Question #f7758

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Question #f7758

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Answer 1 · 2017-12-18T07:01:19

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

Explanation:

$y$ $y$ varies directly with $x$ $x$

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

Writing with proportionality sign: $x \propto y$ $x prop y$

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

$x = a \times y$ $x = a xxy$ .... where $a$ $a$ is proportionality constant.

Given : y=5 when x=160,

$\Rightarrow x = a y$ $=> x = a y$
OR
$y = \frac{x}{a}$ $y = x/a$

We will first calculate the value of proportionality constant from above equation:
$\Rightarrow a = \frac{x}{y}$ $=> a= x/y$

$\Rightarrow a = \frac{160}{5} = 32$ $=> a =160/5 = 32$

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

$y = \frac{x}{a} = \frac{368}{32} = 11.5$ $y = x/a = 368 / 32= 11.5$

We can see that as the value of $x$ $x$ increased, the value of $y$ $y$ 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 · 2017-12-18T09:26:38

$y = 11.5$ $y=11.5$

Explanation:

$the initial statement is y \propto x$ $"the initial statement is "ypropx$

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

$\Rightarrow y = k x$ $rArry=kx$

$to find k use the given condition$ $"to find k use the given condition"$

$y = 5 when x = 160$ $y=5" when "x=160$

$y = k x \Rightarrow k = \frac{y}{x} = \frac{5}{160} = \frac{1}{32}$ $y=kxrArrk=y/x=5/160=1/32$

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

$"when "x=368$

$y=368/32=11.5$

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