A request to express one letter in terms of the others means rearrange a formula, not plugging in numbers. Treat the other letters as fixed and use inverse operations: clear the denominator and coefficient before undoing the target’s power. For a physical length, keep the nonnegative root; taking one square root of a fourth power stops too early.
Hints
- Hint 1
To isolate a variable means to leave it alone on one side. Here is under the product . Which operation removes that denominator from the whole right side?
- Hint 2
After you remove the denominator, still multiplies the fourth power of the radius. Divide both sides by first; then an inverse operation can undo the fourth power.
- Hint 3
A fourth root undoes raising a number to the fourth power. Positive and negative numbers can have the same fourth power, but a pipe’s radius is nonnegative. Which root fits?
Step-by-step
Isolate the radius by hand
Step 1Clear the denominator
No Desmos needed. The answer must be a formula in letters, so rearrange it by hand. A pipe has nonzero length, so multiply both sides of the given equation by :
- Step 2
Get the fourth power alone
Since multiplies , divide both sides by (assuming ):
- Step 3
Undo the fourth power
A fourth root undoes a fourth power. Both positive and negative numbers can have the same fourth power, but a pipe radius is nonnegative, so take the nonnegative fourth root:
That expresses the pipe radius in terms of , , and . Choice B.