Match the following: (a) 104°F 1. 30°C (b) 212°F 2. 100°C (c) 86°F 3. 40°C (d) 122°F 4. 50°C
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Answer:
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class 12
>>applied mathematics
>>linear equations
>>solving a pair of linear equations - substitution method
>>the linear equation that converts fahren
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the linear equation that converts fahrenheit (f) to celsius (c) is given by the relation:
c=
9
5f−160
(i) if the temperature is 86f, what is the temperature in celsius?
(ii) if the temperature in 35 c, what is the temperature in fahrenheit?
(iii) if the temperature is 0 c, what is the temperature in fahrenheit and if the temperature is 0 f, what is the temperature in celsius?
(iv) what is the numerical value of the temperature which is same in both the scales?
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solution
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c=
9
5f−160
(i) putting f=86
∘
, we get c=
9
5(86)−160
=
9
430−160
=
9
270
=30
∘
hence, the temperature in celsius in 30
∘
c.
(ii) putting c = 35
∘
, we get 35
∘
=
9
5(f)−160
⇒315
∘
=5f−160
⇒5f=315+160=475
∴f=
5
475
=95
∘
hence, the temperature in fahrenheit is 95
∘
f.
(iii) putting c = 0
∘
, we get
0=
9
5f−160
⇒0=5f−160
⇒5f=160
∴f=
5
160
=32
∘
now, putting f = 0
∘
, we get
c=
9
5f−160
⇒c=
9
5(0)−160
=(−
9
160
)
∘
if the temperature is 0
∘
c, the temperature in fahrenheit is 32
∘
and if the temperature is 0
∘
f, then the temperature in celsius is (−
9
160
)
∘
c.
(iv) putting c=f, in the given relation, we get
f=
9
5f−160
⇒9f=5f−160
⇒4f=−160
∴f=
4
−160
=−40
∘
hence, the numerical value of the temperature which is same in both the sacales is −40.
Answer:
answer is referred in attachment
