Mathematics
Consider the relationship between temperature measured in degrees Celsius (°C) and degrees Fahrenheit (°F), which is given by °C = a °F + b. Find a and b, given that ice melts at 0 degrees Celsius and 32 degrees Fahrenheit, and water boils at 100 degrees Celsius and 212 degrees Fahrenheit. (Hint: When °C = 0, °F = 32 and when °C = 100, °F = 212. Use this information to find a and b, and thus, the linear relationship between °C and °F.)
Polynomials
5 Likes
Answer
Given:
The relationship between °C and °F is °C = a(°F) + b.
When °C = 0, °F = 32.
When °C = 100, °F = 212.
Substituting these values into °C = a(°F) + b, we get the following two equations:
0 = 32a + b …(i)
100 = 212a + b …(ii)
From equation (i): b = -32a
Substituting this into equation (ii):
100 = 212a + (-32a)
⇒ 100 = 212a - 32a
⇒ 100 = 180a
⇒ a =
⇒ a =
Substituting a = in b = -32a:
b = -32 ×
=
The linear relationship is:
°C = (°F) - = (°F - 32)
Hence, a = , b = and Linear relationship = (°F - 32)
Answered By
3 Likes
Related Questions
A learning platform charges a fixed monthly fee and an additional cost per digital learning module accessed. A student observes that when she accessed 10 modules, her bill was ₹400. When she accessed 14 modules, her bill was ₹500. If the monthly bill y depends on the number of modules accessed, x, according to the relation y = ax + b, find the values of a and b.
A gym charges a fixed monthly fee and an additional cost per hour for using the badminton court. A student using the gym observed that when she used the badminton court for 10 hours, her bill was ₹800. When she used it for 15 hours, her bill was ₹1100. If the monthly bill y depends on the hours of the use of the badminton court, x, according to the relation y = ax + b, find the values of a and b.
Identify other points on the line y = 2x + 1 by completing the following table.
x y 1 3 2 5 7 15 9 12 20 
Differentiate between the graphs of the equations y = 3x + 1, and y = –3x + 1.