X is partly constant and partly varies with y wheny=3,x=11,and when y=4 x=14.(a)find the relationship between x and y (b)find the x when y=10.
C=a+kt
Y=c+kx
3=c+11k
4=c+14k
C+11k=3
C+14k=4
+25k/25=7/25
K=0.28
Relationship=y=c+kx
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I don't understand
I don't understand
Given, X is partly constant and partly varies with y.
When y=3, x=11 and when y=4, x=14.
Let's find the constant part and the part that varies with y.
Let, X = k + a*y
where, k = constant part
a = part that varies with y
Using the first set of values, we get
11 = k + 3a ---(1)
Using the second set of values, we get
14 = k + 4a ---(2)
Solving (1) and (2) simultaneously,
k = 2
a = 3
Therefore, the relationship between x and y is given by:
X = 3y + 2
To find the value of x when y=10,
X = 3*10 + 2 = 32.
a = ay+b
Using the two points,
3a+b=11
4a+b=14
so, a=3, b=2
x = 3y+2
x(10) = 32