The question asks us to identify the relationship between the first two words and then apply the same relationship to find the word that completes the second pair. This is a word analogy problem where we need to find a semantic connection.
D) Twist is the correct answer. "Twist" is an action that involves bending or deforming an object, often resulting in a bent shape. It shares a similar operational relationship with "Bend" as "Patch" does with "Mend".
Find the value of:\(\sqrt{-1+\sqrt{284+\sqrt{13+\sqrt{144}}}}\)
To solve this problem, we need to evaluate the expression by working from the innermost square root outwards. This involves calculating the square root of perfect squares at each step.
The innermost term is \(\sqrt{144}\).
\[ \sqrt{144} = 12 \]Now substitute this value back into the expression:
\[ \sqrt{13 + \sqrt{144}} = \sqrt{13 + 12} = \sqrt{25} \]\[ \sqrt{25} = 5 \]Substitute this new value back into the expression:
\[ \sqrt{284 + \sqrt{13 + \sqrt{144}}} = \sqrt{284 + 5} = \sqrt{289} \]To find \(\sqrt{289}\), we can recall common perfect squares or estimate. We know that \(10^2 = 100\), \(20^2 = 400\). Since \(289\) ends in \(9\), its square root must end in \(3\) or \(7\). Checking \(17^2\):
\[ 17 \times 17 = 289 \]\[ \sqrt{289} = 17 \]Finally, substitute this value into the outermost expression:
\[ \sqrt{-1 + \sqrt{284 + \sqrt{13 + \sqrt{144}}}} = \sqrt{-1 + 17} = \sqrt{16} \]\[ \sqrt{16} = 4 \]Thus, the value of the entire expression is \(4\).
D) 4 is the correct answer, as derived from the step-by-step calculation.
Na2O is a ________ oxide.
The question asks to identify the type of oxide for Na2O. We need to recall the general properties of oxides formed by metals and non-metals, particularly those from Group 1 elements like Sodium (Na).
A) Alkaline. Sodium is an alkali metal, and its oxide (Na2O) is a typical basic or alkaline oxide. It reacts with water to form sodium hydroxide, a strong base.
The problem presents a series of letters and asks us to find the missing letter. To solve this, we need to identify the pattern or rule governing the sequence of letters. This can often be done by looking at the alphabetical positions of the letters or the difference in positions between consecutive letters.
D) R is the correct option because it fits the established pattern of +6, +5, +5, +5, +5 when considering the alphabetical positions of the letters with a wrap-around from Z to A.
Potential energy is directly proportional to the height of an object above a reference point (usually the ground). The higher an object is, the greater its gravitational potential energy. We need to identify the maximum height reached by the object.
If the question intended sequential additions (e.g., first raised by 5m, then an *additional* 10m, then an *additional* 15m), the maximum height would be \(5+10+15 = 30 \text{ m}\). However, 30 m is not an option. The wording "first by 5 m, then by 10 m, and then by 15 m" implies a sequence of heights it is raised *to*, not *by* additional amounts, especially given the options. Thus, the maximum height attained among the specified levels is 15 m.
B) at 15 m. This is the highest point the object reaches among the specified heights, and potential energy is directly proportional to height.
The question asks to identify an example of a single-atom molecule. This requires understanding the definition of a molecule and recognizing which elements exist as individual atoms in their stable state.
A) Argon is a noble gas and exists as individual, unbonded atoms, making it a single-atom (monoatomic) molecule.
To determine which arguments are strong, we need to evaluate each argument based on its relevance, validity, and whether it directly supports or refutes the question. A strong argument should be logical, factual, and directly address the core issue.
Based on this analysis, only Argument I presents a strong, direct, and logical reason in favor of making higher education compulsory.
Correct Option: C) Only argument I is strong
To solve this problem, we need to recall the formula for acceleration due to gravity on the surface of the Earth. We will then analyze how a change in the Earth's radius affects this acceleration, assuming the mass remains constant. We will use percentage change calculations to find the final answer.
The acceleration due to gravity (\(g\)) on the surface of a planet is given by the formula:
\[ g = \frac{GM}{R^2} \]Where:
The radius of the Earth is reduced by 1%. Let the original radius be \(R_1\) and the new radius be \(R_2\).
\[ R_2 = R_1 - 0.01 R_1 = 0.99 R_1 \]The mass (\(M\)) remains constant.
Let the original acceleration due to gravity be \(g_1\) and the new acceleration be \(g_2\).
\[ g_1 = \frac{GM}{R_1^2} \] \[ g_2 = \frac{GM}{R_2^2} = \frac{GM}{(0.99 R_1)^2} = \frac{GM}{0.99^2 R_1^2} \] \[ g_2 = \frac{1}{0.99^2} \left( \frac{GM}{R_1^2} \right) = \frac{1}{0.99^2} g_1 \]The percentage change in \(g\) is given by:
\[ \text{Percentage Change} = \frac{g_2 - g_1}{g_1} \times 100\% \] \[ \text{Percentage Change} = \left( \frac{g_2}{g_1} - 1 \right) \times 100\% \]Substitute the value of \(g_2/g_1\):
\[ \text{Percentage Change} = \left( \frac{1}{0.99^2} - 1 \right) \times 100\% \] \[ 0.99^2 = 0.9801 \] \[ \text{Percentage Change} = \left( \frac{1}{0.9801} - 1 \right) \times 100\% \] \[ \text{Percentage Change} = (1.0199 - 1) \times 100\% \] \[ \text{Percentage Change} = 0.0199 \times 100\% \approx 1.99\% \]This is approximately a 2% increase.
Since the change is small (1%), we can use differential approximation. For \(g = GM/R^2\), taking the logarithm of both sides:
\[ \ln(g) = \ln(GM) - 2 \ln(R) \]Differentiating both sides:
\[ \frac{dg}{g} = -2 \frac{dR}{R} \]If \(R\) decreases by 1%, then \(\frac{dR}{R} = -0.01\).
\[ \frac{dg}{g} = -2 (-0.01) = +0.02 \]So, \(g\) increases by 2%.
Correct Option: C) will increase by 2%
The question asks to identify the Brazilian football player known by the nickname 'White Pele'. This requires knowledge of famous football players and their common nicknames.
Correct Option: C) Zico
Zico is widely known as 'White Pele' due to his extraordinary footballing talent, vision, and goal-scoring prowess, which drew comparisons to the legendary Pele.
This problem can be solved using Venn diagrams or by applying the rules of syllogism. We will represent each statement as a relationship between sets and then evaluate the conclusions.
Correct Option: A) Only 2 follows