Mathematics
Simotenous equations
Elimination methods
3x+2y=10
4x - 2y=4
Solution
3x + 2y =10_________(1)
4x - 2y =4____________(2)
3x + 2y =10
+ 4x - 2y =4
7x. =14
7x. =14
7. 7 1
X=2
3x +2y =10
3(2) + 2y =10
6.+2y. =10
2y =10. - 6
2y=4
2y =4
Y=4
2
Y=2
,:. X=2 and y=2//
If a convex lens of focal length 12 cm is used to produce a real image four times the size of the object, how far from the lens must the object be placed?
Options:
A. 10 cm
B. 15 cm
C. 20 cm
D. 25 cm
Solution:
Given:
Magnification, �
Focal length, �
Since the image is four times the size of the object:
M = u /u =4
U=4u
Using the lens formula:
f=uv/
U+v
Substitute f=12 and v=4u
12=u(4u) /u+4u
12=4u /5u
12=4u/5
60=4u
U=15cm
Answer =B. 15cm
2026-07-23 20:28:46
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