Given the relation C = 3/2 sqrt(f2 + 4P2Q), express f in terms of C, P, and Q.

Question

ScanSolve AI Tutor · Accepted Answer

Given the relation: C = 3/2 √(f² + 4P²Q) We need to express f in terms of C, P, and Q. Step 1: Multiply both sides by 2. 2C = 3 √(f² + 4P²Q) Step 2: Divide both sides by 3. 2C/3 = √(f² + 4P²Q) Step 3: Square both sides to eliminate the square root. (2C/3)² = f² + 4P²Q; (4C²)/(9) = f² + 4P²Q Step 4: Subtract 4P²Q from both sides to isolate f². f² = (4C²)/(9) − 4P²Q Step 5: Combine the terms on the right side by finding a common denominator. f² = (4C²)/(9) − (36P²Q)/(9); f² = (4C² − 36P²Q)/(9) Step 6: Take the square root of both sides to solve for f. f = ± √((4C² − 36P²Q)/(9)) Step 7: Simplify the expression by taking the square root of the denominator and factoring out 4 from the numerator inside the square root. f = ± (√(4(C² − 9P²Q)))/(√(9)); f = ± (2√(C² − 9P²Q))/(3); The final answer is f = ± (2√(C² − 9P²Q))/(3).

Given the relation C = (3)/(2) sqrt(f2 + 4P2Q), express f in terms of C, P, and Q.

Answer

Step-by-step solution

Multiply both sides by 2.

Divide both sides by 3.

Square both sides to eliminate the square root.

Subtract $4P^2Q$ from both sides to isolate $f^2$ .

Combine the terms on the right side by finding a common denominator.

Take the square root of both sides to solve for $f$ .

Simplify the expression by taking the square root of the denominator and factoring out 4 from the numerator inside the square root.

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