Numerade

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5. Let x, y ∈ R" where x = (x1, x2,..., In), y = (Y1, Y2,, Yn). Define $$d_1(x,y) = Max_{1 \le i \le n}|x_i - y_i|$$ Show that d₁ is a metric on R". (8)

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A certain element has a mass per mole of 54.9380 g/mol. What is the mass of a single atom in (a) atomic mass units and (b) kilograms? (c) How many moles of atoms are in a 312-g sample? (a) $m_{atom}$ = 54.9380 u (b) $m_{atom}$ = kg (c) $n$ = 5.68 mol

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A decrease in interest rates will cause economic and inflation to • contraction; rise • expansion; rise • contraction; fall expansion; fall

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Vygotsky considered it to be important to learning a new skill: - private speech - abstract reasoning - concrete operations - self-efficacy

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2. Show that each equation is homogeneous. Then, solve the equation by substitution. (a) \frac{dy}{dx} = \frac{y - x}{y + x} (b) \frac{dy}{dx} = \frac{y^2 + yx}{x^2} (c) \frac{dy}{dx} = \frac{-y}{x(ln(x) - ln(y) - 1)}

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Question [1]: (20 Marks) Turbo-generator has maximum power of 60MW, efficiency of 50%, load factor of 0.4. Find the average power. to produce 1kwh it needed 860 Kcal/H, if the calorific value of coal is 6000 Kcal/Kg. Find the consumption of coal per KwH, per 24 hours. Question [2]: (20 Marks) The available flow of water for hydrostation is 260 m3/s under a head of 1.7m assuming the speed of turbine Is 50 r.p.m and the efticiency is 82.5%. determine the developed power of station, the number of units, if the approximate speed of tunbire is 890 rpm, the quality of energy. Question [3]: Find the released energy by one a.m.u in Mev if one a.m.u=1.66\cdot 10^{-27}g, speed of light=$3\cdot 10^8$ m/s, one joule=$6.24\cdot 10^{18}$ Mev.

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Blade Incorporated, a US-domiciled company, but operates largely in Peru. As their operations manager, you expect that the Peruvian Sol will depreciate against the dollar from its spot rate of $0.15 to $0.14 in 10 days. The following interbank lending and borrowing rates exist: Lending Rate Borrowing Rate U.S. dollar 8.0% 8.3% Mexican peso 8.5% 8.7% Assume that Blade Incorporated has a borrowing capacity of either $10 million or 70 million Sol in the interbank market, depending on which currency it wants to borrow. a. How could Blade attempt to capitalize on its expectations without using deposited funds? Estimate the profits that could be generated from this strategy. b. Assume all the preceding information with this exception: Blade expects the Sol to appreciate from its present spot rate of $0.15 to $0.17 in 30 days. How could it attempt to capitalize on its expectations without using deposited funds? Estimate the profits that could be generated from this strategy. In your memo, express why Blade should consider one of the options.

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Suppose that many people who earn a living growing pumpkins decide they can make more money selling t-shirts and switch occupations. How will this change affect the number of pumpkins supplied by producers? Choose one: A. supply increases B. supply does not change C. supply decreases

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(b) Prepare journal entries to record the above transactions. E8-2 Transactions follow for the Extreme Sports Ltd, store and three of its customers in the company's first month of business: June 3 Ben Kidd used his Extreme Sports credit card to purchase $1,050 of merchandise. 6 Biljana Pavic used her Extreme Sports credit card to purchase $840 of merchandise. 8 Biljana Pavic returned $210 of merchandise on credit. 9 Nicole Montpetit purchased $421 of merchandise and paid for it with Visa. Visa charges a 2% service fee. 18 Ben Kidd used his Extreme Sports credit card to purchase an additional $348 of merchandise. 19 Bonnie Cutcliffe used her debit card to purchase $230 of merchandise. There is a $0.50 service charge on all debit card transactions. 20 Biljana Pavic made a $315 payment on her credit card account. 23 Nicole Montpetit used her Extreme Sports credit card to purchase $498 of merchandise. 25 Ben Kidd paid the amount owing on his June 3 purchase. 30 Biljana Pavic used her Extreme Sports credit card to purchase $420 of merchandise. Instructions (a) Record the above transactions. Ignore any inventory or cost of goods sold entries for purposes of this question. (b) Set up T accounts for the Accounts Receivable general ledger (control) account and for the Accounts Receivable subsidiary ledger accounts. Post the journal entries to these accounts. (c) Prepare a list of customers and the balances of their accounts from the subsidiary ledger. Prove that the total of the subsidiary ledger is equal to the control account balance.

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5.10 Determine the forces in members BC, CH, and CG in the truss shown. Using the method of sections. 45 kN 60 kN 30 kN 3 m J I H G F 5 kN A B C D E 4 @ 4 m = 16 m 5.19 A pin-connected frame is loaded, as shown. Calculate the pin reactions at A, B, and C. Neglect the weights of the members. 20'-0" 12'-0" C D B 4 kips E 12'-0" 10'-0" 10'-0" 6 kips

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nicol-s m.