QuestionGiven $y$ varies inversely with $x$ and $y=-\frac{3}{2}$ when $x=-8$ , find the equation and $y$ when $x=6$ . $y =$

Studdy Solution

STEP 1

Assumptions1. $y$ varies inversely with $x$ . . $y=-\frac{3}{}$ when $x=-8$ .
3. The inverse variation equation is of the form $y = \frac{k}{x}$ , where $k$ is the constant of variation.

STEP 2

First, we need to find the constant of variation $k$ . We can do this by rearranging the inverse variation equation and plugging in the given values for $x$ and $y$ .
$k = y \times x$

STEP 3

Now, plug in the given values for $x$ and $y$ to calculate $k$ .
$k = -\frac{3}{2} \times -8$

STEP 4

Calculate the constant of variation $k$ .
$k = -\frac{3}{2} \times -8 =12$

STEP 5

Now that we have the constant of variation, we can write the inverse variation equation that relates $x$ and $y$ .
$y = \frac{k}{x}$

STEP 6

Plug in the value for $k$ to write the inverse variation equation.
$y = \frac{12}{x}$ This is the inverse variation equation that relates $x$ and $y$ .

STEP 7

Now, we can use this equation to find $y$ when $x=6$ . Plug in the value for $x$ into the equation.
$y = \frac{12}{6}$

STEP 8

Calculate the value of $y$ .
$y = \frac{12}{6} =2$ So, when $x=6$ , $y=2$ .

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QuestionGiven $y$ varies inversely with $x$ and $y=-\frac{3}{2}$ when $x=-8$ , find the equation and $y$ when $x=6$ . $y =$

Studdy Solution

STEP 1

Assumptions1. $y$ varies inversely with $x$ . . $y=-\frac{3}{}$ when $x=-8$ .
3. The inverse variation equation is of the form $y = \frac{k}{x}$ , where $k$ is the constant of variation.

STEP 2

First, we need to find the constant of variation $k$ . We can do this by rearranging the inverse variation equation and plugging in the given values for $x$ and $y$ .
$k = y \times x$

STEP 3

Now, plug in the given values for $x$ and $y$ to calculate $k$ .
$k = -\frac{3}{2} \times -8$

STEP 4

Calculate the constant of variation $k$ .
$k = -\frac{3}{2} \times -8 =12$

STEP 5

Now that we have the constant of variation, we can write the inverse variation equation that relates $x$ and $y$ .
$y = \frac{k}{x}$

STEP 6

Plug in the value for $k$ to write the inverse variation equation.
$y = \frac{12}{x}$ This is the inverse variation equation that relates $x$ and $y$ .

STEP 7

Now, we can use this equation to find $y$ when $x=6$ . Plug in the value for $x$ into the equation.
$y = \frac{12}{6}$

STEP 8

Calculate the value of $y$ .
$y = \frac{12}{6} =2$ So, when $x=6$ , $y=2$ .

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QuestionGiven yyy varies inversely with xxx and y=−32y=-\frac{3}{2}y=−23​ when x=−8x=-8x=−8, find the equation and yyy when x=6x=6x=6. y= y = y=

Studdy Solution

STEP 1

Assumptions1. yyy varies inversely with xxx. . y=−3y=-\frac{3}{}y=−3​ when x=−8x=-8x=−8.3. The inverse variation equation is of the form y=kxy = \frac{k}{x}y=xk​, where kkk is the constant of variation.

STEP 2

First, we need to find the constant of variation kkk. We can do this by rearranging the inverse variation equation and plugging in the given values for xxx and yyy.k=y×xk = y \times xk=y×x

STEP 3

Now, plug in the given values for xxx and yyy to calculate kkk.k=−32×−8k = -\frac{3}{2} \times -8k=−23​×−8

STEP 4

Calculate the constant of variation kkk.k=−32×−8=12k = -\frac{3}{2} \times -8 =12k=−23​×−8=12

STEP 5

Now that we have the constant of variation, we can write the inverse variation equation that relates xxx and yyy.y=kxy = \frac{k}{x}y=xk​

STEP 6

Plug in the value for kkk to write the inverse variation equation.y=12xy = \frac{12}{x}y=x12​This is the inverse variation equation that relates xxx and yyy.

STEP 7

Now, we can use this equation to find yyy when x=6x=6x=6. Plug in the value for xxx into the equation.y=126y = \frac{12}{6}y=612​

STEP 8

Calculate the value of yyy.y=126=2y = \frac{12}{6} =2y=612​=2So, when x=6x=6x=6, y=2y=2y=2.

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QuestionGiven $y$ varies inversely with $x$ and $y=-\frac{3}{2}$ when $x=-8$ , find the equation and $y$ when $x=6$ . $y =$

Assumptions1. $y$ varies inversely with $x$ . . $y=-\frac{3}{}$ when $x=-8$ .
3. The inverse variation equation is of the form $y = \frac{k}{x}$ , where $k$ is the constant of variation.

First, we need to find the constant of variation $k$ . We can do this by rearranging the inverse variation equation and plugging in the given values for $x$ and $y$ .
$k = y \times x$

Now, plug in the given values for $x$ and $y$ to calculate $k$ .
$k = -\frac{3}{2} \times -8$

Calculate the constant of variation $k$ .
$k = -\frac{3}{2} \times -8 =12$

Now that we have the constant of variation, we can write the inverse variation equation that relates $x$ and $y$ .
$y = \frac{k}{x}$

Plug in the value for $k$ to write the inverse variation equation.
$y = \frac{12}{x}$ This is the inverse variation equation that relates $x$ and $y$ .

Now, we can use this equation to find $y$ when $x=6$ . Plug in the value for $x$ into the equation.
$y = \frac{12}{6}$

Calculate the value of $y$ .
$y = \frac{12}{6} =2$ So, when $x=6$ , $y=2$ .