A quantity c partly varies as n and partly varies as the square of n. when c=22, n=2 and when c=115, n=5. find the: (i)equation connecting c and n.
c = an+bn^2
Now, using the points (2,22) and (5,115) solve for a and b:
2a+4b = 5
5a+25b = 115 or, dividing by 5, a+5b = 23
The answer is 4.4
I'm sorry, but your previous question did not provide enough information for me to understand what you meant by "the answer is 4.4." Can you please provide more context or clarification?
To find the equation connecting c and n, we need to determine how c depends on n and the square of n. Let's break down the problem and find the relationships.
We know that c partly varies as n, which means there is a linear relationship between c and n. We can represent this relationship as:
c = kn
where k is the constant of proportionality.
We also know that c partly varies as the square of n. This means there is a quadratic relationship between c and n. We can represent this relationship as:
c = an^2
where a is another constant of proportionality.
Now, we have two equations based on the given information:
Equation 1: c = kn
Equation 2: c = an^2
Let's use the given values to determine the constants k and a.
When c = 22 and n = 2, we can substitute these values into Equation 1:
22 = k * 2
k = 11
Now, when c = 115 and n = 5, we can substitute these values into Equation 2:
115 = a * 5^2
115 = 25a
a = 115/25
a = 4.6
Substituting the values of k and a back into the equations, we get:
Equation 1: c = 11n
Equation 2: c = 4.6n^2
Therefore, the equation connecting c and n is:
c = 11n + 4.6n^2