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serg [7]
3 years ago
11

one days discharge at its mouth, 3 trillion gallons, could supply all of country A’s household for 5 months. how much water an a

verage household uses each month. assume there are 200 million households
Mathematics
1 answer:
serious [3.7K]3 years ago
5 0

let's use engineering notation for the sake of brevity.

1 trillion is 1,000,000,000,000, or just 1E12, twelve zeros.

1 million is then 1E6, six zeros.

we know the discharge for one day is 3E12 gallons, and that'd do just fine for country A for 5 months.  How many gallons in 1 month only?

\bf \begin{array}{ccll} gallons&months\\ \cline{1-2} 3E12&5\\ x&1 \end{array}\implies \cfrac{3E12}{x}=\cfrac{5}{1}\implies 3E12=5x \\\\\\ \cfrac{3E12}{5}=x\implies 6E11=x\implies 600000000000=x

if there are 200million inhabitants in A, namely 200E6 or 2E8 inhabitants, how many gallons per inhabitant from all those 6E11 gallons?

\bf \begin{array}{ccll} gallons&households\\ \cline{1-2} 6E11&2E8\\ x&1 \end{array}\implies \cfrac{6E11}{x}=\cfrac{2E8}{1}\implies 6E11=2E8x \\\\\\ \cfrac{6E11}{2E8}=x\implies \cfrac{600000000000}{200000000}=x\implies 3000=x

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Someone ask me to solve this.
Semenov [28]
X=2h, y=3k

Substitute these values into equations.

y+2x = 4 ------> 3k+2*2h=4 ----->  3k +4h =4

2/y - 3/2x = 1-----> 2/3k -3/(2*2h) = 1 ------> 2/3k - 3/4h =1

We have a system of equations now.

 3k +4h =4          ------> 3k = 4-4h ( Substitute 3k in the 2nd equation.)
2/3k - 3/4h =1

2/(4-4h) -3/4h = 1
2/(2(2-2h)) - 3/4h = 1
1/(2-2h) -3/4h - 1=0

4h/4h(2-2h) -3(2-2h)/4h(2-2h) - 4h(2-2h)/4h(2-2h) =0

(4h- 3(2-2h) - 4h(2-2h))/4h(2-2h) = 0
Numerator should be = 0
4h- 3(2-2h) - 4h(2-2h)=0

Denominator cannot be = 0
4h(2-2h)≠0

Solve equation for numerator=0
4h- 3(2-2h) - 4h(2-2h)=0
4h - 6+6h-8h+8h² =0
8h² +2h -6=0
4h² + h-3 =0
(4h-3)(h+1)=0
4h-3=0, h+1=0
h=3/4  or h=-1

Check which
4h(2-2h)≠0
1) h= 3/4  , 4*3/4(2-2*3/4)=3*(2-6)= -12 ≠0, so we can use h= 3/4
2)h=-1, 4(-1)(2-2*(-1)) =-4*4=-16 ≠0, so we can use h= -1, also.

h=3/4, then  3k = 4-4*3/4 =4 - 3=1 , 3k =1, k=1/3
h=-1, then  3k = 4-4*(-1) =8 , 3k=8, k=8/3 

So,
if h=3/4, then  k=1/3,
and if h=-1, then  k=8/3 .




6 0
3 years ago
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