F(x)=-1/x
g(x)=√(3x-9)
Domain of (f/g)(x): ??
1We find out the domain of f(x):
f(x) is a rational function, therefore can take real values if the denominator is not ("0"), therefore the domain of f, will be all values excpet "0"
Domain of f: (-∞,0)U(0,+∞);
o
----------------------------------------------O-------------------------------------------
←-------- -∞ +∞ ----------→
g(x) is a radical square root function, therefore the radicand have to be greater than o equal to "0"
3x-9≥0
3x≥9
x≥3
3
.........................................................Ф--------------------------------
←--------- - ∞ +∞ -----------→
(f/g)(x) = (-1/x) / (√(3x-9)) is a rational function with a square root in the denominator,also the square root don´t take the value of "0";
Therefore:
3x-9>0
3x>9
x>3
The domain of the function (f/g)(x) only can take the values found in all three domains at once.
3
............................................................0---------------------------------
←--------- -∞ +∞-------------→
Answer: (3,+∞)
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Answer:
Mass = 14.3 g
Explanation:
Given data:
Mass of Mg(OH)₂ = 16.0 g
Mass of HCl = 11.0 g
Mass of MgCl₂ = ?
Solution:
Chemical equation:
Mg(OH)₂ + 2HCl → MgCl₂ + 2H₂O
Number of moles of Mg(OH)₂ :
Number of moles = mass/ molar mass
Number of moles = 16.0 g/ 58.3 g/mol
Number of moles = 0.274 mol
Number of moles of HCl :
Number of moles = mass/ molar mass
Number of moles = 11.0 g/ 36.5 g/mol
Number of moles = 0.301 mol
Now we will compare the moles of Mg(OH)₂ and HCl with MgCl₂.
Mg(OH)₂ : MgCl₂
1 : 1
0.274 : 0.274
HCl : MgCl₂
2 : 1
0.301 : 1/2×0.301 = 0.150
The number of moles of MgCl₂ produced by HCl are less so it will limiting reactant.
Mass of MgCl₂:
Mass = number of moles × molar mass
Mass = 0.150 × 95 g/mol
Mass = 14.3 g
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