Two quantities M and N are such that M varies partly as the square of N.Determine the relationship between M and N given that when M=1050,N=10 and when M=1272,N=12
If If m varies partly as the square of n, then there must another constant part.
m = a + kn^2
Using the two points, we get
a + 100k = 1050
a + 144k = 1272
solve those to get (a,b) = (12000/22, 111/22)
an odd solution, unless there's a typo somewhere.
Apologies for the confusion. You are correct, if M varies partly as the square of N, then there must be another constant part. Let's rewrite the relationship as:
M = a + kN^2
where a is a constant.
Using the given values, we can form two equations:
1) When M = 1050 and N = 10:
1050 = a + k(10)^2
1050 = a + 100k
2) When M = 1272 and N = 12:
1272 = a + k(12)^2
1272 = a + 144k
Subtracting equation 1 from equation 2, we get:
1272 - 1050 = a + 144k - (a + 100k)
222 = 44k
k = 222/44
k = 5
Substituting the value of k back into equation 1, we can solve for a:
1050 = a + 100(5)
1050 = a + 500
a = 1050 - 500
a = 550
Therefore, the relationship between M and N is:
M = 550 + 5N^2
To determine the relationship between M and N, we can use the given information.
Let's denote the relationship between M and N as M = kN², where k is a constant.
Given that when M = 1050 and N = 10:
1050 = k * (10)²
1050 = k * 100
k = 1050 / 100
k = 10.5
Thus, the equation becomes M = 10.5N².
Now, let's verify this relationship using the second set of values:
Given that when M = 1272 and N = 12:
1272 = 10.5 * (12)²
1272 = 10.5 * 144
1272 = 1512
The equation holds true.
Therefore, the relationship between M and N is M = 10.5N².
If M varies partly as the square of N, we can write this relationship as:
M = kN^2
where k is a constant.
Using the given values, we can form two equations:
1) When M = 1050 and N = 10:
1050 = k(10)^2
1050 = 100k
2) When M = 1272 and N = 12:
1272 = k(12)^2
1272 = 144k
Dividing equation 2 equation by equation 1, we get:
1272/1050 = (144k)/(100k)
1.2114 = 1.44
This is not possible, so there must be an error in the given values or the assumption that M varies partly as the square of N might not be valid.