \(\frac{1}{3} \times\pi\times 5^2 x 12 = 100\pi\) cm\(^2\)

Correct Answer: D. Portuguese

Correct Answer: B. realistic

Explanation

\(\overline{MN}\) = 8i + 3j

\(\overline{MO}\) = 14i - 5j

Consider ?MON

\(\overline{MN}\) + \(\overline{NO}\) = \(\overline{MO}\)

\(\overline{NO}\) = \(\overline{MO}\) - \(\overline{MN}\)

\(\overline{NO}\) = 14i - 5j - (8i + 3j) = 6i - 8j

Since P is the midpoint of \(\overline{NO}\), then

\(\overline{NP} =\frac{1}{2}( \overline{NO} )\)

\(=\frac{1}{2}(6i - 8j) = 3i - 4j\)

Consider ?MNP

\(\overline{MN}\) + \(\overline{NP}\) = \(\overline{MP}\)

(8i + 3j) + (3i - 4j) = \(\overline{MP}\)

\(\overline{MP}\) = 8i + 3i + 3j - 4j

∴ \(\overline{MP}\) = 11i - j

Correct Answer: A. selling shares to the public

Correct Answer: D. 123.75m

Explanation

Distance x = vt/2 = 1650 x 0.15/2 = 123.75m

Correct Answer: C)

1.30 \(\times\) 10\(^{-7}\) mol\(^2\)dm\(^{-6}\)

Explanation

AgCl is the chemical formula for silver chloride, which is a sparingly soluble salt in water. A saturated solution of AgCl means that the maximum amount of AgCl has been dissolved in the water. The concentration of the saturated solution is given as 1.30 \(\times\) 10\(^{-5}\) moldm\(^{-3}\). The solubility product (K\(_{sp}\)) of AgCl is a measure of the extent to which the salt dissociates in water. It is defined as the product of the concentrations of the ions formed when the salt dissolves. For AgCl, the dissolution equation is AgCl(s) \(\rightleftharpoons\) Ag\(^+\)(aq) + Cl\(^-\)(aq), and its K\(_{sp}\) is given by the expression [Ag\(^+\)] [Cl\(^-\)]. To find the solubility product of AgCl, we need to determine the concentration of the ions in the saturated solution. Since AgCl is a sparingly soluble salt, we can assume that almost all of the AgCl remains undissolved and the concentrations of Ag\(^+\) and Cl\(^-\) are equal to each other and to the concentration of AgCl. Therefore, the concentration of each ion is 1.30 \(\times\) 10\(^{-5}\) moldm\(^{-3}\). Substituting the concentrations of the ions in the expression for K\(_{sp}\) gives [Ag\(^+\)] [Cl\(^-\)] = (1.30 \(\times\) 10\(^{-5}\) moldm\(^{-3}\))\(^2\) = 1.69 \(\times\) 10\(^{-10}\) mol\(^2\)dm\(^{-6}\). Therefore, the correct option is C: 1.30 \(\times\) 10\(^{-7}\) mol\(^2\)dm\(^{-6}\), which is the value of K\(_{sp}\) for AgCl. To recap, the solubility product of AgCl is the product of the concentrations of the ions formed when the salt dissolves. We can determine the solubility product of AgCl from the concentration of a saturated solution of AgCl, which is 1.30 \(\times\) 10\(^{-5}\) moldm\(^{-3}\). Substituting this value into the expression for K\(_{sp}\) gives the correct answer, which is C: 1.30 \(\times\) 10\(^{-7}\) mol\(^2\)dm\(^{-6}\).

Correct Answer: C. enable a uniform couple to act on the coil.

Explanation

The purpose of commutators in a direct current (DC) motor is to reverse the direction of the current after every half rotation.

Correct Answer: C. on

Explanation

The phrase take on means to fight against or compete against someone. In the context of a skillful boxer, it means he was not afraid to fight anyone.

Let's look at the options:

• A. to: Take to means to develop a liking for something/someone, or to start doing something habitually. (e.g., She took to him immediately, or He took to drinking.) This doesn't fit the context of a boxing challenge.

• B. upon: Take upon is usually part of take upon oneself, meaning to assume responsibility for something. (e.g., He took it upon himself to organize the event.) This doesn't fit here.

• C. on: Take on means to engage in a contest or fight with someone. (e.g., The team is ready to take on their rivals.) This fits perfectly with a boxer not being afraid to fight anyone.

• D. in: Take in has many meanings (understand, absorb, deceive, make smaller, etc.) but none fit the context of challenging someone in a fight.

Therefore, on is the best word to complete the sentence.

The final answer is C

Correct Answer: A. 60cm²

Explanation

New are = (2 x 15) x (2 x x) = 60cm²