Because 18n = 45k → 2n = 5k → n = 5a, k = 2a → θ = 18×5a = 90a → so only multiples of 90.

Why 18n = 45k Implies Only Multiples of 90: A Simple Mathematical Breakdown

When solving equations involving variables, especially in algebra, understanding the chain of logic can clarify their implications. One such equation—18ₙ = 45ₖ—may seem straightforward, but unpacking it reveals deeper relationships that define specific values. Let’s explore step-by-step why this equation leads uniquely to θ = 90a, meaning only multiples of 90 are valid solutions.

The Equation: 18ₙ = 45ₖ

Understanding the Context

This notation expresses a proportional relationship between two expressions: 18 times the unknown variable n, and 45 times another unknown variable k. At first glance, the equation seems symbolic, but we can simplify it through algebraic manipulation.

Step 1: Simplify 18ₙ = 45ₖ

Although written with superscripts (often used for exponents), here n and k represent variables, so 18ₙ means 18 times n, and 45ₖ means 45 times k. Thus, the equation becomes:

. For n = −(2k + 1)/2, k ℕ 0 the real part of the volume (51) equals ...

Image Gallery

2. an=n+7n25+4n2 b. ∫n=1∞[n(n+1)3+3n2−2n] | Chegg.com

Solved Let an=n2+n+18n. We would like to prove that an→0 as | Chegg.com

Solved 8. ∑n=0∞2n+57n a) The name of the method hth term | Chegg.com

Key Insights

18n = 45k

Step 2: Reduce the Equation

We simplify 18n = 45k by dividing both sides by the greatest common divisor of 18 and 45, which is 9:

(18n ÷ 9) = (45k ÷ 9)
→ 2n = 5k

🔗 Related Articles You Might Like:

📰 Discover 7 Hidden Word Wonders Every Writer Needs To Master! 📰 Secrets Behind These 9 Word Wonders Everyone Should Know Today! 📰 You Wont Believe What Wo Mic Cost Me—Youll Regret Not Checking This Out! 📰 You Wont Believe What This Slurp Juice Does To Your Taste Buds 6282903 📰 Red Lot Rage This Parking Spot Will Haunt You Forever 6977139 📰 La Prensa De Nicaragua 3699076 📰 You Wont Believe What Happened When Vts Stock Took Off Like A Rocketheres How 9398426 📰 785 Cm 7783277 📰 5 Stop Forgetting Where You Wentinside The Best Selling Trip Notebook Today 8460498 📰 The Untold Truth About Granville Ohio Shocking Revelations No One Wants To Share 4213810 📰 Pay My Credit Card 2193709 📰 Unifi Connect Unleashed The Ultimate Way To Streamline Your Smart Home 5412806 📰 5Fr Fidelity 401K Rollover Address Exposedavoid These Costly Errors Now 1182046 📰 Jollof Bowl 3700736 📰 Hqpotner Hacks How This Must Have Gadget Boosts Your Workout Game 8994041 📰 Internal Medicine Vs Family Medicine 562750 📰 Dodgers Vs Diamondbacks Tickets 4124649 📰 Betting On Sudden Twists Free Murder Mystery Games Online You Can Play Instantly 358819

Final Thoughts

This reduced form reveals a direct proportional relationship between n and k. Because 2 and 5 have no common factors, n must increase in multiples of 5 and k in multiples of 2 to maintain the equality.

Step 3: Express One Variable in Terms of a Shared Parameter

From 2n = 5k, solve for n:

n = (5k) / 2

For n to be an integer, k must be even. Let k = 2a (where a is any positive integer). Substituting:

n = (5 × 2a) / 2 = 5a

Step 4: Solve for θ (or θ = 18n)

Earlier, we derived θ = 18n. Substituting n = 5a: