1. Factor a trinomial whose leading coefficient is 1. Pick any one of the problems and solve the trinomial. If the trinomial is prime, state this and explain why. a. x2+8x+15 b. x2–4x –5 c. x2–14x+45 2.
Find a symbolic representation of the inverse function of each of the following: a) [pic] b) [pic] c) [pic] d) [pic] e) [pic] f) [pic] 5. Use the table in #2d to find the following: a) [pic] b) [pic] c) [pic] d) [pic] 6. Use the graph of the function f on the right to sketch a graph of its inverse. 7. Say a function y = g(x) models the birth rate x years after 1990.
Begin by writing the corresponding linear equations, and then use back-substitution to solve your variables. 10–1301–8001 159–1 x,y,z=( , , ) 10–1301–8001 159–1 = x-13z=15y-8z=9z=-1 = x-13(-1)=15y-8(-1)=9z=-1 = x=2y=1z=-1 x,y,z=(2 , 1 , -1) Determinants and Cramer’s Rule: 2. Find the determinant of the given matrix. 8–2–12 8–2–12 = 8*2 - (-1)(-2) = 16 - 2 = 14 3. Solve the given linear system using Cramer’s rule.
Located on page 304, problem #90 states, “P dollars is invested at annual interest rate r for 1 year. If the interest is compounded the polynomial P(1+r/2)2 represents the value of the investment after 1 year.” (Dugopolski, 2012, p.304) For the first part rewrite the expression without parenthesis. This would require the use of FOIL, which means multiply First, Outer, Inner, Last. Do this to the binomial (1+r/2)2 and then multiply all of the terms by P. The following is an example: P(1+r/2)2 This is the original expression with the exponent ONLY with the binomial. P(1+r/2)(1+r/2) Next step is to multiply the squared quantity.
Given the following cash flow stream at the end of each year: Year 1: $4,000 Year 2: $2,000 Year 3: 0 Year 4: -$1,000 Using a 10% discount rate, the present value of this cash flow stream is: a. $4,606 b. $3,415 c. $3,636 d. Other 8. Consider a 10-year annuity that promises to pay out $10,000 per year, given this is an ordinary annuity and that an investor can earn 10% on her money, the future value of this annuity, at the end of 10 years, would be: a. $175,312 b.
Write assignment statements that perform the following operations with the variables a, b, and c. a) Adds 2 to a and stores the result in b * b=a+2 b) Multiplier b times 4 and stores the result in a * a=b*4 c) Divides a by 3.14 and stores the result in b * b=a/3.14 d) Subtract 8 from b and stores the result in a * a=b-8 4. Assume the variables result, w, x, y, and z are all integers, and that w=5, x=4, y=8, and z=2. What value will be stored in result in each of the following statements? a) Set result = x + y * 12= x + y b) Set result = z + 2 * 4=z * 2 c) Set result = y / x * 2=y / x d) Set result =y – z * b=y – z 5. Write a pseudocode statement that declares the variable cost so it can hold real numbers.
3. 3. Generate all the PIs of f, {Pj} Generate all the Generate all the minterms of f, {mi} Generate all the Build the Boolean constraint matrix B, where Bij iis 1 if s Boolean mi∈ Pj and is 0 otherwise 4. Solve the minimum column covering problem for B 4. Solve ENEE 644 2 Example: Quine-McCluskey Method Example: Quine f(w,x,y,z) = x’y’ + wxy + x’yz’ + wy’z wxy x’y’ x’z’ wx’y’z’ 1 1 w’x’y’z 1 w’x’y’z’ 1 wxyz 1 wxyz’ wxz wyz’ wy’z 1 1 1 {x’y’, x’z’,wxy, wxz}, {x’y’, x’z’,wxy, wy’z}, {x’y’, x’z’,wxz, wyz’}.
3. Solve the system of equations by the substitution method x + 3y = 32 -3x + 2y = 3 Solution: x + 3y = 32 x = -3y + 32 (subtracted 3y from both sides) -3x + 2y = 3 -3x + 2y = 3 (top equation) -3(-3y + 32) + 2y = 3 (substituted -3y + 32, for x, into top equation) 9y - 96 + 2y = 3 11y - 96 = 3 11y = 99 (added 96 to both sides) y = 9 (divided both
ALTERNATIVE PROBLEMS AND SOLUTIONS ALTERNATIVE PROBLEMS 11- 1A. (Individual or Component Costs of Capital) Compute the cost for the following sources of Financing: a. A bond that has a $1,000 par value (face value) and a contract or coupon interior rate of 12%. A new issue would have a flotation cost of 6% of the $1,125 market value. The bonds mature in 10 years.
differentiates between a quadratic function and a quadratic equation. represents and describes a quadratic function using its: (a) tables of values; (b) graph; (c) equation. finds the domain and range of a quadratic function. graphs quadratic functions and determines or describes its: (a) intercepts; (b) zeroes; (c) axis of symmetry; (d) maximum or minimum point; (e) shape. writes the equation of a quadratic function given: (a) a table of values;(b) graph; (c) zeroes.transforms the quadratic functionyax2bxcinto the formya(xh2 k | | | | solves quadratic equations by: (a) extracting square roots; (b) factoring; (c) completing the square; (d) the quadratic formula.