If c is partly constant and partly varies to t find the relation between c and t if c equal to 30 when t equal to 2 and c equal to 50 when t equal to 6 find c when t equal to 3
c = a + b t
30 = a + 2 b
50 = a + 6 b
--------------------- subtract
-20 = -4 b
b = 5
30 = a + 10
a = 20
so
c = 20 + 5 t
so now you finish
c = mt + k
when c = 30, t = 2, c = 50
but you already told me that c = 30
the rest is"
" and c equal to 50 when t equal to 6 find c when t equal to 3"
which is a lot of gobbledegook.
So I will wait till you fix the problem
ahh, looks like Anonymous
figured out what you were saying , go with his solution
To find the relation between c and t, we can create an equation based on the given information. Let's assume that c varies linearly with t.
We are given two sets of values:
- When t = 2, c = 30
- When t = 6, c = 50
To find the equation, we need to determine the change in c for every 1 unit change in t.
Change in c = c2 - c1 = 50 - 30 = 20
Change in t = t2 - t1 = 6 - 2 = 4
Now, we need to find the change in c for every 1 unit change in t:
Change in c per unit change in t = (Change in c) / (Change in t)
= 20 / 4
= 5
We have found that for every 1 unit change in t, c changes by 5. This means the relation between c and t is:
c = 5t + k
Now, we can substitute one of the given points to find the value of k.
When t = 2, c = 30:
30 = 5(2) + k
30 = 10 + k
k = 30 - 10
k = 20
We have found the value of k as 20, so the final relation between c and t is:
c = 5t + 20
To find c when t = 3, we can substitute t = 3 into the equation:
c = 5(3) + 20
c = 15 + 20
c = 35
Therefore, when t = 3, c equals 35.