The fourth proportional to st⁵, s²t³, and s³t² (where s and t are non-zero) is:
2024
The fourth proportional to st⁵, s²t³, and s³t² (where s and t are non-zero) is:
Answer: D. s⁴ — ConceptIf a : b = c : d, then d is the fourth proportional to a, b, and c. Cross-multiplication gives ad = bc, so d = bc/a when a is non-zero. ApplicationTake…
- A.
s
- B.
s²
- C.
s³
- D.
s⁴
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Correct answer: D
Concept
If a : b = c : d, then d is the fourth proportional to a, b, and c.
Cross-multiplication gives ad = bc, so d = bc/a when a is non-zero.
Application
Take a = st⁵, b = s²t³, and c = s³t².
Substitute into d = bc/a: d = (s²t³)(s³t²)/(st⁵).
Combine like bases in the numerator: d = s⁵t⁵/(st⁵).
Subtract exponents while dividing: d = s⁵⁻¹t⁵⁻⁵ = s⁴.
Cross-check
Using d = s⁴, the two ratios are st⁵/(s²t³) = t²/s and s³t²/s⁴ = t²/s.
They are equal, so s⁴ is the required fourth proportional.