Solved on Mar 06, 2024

Find $y$ when $x$ is inversely proportional to $\sqrt{x}$ and $y=79$ when $x=625$ , given $x=390625$ . (Round to nearest hundredth)

STEP 1

Assumptions
1. The variable $y$ is inversely proportional to the square root of $x$ .
2. The value of $y$ is 79 when $x$ is 625.
3. We need to find the value of $y$ when $x$ is 390625.

STEP 2

Since $y$ is inversely proportional to the square root of $x$ , we can write this relationship as:
$y = \frac{k}{\sqrt{x}}$
where $k$ is the constant of proportionality.

STEP 3

We will use the given values of $y$ and $x$ to find the constant of proportionality $k$ .
$79 = \frac{k}{\sqrt{625}}$

STEP 4

Calculate the square root of 625.
$\sqrt{625} = 25$

STEP 5

Substitute the square root of 625 into the equation to find $k$ .
$79 = \frac{k}{25}$

STEP 6

Multiply both sides of the equation by 25 to solve for $k$ .
$79 \times 25 = k$

STEP 7

Calculate the value of $k$ .
$k = 79 \times 25 = 1975$

STEP 8

Now that we have the value of $k$ , we can use it to find $y$ when $x$ is 390625.
$y = \frac{1975}{\sqrt{390625}}$

STEP 9

Calculate the square root of 390625.
$\sqrt{390625} = 625$

STEP 10

Substitute the square root of 390625 into the equation to find $y$ .
$y = \frac{1975}{625}$

STEP 11

Divide 1975 by 625 to calculate the value of $y$ .
$y = \frac{1975}{625} = 3.16$
The value of $y$ when $x$ is 390625 is approximately 3.16 (rounded to the nearest hundredth).

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Find $y$ when $x$ is inversely proportional to $\sqrt{x}$ and $y=79$ when $x=625$ , given $x=390625$ . (Round to nearest hundredth)

STEP 1

Assumptions
1. The variable $y$ is inversely proportional to the square root of $x$ .
2. The value of $y$ is 79 when $x$ is 625.
3. We need to find the value of $y$ when $x$ is 390625.

STEP 2

Since $y$ is inversely proportional to the square root of $x$ , we can write this relationship as:
$y = \frac{k}{\sqrt{x}}$
where $k$ is the constant of proportionality.

STEP 3

We will use the given values of $y$ and $x$ to find the constant of proportionality $k$ .
$79 = \frac{k}{\sqrt{625}}$

STEP 4

Calculate the square root of 625.
$\sqrt{625} = 25$

STEP 5

Substitute the square root of 625 into the equation to find $k$ .
$79 = \frac{k}{25}$

STEP 6

Multiply both sides of the equation by 25 to solve for $k$ .
$79 \times 25 = k$

STEP 7

Calculate the value of $k$ .
$k = 79 \times 25 = 1975$

STEP 8

Now that we have the value of $k$ , we can use it to find $y$ when $x$ is 390625.
$y = \frac{1975}{\sqrt{390625}}$

STEP 9

Calculate the square root of 390625.
$\sqrt{390625} = 625$

STEP 10

Substitute the square root of 390625 into the equation to find $y$ .
$y = \frac{1975}{625}$

STEP 11

Divide 1975 by 625 to calculate the value of $y$ .
$y = \frac{1975}{625} = 3.16$
The value of $y$ when $x$ is 390625 is approximately 3.16 (rounded to the nearest hundredth).

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Find yyy when xxx is inversely proportional to x\sqrt{x}x​ and y=79y=79y=79 when x=625x=625x=625, given x=390625x=390625x=390625. (Round to nearest hundredth)

STEP 1

Assumptions1. The variable yyy is inversely proportional to the square root of xxx.2. The value of yyy is 79 when xxx is 625.3. We need to find the value of yyy when xxx is 390625.

STEP 2

Since yyy is inversely proportional to the square root of xxx, we can write this relationship as:y=kxy = \frac{k}{\sqrt{x}}y=x​k​where kkk is the constant of proportionality.

STEP 3

We will use the given values of yyy and xxx to find the constant of proportionality kkk.79=k62579 = \frac{k}{\sqrt{625}}79=625​k​

STEP 4

Calculate the square root of 625.625=25\sqrt{625} = 25625​=25

STEP 5

Substitute the square root of 625 into the equation to find kkk.79=k2579 = \frac{k}{25}79=25k​

STEP 6

Multiply both sides of the equation by 25 to solve for kkk.79×25=k79 \times 25 = k79×25=k

STEP 7

Calculate the value of kkk.k=79×25=1975k = 79 \times 25 = 1975k=79×25=1975

STEP 8

Now that we have the value of kkk, we can use it to find yyy when xxx is 390625.y=1975390625y = \frac{1975}{\sqrt{390625}}y=390625​1975​

STEP 9

Calculate the square root of 390625.390625=625\sqrt{390625} = 625390625​=625

STEP 10

Substitute the square root of 390625 into the equation to find yyy.y=1975625y = \frac{1975}{625}y=6251975​

STEP 11

Divide 1975 by 625 to calculate the value of yyy.y=1975625=3.16y = \frac{1975}{625} = 3.16y=6251975​=3.16The value of yyy when xxx is 390625 is approximately 3.16 (rounded to the nearest hundredth).

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Find $y$ when $x$ is inversely proportional to $\sqrt{x}$ and $y=79$ when $x=625$ , given $x=390625$ . (Round to nearest hundredth)

Assumptions
1. The variable $y$ is inversely proportional to the square root of $x$ .
2. The value of $y$ is 79 when $x$ is 625.
3. We need to find the value of $y$ when $x$ is 390625.

Since $y$ is inversely proportional to the square root of $x$ , we can write this relationship as:
$y = \frac{k}{\sqrt{x}}$
where $k$ is the constant of proportionality.

We will use the given values of $y$ and $x$ to find the constant of proportionality $k$ .
$79 = \frac{k}{\sqrt{625}}$

Calculate the square root of 625.
$\sqrt{625} = 25$

Substitute the square root of 625 into the equation to find $k$ .
$79 = \frac{k}{25}$

Multiply both sides of the equation by 25 to solve for $k$ .
$79 \times 25 = k$

Calculate the value of $k$ .
$k = 79 \times 25 = 1975$

Now that we have the value of $k$ , we can use it to find $y$ when $x$ is 390625.
$y = \frac{1975}{\sqrt{390625}}$

Calculate the square root of 390625.
$\sqrt{390625} = 625$

Substitute the square root of 390625 into the equation to find $y$ .
$y = \frac{1975}{625}$

Divide 1975 by 625 to calculate the value of $y$ .
$y = \frac{1975}{625} = 3.16$
The value of $y$ when $x$ is 390625 is approximately 3.16 (rounded to the nearest hundredth).