Let, coordinate of point A' is (x,y).
Since, A' is the symmetric point A(3, 2) with respect to the line 2x + y - 12 = 0.
So, slope of line containing A and A' will be perpendicular to the line 2x + y - 12 = 0 and also their center lies in the line too.
Now, their center is given by :
Also, product of slope will be -1 .( Since, they are parallel )
x = 2y - 1
So, 
Also, C satisfy given line :
Also,
Therefore, the symmetric points is
.
Answer:
Answer is C
Step-by-step explanation:
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Answer:
1.778 times more or 16/9 times more
Step-by-step explanation:
Given:
- Mirror 1: D_1 = 8''
- Mirror 2: D_2 = 6"
Find:
Compare the light gathering power of an 8" primary mirror with a 6" primary mirror. The 8" mirror has how much light gathering power?
Solution:
- The light gathering power of a mirror (LGP) is proportional to the Area of the objects:
LGP ∝ A
- Whereas, Area is proportional to the squared of the diameter i.e an area of a circle:
A ∝ D^2
- Hence, LGP ∝ D^2
- Now compare the two diameters given:
LGP_1 ∝ (D_1)^2
LGP ∝ (D_2)^2
- Take a ratio of both:
LGP_1/LGP_2 ∝ (D_1)^2 / (D_2)^2
- Plug in the values:
LGP_1/LGP_2 ∝ (8)^2 / (6)^2
- Compute: LGP_1/LGP_2 ∝ 16/9 ≅ 1.778 times more
Answer:
n = 0, n =2
Step-by-step explanation:
Given
(n + 1) + 3(n - 1) = 2(n - 1)(n + 1) ← distribute parenthesis on both sides
n + 1 + 3n - 3 = 2(n² - 1), that is
4n - 2 = 2n² - 2 ( subtract 4n - 2 from both sides )
0 = 2n² - 4n ← factor out 2n from each term )
0 = 2n(n - 2)
Equate each factor to zero and solve for n
2n = 0 ⇒ n = 0
n - 2 = 0 ⇒ n = 2
