Question

Question #f7758

Answer 1

`y = 11.5`
We can know if something is a direct variation, if both the quantities increase or decrease simultaneously.

Explanation:

`y` varies directly with `x`

Direct variation means: When the value of `x`increases, the value of `y` also increases, and vice versa, i.e. the values of both the variables will increase or decrease simultaneously.

Writing with proportionality sign: `x prop y`

When the proportionality sign is replaced by equal- to sign, a proportionality constant is to be multiplied:

`x = a xxy` .... where `a` is proportionality constant.

Given : y=5 when x=160,

`=> x = a y`
OR
`y = x/a`

We will first calculate the value of proportionality constant from above equation:
`=> a= x/y`

`=> a =160/5 = 32`

Asked :what is `y` when `x=368` ?

`y = x/a = 368 / 32= 11.5`

We can see that as the value of `x` increased, the value of `y` also increased.
Hence we can know if something is a direct variation by observing the variation proportionality.

When the value of one variable decreases with increase in value of other (and vice versa), it is inverse variation. Ex: If the speed of a vehicle is more, the time taken to cover a certain distance is less. Here Speed and time are the variables which are inversely proportional.

Answer 2

`y=11.5`

Explanation:

`"the initial statement is "ypropx`

`"to convert to an equation multiply by k the constant"`
`"of variation"`

`rArry=kx`

`"to find k use the given condition"`

`y=5" when "x=160`

`y=kxrArrk=y/x=5/160=1/32`

`"equation is " color(red)(bar(ul(|color(white)(2/2)color(black)(y=x/32)color(white)(2/2)|)))`

`"when "x=368`

`y=368/32=11.5`