Hello from MrBillDoesMath!
Answer:
Your answer is correct. (You have earned the unofficial title of Genius, Jr. );
Discussion:
Whew! This is a long problem. Let me see what I get and compare it to your answer. First each of the 3 terms contains the sqrt(yz) so let's factor that terms out. You equations equals
sqrt(yz) ( sqrt(108) + 3 sqrt(98) + 2 sqrt(75) ) (A)
Hmm.... let's look at the prime factorizations....
108 = 3 * 36 = 3 * (4*9) = 3 * 2^2* 3^2
98 = 2 * 49 = 2 * 7^2
75 = 3 * 25 = 3 * 5^2
So (A) =
sqrt(yz) ( 6 sqrt(3) + 3*7 sqrt(2) + 2*5 sqrt(3) ) =
sqrt(yz) ( ( 6 + 2*5) sqrt(3) + 21 sqrt(2) ) =
sqrt(yz) ( (6 + 10) sqrt(3) + 21 sqrt(2)) =
sqrt(yz) ( 16 sqrt(3) + 21 sqrt(2) )
Our answers agree!
Thank you,
MrB
1. So first of all we have to divide the 3 fractions into decimals to get a decimal to compare. So 5/6 is the same as 5 divided by 6 which is .83 bar and so on...
5/6= .83 bar
1/4= .25
2/3= .66 bar
So 5/6 and 2/3 are closer to one.
2. The two shortest pieces are 2/3 and 1/4 so you se 1/4 + 2/3. Let’s get a common denominator for these fractions. The common denominator is 12. So multiply 1/4 • 3 to get 3/12 and multiply 2/3 by • 4 to get 8/12. Add them together and you get 11/12. So he would need 1/12 more cable or 0.083 bar.
3. Now we have to find a common denominator for all of them. The common denominator is 12 again. Multiply 5/6•2 and then you get 10/12, then add 10/12 +2/12(from 1/4) and then you get leftover with 9/12 or 3/4 more wire.
Answer:
Coefficient is equal to 12
