Question

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​

Answer 1

Answer:

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Step-by-step explanation:

A=kC

B=jC

A+B= kC +jC = (k+j)C k+j is a constant, so A+B = mC where m=k+j

A-B = kC-jC = (k-j)C k-j is a constant, so A-B = nC where n=k-j

sqrAB = sqrAsqrB = sqrkCsqrjC = sqrkjC

square both ends

sqrAB^2 = sqrkjC^2

AB = kjC kj is a constant,

AB =pC where p =kj, a constant

Answer 2

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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