$$ 17 Q $$ is directly proportional to the square root of $$ d $$ $$ Q=4.5 $$ when $$ d=324 $$ Find a formula for $$ Q $$ in terms of $$ d $$

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UpStudy AI · Accepted Answer

To find a formula for $$ Q $$ in terms of $$ d $$, we start with the information given:

1. $$ 17Q $$ is directly proportional to $$ \sqrt{d} $$. This can be expressed mathematically as:
   $$
   17Q = k \sqrt{d}
   $$
   where $$ k $$ is the constant of proportionality.

2. We know that $$ Q = 4.5 $$ when $$ d = 324 $$. We can use this information to find the value of $$ k $$.

### Step 1: Substitute the known values into the equation

Substituting $$ Q = 4.5 $$ and $$ d = 324 $$ into the equation:
$$
17(4.5) = k \sqrt{324}
$$

### Step 2: Calculate $$ \sqrt{324} $$

Calculating $$ \sqrt{324} $$:
$$
\sqrt{324} = 18
$$

### Step 3: Substitute back to find $$ k $$

Now substituting this back into the equation:
$$
17(4.5) = k(18)
$$
Calculating $$ 17(4.5) $$:
$$
17(4.5) = 76.5
$$
So we have:
$$
76.5 = k(18)
$$

### Step 4: Solve for $$ k $$

Now, we can solve for $$ k $$:
$$
k = \frac{76.5}{18}
$$

Calculating $$ k $$:
$$
k = 4.25
$$

### Step 5: Write the formula for $$ Q $$

Now that we have $$ k $$, we can substitute it back into the original proportionality equation:
$$
17Q = 4.25 \sqrt{d}
$$

To express $$ Q $$ in terms of $$ d $$, we divide both sides by 17:
$$
Q = \frac{4.25 \sqrt{d}}{17}
$$

### Final Formula

Thus, the formula for $$ Q $$ in terms of $$ d $$ is:
$$
Q = \frac{4.25}{17} \sqrt{d}
$$

This can be simplified further if needed, but this is the required formula.
$$ Q = \frac{4.25}{17} \sqrt{d} $$

\( 17 Q \) is directly proportional to the square root of \( d \) \( Q=4.5 \) when \( d=324 \) Find a formula for \( Q \) in terms of \( d \)

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