advertisement

Math 1090 Section 5 Review2 (3.1-4.4) 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Read all directions carefully. This will be graded on completion, but you need to show signicant work toward the solution of the problem. Find all solutions to the following system of equations. 2x y + z = 8 3x + 2y + 2z = 19 5x 3y + 3z = 7 Say that you have a window constructed by attaching half of a circle exactly onto opposite sides of a rectangle (the diameter of the circle is equal to the length of one of the sides of the rectangle). Given that the area of a circle is r2 where r is the radius, and the perimeter of a circle is 2r if the total perimeter of the window is 50ft what is the largest area the window can enclose? Find the equation for the linear function f (x) if f (5) = 1 and f ( 2) = 6. Then nd the equation for the inverse function f 1(x) and note that f 1(1) = 5 and f 1 (6) = 2. Why are these two functions parallel, perpendicular, or neither? You go to two dierent banks and deposit $10,000 in savings accounts in each of the banks. One bank gives you an interest rate of 5% compounded daily, and the second bank gives you an interest rate of 6% compounded annually. After 10 years which account has the most money in it? What about after 20 years? Say that you have a quadradic function g(x) = ax2 + bx + c if g(1) = 4, g ( 1) = 2, and g (4) = 19 nd g (x). Find all solutions to the equation log +2(4 + 3x x2 ) = 2 Given that log4 (x + 1) = a and log4(x 2) = b nd log2((x 2)10(x2 x 2)100 (x + 1) 46)) in terms of a and b. Find the slope-intercept and general linear form of the line that passes through (2,1) and is perpendicular to the line 3x+2y-3=0 Find all solutions to the equation. 2ln(x 1) + ln4 = ln(x2 + 4) Find all solutions to the following system of equations. log (x 3) + log 3 = log (z + 1) 1000 5 = 10000 3 x+y+z =0 Find the vertex of the parabola y = 15x2 +14x 8 and state why it opens down or up. Find the equations of two lines through the x-intercepts that intersect at (0,3). x x 11. y 12. Say that you invest $45,000 in a savings account with 7% interest compounded semi-annually in 1954. What year will the account balance be one million dollars? How long does it take the account balance to double? (hint: nd when the account balance is 90,000) 13. Find the slope-intercept and general linear form of the line that passes through (5,-3) and is parallel to the line 4x+7y=0 14. Say that a farmer wants to build a rectangular fence on his property. Two parallel sides of the rectangle he wishes to build with solid mahogany wood that will cost $10 per foot. The other sides he will build with standard pine wood that costs $4 per foot. If he wants to build a fence that is worth $50,000 what is the maximum area that he can enclose? 15. Find all solutions to the following system of equations. 3x + 4y z = 3 5x + 2y + 3z = 1 8x + 6y + 2z = 4 (x 5)2(x+3)3 16. Given that log(x 5) = d and log(x + 3) = c nd ln( px2 2x 15 ) in terms of c and d. 17. Find all solutions to the equation log3(x + 1) + 1 = log9(x2 + 3x 2) 18. Find all solutions to the equation 4 2+3 +716 2 = 1 19. Find all solutions to the equation log +1(x3 + 2) = 3 20. Fred is traveling across the united states in a Jet. If it takes 3 hours to get to New York from Los Angeles (a distance of 3,000 miles), and 5 hours to get to Los Angeles from New York then how fast is the plane ying and how fast is the wind, assuming both are constant. Hint(Distance=rate times time) 21. Find the equation of the three lines that pass through two of the points (1,2), (2,4), and (-3,6). Do the lines form a right triangle? Hint(are any of the pairs of lines perpendicular?) 22. If you invest $30,0000 in a savings account with 3% interest compounded monthly how much money will be in the account 10 years later? When will the account balance reach $120,000? 23. Find the vertex, x-intercepts, and y-interepts of the quadradic function T (x) = 3x2 + 7x 19. 24. Due to loss of manufacturing jobs the number of people living in Farmland, IN is decreasing. If the population was 3,000 in 1989 and is 2,500 today then construct two functions to model the population loss. F1(t) = a(t 1989) + b and F2(t) = p b 1989 using the points (1989,3000), and (2006,2500). x x x t x