a variable R is partly constant and partly varies as T when t=27 r=55 and when t=57 r=58.find the relationship between R and T
Where is the answer
To find the relationship between R and T, we need to determine the constant part and the varying part of R.
Let's denote the constant part as a and the varying part as b. Therefore, we can write the relationship as:
R = a + bT
Now, let's use the given information to form two equations:
When t = 27, r = 55:
55 = a + 27b ----(Equation 1)
When t = 57, r = 58:
58 = a + 57b ----(Equation 2)
Now, we have a system of two equations with two variables (a and b). We can solve these equations to find the values of a and b.
Subtracting Equation 1 from Equation 2, we get:
58 - 55 = (a + 57b) - (a + 27b)
3 = 30b
b = 3/30
b = 1/10
Substituting the value of b into Equation 1, we get:
55 = a + 27(1/10)
55 = a + 27/10
55 - 27/10 = a
a = 550/10 - 27/10
a = 523/10
Therefore, the relationship between R and T is:
R = (523/10) + (1/10)T
or
R = (523 + T)/10
To find the relationship between R and T, we need to first understand the given information:
We have a variable R that is partly constant and partly varies as T. This means that R can be expressed as the sum of a constant term and a term that is dependent on T.
We are given two sets of values:
- When t = 27, r = 55
- When t = 57, r = 58
Let's denote the constant term as C and the term that varies with T as kT. So, we can express R as:
R = C + kT
Now, we can use the given information to find the values of C and k.
When t = 27, r = 55:
Substituting these values into the expression for R, we get:
55 = C + 27k -- equation 1
When t = 57, r = 58:
Substituting these values into the expression for R, we get:
58 = C + 57k -- equation 2
We now have a system of two equations (equation 1 and equation 2) with two variables (C and k). We can solve this system to find the relationship between R and T.
Subtracting equation 1 from equation 2, we eliminate C:
58 - 55 = C + 57k - (C + 27k)
3 = 30k
k = 3/30 = 1/10
Now, substitute this value of k back into equation 1 to find C:
55 = C + 27(1/10)
55 = C + 27/10
55 - 27/10 = C
C = 529/10
Therefore, the relationship between R and T is:
R = (529/10) + (1/10)T
or simplified as:
R = (529 + T)/10
Thus, R is partly constant (529/10) and partly varies (1/10) as T.