So for same distance, ∝ mass. So smaller separation → smaller mass.
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- But 0.8 < 1.6 → so mass must be less — but lensing is weaker. So smaller separation makes sense — weaker lensing.
- So the given separateion (0.8) corresponds to less mass? But the claim is scale with mass.
- Resolution: the proportionality is approximate, but the problem says "∝ mass / distance".
- Therefore, 0.8 < 1.6 → mass of distant cluster is 0.8 / 1.6 = 0.5 times that of nearby.
- So ratio = 0.5
- But the question asks: "what is the ratio of the lensing mass of the distant cluster to the nearby one?"
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Let the integers be \( n-1 \), \( n \), and \( n+1 \).
Their sum:
n = \frac{96}{3} = 32
The integers are 31, 32, 33. The largest is 33.
#### 33
A line passes through the points (2, 5) and (6, 17). What is the slope of the line?
Slope \( m \) is:
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{17 - 5}{6 - 2} = \frac{12}{4} = 3
If \( x^2 - 5x + 6 = 0 \), what are the values of \( x \)?
Factor the quadratic: