x is partly constant and partly varies as y .when y=5,x =7;and when y=7 x=8.find the law of variation and also x when y=11
x = ky+m
7 = 5k+m
8 = 7k+m
so, k = 1/2 and m = 9/2
...
x=a and x=ky
[x=a+ky]
when x=7 ,y=5
x=a+ky
7=a+5k
a+5k=7 eqn [1]
when x=8,y=7
x=a+ky
8=a+7k
a+7k=8
subtract eqn 1 from eqn 2
a-a+7k-5k=8-7
2k=1
k=1\2
substitute k=1\2 in eqn 1
a+5k=7
a+5[1/2]=7
a+5/2=7
a=7-5/2
a=14-5/2
a=9/2
[x=9/2+1/2]
find x when y=11
x=9/2+1/2[11]
x=9/2+11/2
x=9+11/2
x=20/2
x=10
This is so helpful...
Well, it seems x can't make up its mind, being partly constant and partly varying as y! It's like an indecisive character in a sitcom.
Anyway, let's talk about the law of variation - based on the given information, we can determine that x increases by 1 as y increases by 2. So, we can say x = y/2 + 5/2.
Now, to find x when y = 11. Let's plug in the value of y into our equation:
x = 11/2 + 5/2 = 8.
So, when y is 11, x turns into an 8. Just like that, it couldn't resist switching things up again!
To find the law of variation between x and y, we can use the given information and create an equation. Let's assume that x varies as y and is partly constant.
When y = 5, x = 7. This means that there is a constant component of x when y is 5, which we'll call "c". So we can write the equation as x = c + ky, where k represents the variable part of the variation.
Substituting the given values, we have 7 = c + 5k.
When y = 7, x = 8. We can use this information to find the values of c and k. Substituting these values in the equation, we get 8 = c + 7k.
Now, we have a system of two equations:
7 = c + 5k
8 = c + 7k
We can solve this system to find the values of c and k.
Subtracting the first equation from the second equation, we get:
8 - 7 = (c + 7k) - (c + 5k)
1 = 2k
k = 1/2
Substituting k = 1/2 into the first equation, we get:
7 = c + 5(1/2)
7 = c + 5/2
7 - 5/2 = c
(14/2) - (5/2) = c
9/2 = c
c = 9/2
Therefore, the equation of variation between x and y is x = (9/2) + (1/2)y.
To find x when y = 11, substitute y = 11 into the equation:
x = (9/2) + (1/2)(11)
x = (9/2) + (11/2)
x = (9 + 11)/2
x = 20/2
x = 10
So, when y = 11, x = 10.