5. If A is directly proportional to C and B is directly proportional to C, prove that each of the following is
directly proportional to C.
(a) A + B
(b) A-B
(c) (AB)^1/2
Answers
Step-by-step explanation:
f A is directly proportional to C and B is directly proportional to C, prove that each of the following is
directly proportional to C.
(a) A + B
(b) A-B
(c) (AB)^1
Given : A is directly proportional to C and B is directly proportional to C
To Find : prove that each of the following is directly proportional to C
Solution:
A is directly proportional to C
A ∝ C
=> A = mC
m is constant
B is directly proportional to C
B ∝ C
=> B = nC
n is constant
A + B = mC + nC
=> A + B = ( m + n ) C
m + n is constant
=> A + B ∝ C
A - B = mC - nC
=> A - B = ( m - n ) C
m - n is constant
=> A - B ∝ C
√AB = √mCnC
=> √AB = √mn *C
√mn is contant
Hence √AB ∝ C
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