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3 years ago

2x=10y Determine the constant of proportionality. Assume that y represents all of the outputs and x represents the inputs

Mathematics

1 answer:

Art [367]3 years ago

3 0

Answer:

a = 0.2

Step-by-step explanation:

Let y = ax be a linear equation, where x is the input variable and y is the output variable, then "a" is the proportionality constant between x and y.

To find the proportionality constant of the given equation, we must take it to the form y = ax.

We have:

2x = 10y

We divide both sides of the equation by 10.

0.2x = y

y = 0.2x.

Then the constant of proportionality is:

a = 0.2

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Answer:

Presumably you're solving for x here? Without further information we'll assume that.

With that in mind, x is approximately equal to 0.86 and -0.46

Step-by-step explanation:

Let's start by putting it in the usual ax² + bx + c format.

$5x^2- 2x = 2\\5x^2 - 2x - 2 = 0\\$

let's solve it. First we'll multiply both sides by five, making the first term a perfect square:

$25x^2 - 10x - 10 = 0\\$

Now we'll add 11 to both sides:

$25x^2 - 10x + 1 = 11\\$

Which makes the left side a perfect square:

$(5x - 1)^2 = 11$

And now we can solve for x:

$(5x - 1)^2 = 11\\\\5x - 1 = \sqrt{11} \\\\5x = 1 + \sqrt{11}\\\\x = \frac{1 + \sqrt{11}}{5}$

Note that there's no apparent way of drawing the ± symbol when editing equations, so take that + sign as actually being ±.

That gives us two answers:

$x = \frac{1 + \sqrt{11}}{5}\\\\x \approx \frac{1 + 3.32}5\\\\x \approx \frac{4.32}5\\\\x \approx 0.86$ $x = \frac{1 - \sqrt{11}}{5}\\\\x \approx \frac{1 - 3.32}5\\\\x \approx \frac{-2.32}5\\\\x \approx -0.46$

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