8. In countries like USA and Canada, temperature is measured in Fahrenheit, whereas in
countries like India, it is measured in Celsius. Here is a linear equation that converts
Fahrenheit to Celsius:
F=
C + 32
0 Draw the graph of the linear equation above using Celsius for x-axis and Fahrenheit
for y-axis.
(i) If the temperature is 30°C, what is the temperature in Fahrenheit?
(iii) If the temperature is 95°F, what is the temperature in Celsius?
(iv) 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?
(v) Is there a temperature which is numerically the same in both Fahrenheit and
Celsius? If yes, find it.
Answers
Step-by-step explanation:
Given equation is
F = (9/5)C + 32 ....................1
We have to take Celsius for x-axis and Fahrenheit for y-axis.
Now put C = 0 in equation1, we get
F = (9/5)*0 + 32
=> F = 32
Again put C = 5 in equation1, we get
F = (9/5)*5 + 32
=> F = 9 + 32
=> F = 41
Again put C = -5 in equation1, we get
F = (9/5)*(-5) + 32
=> F = -9 + 32
=> F = 23
So
C: 0 5 -5
F: 32 41 23
Graph
When C = 30, the from equation 1
F = (9/5)*30 + 32
=> F = 9*6 + 32
=> F = 54 + 32
=> F = 86
When F = 95, the from equation 1
95 = (9/5)*C + 32
=> (9/5)*C = 95 - 32
=> (9/5)*C = 63
=> C = (63*5)/9
=> C = 7*5
=> C = 35
When C = 0, the from equation 1
F = (9/5)*0 + 32
=> F = 32
When F = 0, the from equation 1
0 = (9/5)*C + 32
=> (9/5)*C = - 32
=> C = (-32*5)/9
=> C = - 160/9
=> C = - 17.8
Let X degree of celcius = X degree of Fahrenheit, then from eqaution 1, we get
X = (9/5)*X + 32
=> X - 32 = (9/5)*X
=> 5(X - 32) = 9X
=> 5X - 160 = 9X
=> 9X - 5X = -160
=> 4X = -160
=> X = -160/4
=> X = -40
So at X = -40, both Celsius and Fahrenheit are same.