a silver ornament of mass m gram is polished with a gold equivalent to one percent of the mass of silver. compute the ratio of the number of atoms of gold and silver in the ornament
Answers
Step by step solution :STEP1:Equation at the end of step 1 (22m2 - 24m) + 36 = 0 STEP2:STEP3:Pulling out like terms
3.1 Pull out like factors :
4m2 - 24m + 36 = 4 • (m2 - 6m + 9)
Trying to factor by splitting the middle term
3.2 Factoring m2 - 6m + 9
The first term is, m2 its coefficient is 1 .
The middle term is, -6m its coefficient is -6 .
The last term, "the constant", is +9
Step-1 : Multiply the coefficient of the first term by the constant 1 • 9 = 9
Step-2 : Find two factors of 9 whose sum equals the coefficient of the middle term, which is -6 .
-9 + -1 = -10 -3 + -3 = -6 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -3 and -3
m2 - 3m - 3m - 9
Step-4 : Add up the first 2 terms, pulling out like factors :
m • (m-3)
Add up the last 2 terms, pulling out common factors :
3 • (m-3)
Step-5 : Add up the four terms of step 4 :
(m-3) • (m-3)
Which is the desired factorization