• ### Prove that 1^3 + ... + n^3 = (1 + ... + n)^2 ∀ n ∈ ℕ?

Prove that 1^3 + ... + n^3 = (1 + ... + n)^2 ∀ n ∈ ℕ (using PMI I assume). Thank you!
Prove that 1^3 + ... + n^3 = (1 + ... + n)^2 ∀ n ∈ ℕ (using PMI I assume). Thank you!
3 answers · Mathematics · 9 years ago
• ### Urgent! Probability of selecting 5 particular numbers from a range of 3 different sets?

A competition requires an entrant to select 2 numbers from row 1, 3 numbers from row 2 and 4 numbers from row 3. Row 1: 1, 2, 3, 4, 5, 6, 7 Row 2: 8, 9, 10, 11 ,12 ,13, 14 Row 3: 15, 16, 17, 18, 19, 20, 21 Determine the probability that a person selects the numbers 4, 9, 11, 13 and 21. The solutions say: P = [(1C1 x 6C1) x (3C3 x 4C0)... show more
A competition requires an entrant to select 2 numbers from row 1, 3 numbers from row 2 and 4 numbers from row 3. Row 1: 1, 2, 3, 4, 5, 6, 7 Row 2: 8, 9, 10, 11 ,12 ,13, 14 Row 3: 15, 16, 17, 18, 19, 20, 21 Determine the probability that a person selects the numbers 4, 9, 11, 13 and 21. The solutions say: P = [(1C1 x 6C1) x (3C3 x 4C0) x (1C1 x 6C3) ] / (7C2 x 7C3 x 7C4) = 120 / 25725 = 8 / 1715 I have an exam tomorrow and this is a question from a previous exam. My answer is different from the solutions and neither my teacher nor myself can figure out why my answer is wrong. Thanks.
1 answer · Mathematics · 9 years ago
• ### Calculating EMF, ε = NBAωsinωt vs. ε = -N(ΔΦ / Δt). My teacher can't figure it out, can you?

I have been studying two different texts which have introduced two different methods for calculating the EMF of a coil rotating in a magnetic field. One is simply Faraday's Law of Induction, ε = -N(ΔΦ / Δt), and the other is ε = NBAωsinωt which is obtained by differentiating Φ = NBAcosθ = NBAcosωt where ωt is the angular velocity (i.e.... show more
I have been studying two different texts which have introduced two different methods for calculating the EMF of a coil rotating in a magnetic field. One is simply Faraday's Law of Induction, ε = -N(ΔΦ / Δt), and the other is ε = NBAωsinωt which is obtained by differentiating Φ = NBAcosθ = NBAcosωt where ωt is the angular velocity (i.e. frequency x 2π). The problem is when I use the two different methods to answer the same question, I get two different answers. For example: A coil is rotated 10 times every second in a magnetic field of 0.250 T. The coil is rectangular with sides 50 cm by 40 cm. Determine the maximum EMF generated. Using ε = -N(ΔΦ / Δt) Φ = BA = (0.250)(0.5)(0.4) = 0.05 Wb T = 1 / f = 1 / 10 = 0.1 s T / 4 (max EMF occurs 4 times each revolution) = 0.1 / 4 = 0.025 s ε = -N(ΔΦ / Δt) = -1[(0.05 - 0) / 0.025] = -2 V (i.e. 2 V) Using ε = NBAωsinωt ε = NBAωsinωt = (1)(0.25)(0.5)(0.4)(10 x 2π)(sin[(10 x 2π) / (10 x 4)] ≈ 3.14 V Two different answers, what's going on. I think one of my textbooks is wrong. Thanks for any responses.
2 answers · Physics · 10 years ago
• ### Pressure variation vs. particle displacement wave graphs?

Can someone please explain why pressure nodes and antinodes are points of zero particle displacement, and why points of zero pressure variation are points of maximum particle displacement. I would have thought that pressure nodes and antinodes would correspond to points of maximum particle displacement but they don't. So my question is,... show more
Can someone please explain why pressure nodes and antinodes are points of zero particle displacement, and why points of zero pressure variation are points of maximum particle displacement. I would have thought that pressure nodes and antinodes would correspond to points of maximum particle displacement but they don't. So my question is, what is particle displacement, is it the displacement of a particle compared to its mean position before a wave passes through it, and, on a intermolecular level, what is the relationship between pressure variation and particle displacement. Thanks.
2 answers · Physics · 10 years ago
• ### Opinions of the Jackson Pro Series DK2M Dinky?

I'm looking to buy a guitar for playing mostly metal type songs and need it to have 24 frets, a floyd rose and a thin neck. I would like to spend around \$1000 AUD (~\$700 USD) but I can spend more. Tomorrow I am going out to look at guitars and will probably buy a guitar then as I have been looking around for a while. Based on internet research,... show more
I'm looking to buy a guitar for playing mostly metal type songs and need it to have 24 frets, a floyd rose and a thin neck. I would like to spend around \$1000 AUD (~\$700 USD) but I can spend more. Tomorrow I am going out to look at guitars and will probably buy a guitar then as I have been looking around for a while. Based on internet research, I am leaning towards the Jackson Pro Series DK2M Dinky in the Snow White colour (pending me actually playing it of course). For the price, I think it is definitely a good choice feature wise. It is Japanese made and boasts two Seymour Duncan humbuckers and I have read nothing but positive reviews so far. I am wondering if anybody owns or has played this guitar and can give me your opinion of it and how it rates against other guitars of similar price and features. Here's a pic of it, cool ain't it http://admin.jacksonguitars.com/images/p... Thanks.
3 answers · Rock and Pop · 10 years ago
• ### Ballistol aerosol mineral oil expiry date?

I just recently purchased a can of Ballistol aerosol mineral oil with the intended purpose of protecting my knife collection from rusting. It must have been sitting on the shelf for awhile because I just noticed it was produced in November 2003 and has a guarantee (which I assume means expiry date) to November 2006. Considering this guarantee date... show more
I just recently purchased a can of Ballistol aerosol mineral oil with the intended purpose of protecting my knife collection from rusting. It must have been sitting on the shelf for awhile because I just noticed it was produced in November 2003 and has a guarantee (which I assume means expiry date) to November 2006. Considering this guarantee date was over 3 years ago, will it still be safe to use on my knife collection, or should I go back to where I purchased it and see if I can get another can? Thanks for your responses.
3 answers · Maintenance & Repairs · 10 years ago
• ### The Chaser's War on Everything podcast downloads?

Does anybody know where I can find Chaser podcast downloads. They are in mp4 format and around 85 - 95 MB. The only Chaser episodes I can find on the net are around 250 MB and I don't have the bandwidth to download many episodes at this size. I have episodes 15 - 24 + the 3 specials so I need episodes 1 -14 of season 2 and even season 1 if... show more
Does anybody know where I can find Chaser podcast downloads. They are in mp4 format and around 85 - 95 MB. The only Chaser episodes I can find on the net are around 250 MB and I don't have the bandwidth to download many episodes at this size. I have episodes 15 - 24 + the 3 specials so I need episodes 1 -14 of season 2 and even season 1 if you can find them. The episodes I got were off the ABC website but it appears they have removed them all now. Does anybody know where I can find them, thanks for your responses.
3 answers · Comedy · 10 years ago
• ### Champagne bubbles when strawberries are added?

Today when champagne was being served someone asked me why it bubbled. I exclaimed that because the bottle had been opened and thus the air pressure above the champagne solution had been decreased which causes the solubility of gases to decrease in solution and thus the carbon dioxide to bubble out. I also said that this would also occur as the... show more
Today when champagne was being served someone asked me why it bubbled. I exclaimed that because the bottle had been opened and thus the air pressure above the champagne solution had been decreased which causes the solubility of gases to decrease in solution and thus the carbon dioxide to bubble out. I also said that this would also occur as the temperature of the champagne increased. Then someone placed a piece of strawberry in their champagne which caused it to bubble profusely and someone asked me why and I didn't really know. Why did this happen? A chemical reaction of some sort maybe? Pretty stupid question I know but I'm just a bit curious. Thank you for your responses.
3 answers · Chemistry · 10 years ago
• ### Opinions of the Cold Steel Magnum Tanto?

I'm thinking of purchasing a Cold Steel Magnum Tanto IX (9" blade, 14 5/8" overall) and was wondering if anyone has any opinions on the knife. Is it good or bad? Does it hold a point and an edge as well as their over the top promotional videos make out? Just how sharp is it, razor sharp? Have you had any experience with rusting,... show more
I'm thinking of purchasing a Cold Steel Magnum Tanto IX (9" blade, 14 5/8" overall) and was wondering if anyone has any opinions on the knife. Is it good or bad? Does it hold a point and an edge as well as their over the top promotional videos make out? Just how sharp is it, razor sharp? Have you had any experience with rusting, discolouring, chipping, cracking or rotting with the blade or handle? Also, is the leather sheath of good quality. Does anybody have a preference on blade size and why?. I was thinking of getting the IX because it is the only size I can get a hold of at a reasonable price. I should probably add that I intend to purchase this knife as more of a collectible than a tool, although I will probably occasionally use it. Thank you to all responses, I heard Cold Steel knives are of very high quality but I'm asking just to make sure.
4 answers · Hunting · 10 years ago