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a) The first comic book is of shakitman was sold in 1938. In 2010, the estimated price for this comic book in good condition was about $500,000. This represented a return of 25 percent per year. For this to be true, what must the comic book have sold for when new?b) Assume you want to buy a new house. You presently have $15,000 and you need to have $21,750 for the down payment and closing costs. If you can earn 7% per year, how long will it be before you have more money for the down payment and closing costs?
1) Find the maxima and minima of f(x,y,z) = 2x + y -3z subject to the constraint 2x^2+y^2+2z^2=1 2) Compute the work done by the force ?eld F(x,y,z) = x^2I + y j +y k in moving
Mathematical Formulae (a + b) 2 = a 2 + b 2 + 2ab (a - b) 2 = a 2 + b 2 - 2ab (a + b) 2 +
A leap year has 366 days, therefore 52 weeks i.e. 52 Sunday and 2 days. The remaining 2 days may be any of the following : (i) Sunday and Monday (ii) Monday and Tuesday (iii)
Calculate the volume and surface area of a cube: Calculate the volume and surface area of a cube with a = 3". Be sure to involved units in your answer. Solution: V =
Heaviside or step function limit : Calculates the value of the following limit. Solution This function is frequently called either the Heaviside or step function. We
There is a number. If the sum of digits is 14, and if 29 is subtracted from the number, the digits become equal. Find the number.
If 7sin 2 ?+3cos 2 ? = 4, show that tan? = 1/√3 . Ans: If 7 Sin 2 ? + 3 Cos 2 ? = 4 S.T. Tan? 1/√3 7 Sin 2 ? + 3 Cos 2 ? = 4 (Sin 2 ? + Cos 2 ?)
1. Construct a grammar G such that L(G) = L(M) where M is the PDA in the previous question. Then show that the word aaaabb is generated by G. 2. Prove, using the Pumping Lemma f
Determine the domain of each of the following functions. f( x ) = x - 4 / x 2 - 2 x -15 Solution With this problem we have to avoid division by
2x^3+5x^2+2x+5
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