Solve the following inequalities
Questions a)
solve inequality question a
Solution
We first arrange the zeros of the numerator and the denominator, of the rational expression on the left of the inequality symbol, on the number line, from smallest to the largest as follows.
-∞ - 1 2 +∞
Select a value of x in any of the intervals and use it to find the sign of the rational expression. Example for x = -3 in the interval (-∞ , -1), the rational expression (x - 2)/(x + 1) = (- 3 - 2)/(- 3 + 1) = 5 / 2. Hence the rational expression (x - 2)/(x + 1) is positive on the interval (-∞ , -1) .
-∞ + - 1 2 +∞
The zeros -1 and 2 are of odd multiplicity and therefore the sign of the expression (x - 2)/(x + 1) will change at both zeros as we go from on interval to another. Hence the signs of the expression (x - 2)/(x + 1) as we go from left to right are
-∞ + - 1 - 2 + +∞
The solution set of the inequality is given by the union of all intervals where (x - 2)/(x + 1) is positive or equal to 0. Hence the solution set for the above inequality, in interval notation, is given by:
(-∞ , -1) ∪ [ 2 , +∞)
Questions b)
solve inequality question b
Answers
Answer:Answer
Solution:-
OF
2
(g)
+H
2
O
(g)
⟶O
2
(g)
+2HF
(g)
ΔH
R
=∑ΔH
f
(product)
−∑ΔH
f
(reactant)
∴ΔH
R
=(2×(−268.6))−(23+(−241.8))
⇒ΔH
R
=−756kJ/mol
Hence the standard enthalpy change will be −756kJ/mol
Now, as we know that,
ΔH=ΔU+Δn
g
RT
⇒ΔU=ΔH−Δn
g
RT
Now from the given reaction,
Δn
g
=n
P
−n
R
=(2+1)−(1+1)=1
T=300K(Given)
R=8.314×10
−3
J/mol−K
∴ΔU=(−756)−(1×8.314×10
−3
×300)
⇒ΔU=−756−2.494=−753.506kJ/mol
Hence the standard internal energy change will be −753.506kJ/mol.
Step-by-step explanation:
Answer:
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