X partly constant and partly varies as y when x =7,y=3 when x =9 and y =6
(a) find the relationship equation between x and y
(b) find x when y=4
x = c + ky
When x=7, y=3
7 = c + 3k
when x = 9, y = 6
9 = c + 6k
subtract them,
2 = 3k
k = 2/3
sub into the first equation: 7 = c + 3k
c = 7 - 3(2/3) = 7 - 2 = 5
x = 5 + (2/3)y
sub in y = 4 to find x
X=5+2/3×4+4=23/3
5.6666666667
Yes, the decimal approximation for 23/3 is 7.6666666667, which rounds to 5.6666666667 when rounded to ten decimal places.
(a) To find the relationship equation between x and y, we need to determine the constant part and the varying part.
Let's first look at the constant part.
When x = 7 and y = 3, we have:
7 = constant part + 3
constant part = 7 - 3
constant part = 4
Now let's look at the varying part.
When x = 9 and y = 6, we have:
9 = constant part + 6
constant part = 9 - 6
constant part = 3
So, the constant part is 3.
Now that we have both the constant part and the varying part, we can form the relationship equation:
x = constant part + (varying part * y)
x = 3 + 4y
Therefore, the relationship equation between x and y is x = 3 + 4y.
(b) To find x when y = 4, we can substitute y = 4 into the relationship equation we found in part (a):
x = 3 + 4 * y
x = 3 + 4 * 4
x = 3 + 16
x = 19
So, when y = 4, x is equal to 19.
To find the relationship equation between x and y, we need to examine how x and y change together.
From the given information, we can observe that as x changes from 7 to 9, y changes from 3 to 6. This suggests that for every increase in x by 2 units, y increases by 3 units.
Now let's find the constant and variable parts of x.
The constant part is the value of x when y does not change. In this case, when y is 3 and x is 7, the constant part of x is 7.
The variable part is the change in x corresponding to the change in y. From the given information, as y increases from 3 to 6, x increases from 7 to 9. This means that the variable part of x is 2.
Therefore, the relationship equation between x and y is:
x = constant + variable * y
Substituting the values we found:
x = 7 + 2 * y
Next, to find x when y = 4, we can substitute y = 4 into the relationship equation:
x = 7 + 2 * 4
x = 7 + 8
x = 15
So, when y = 4, x = 15.