1. Using Descrates' rule of signs, how many real roots does f(x)=8x^3 + x^2 -7x - 13 contain? a. No positive real roots, no negative real roots b. two or zero positive real roots, one or zero negative real roots c. one or zero positive real roots, two or zero negative real roots d. two or zero positive real roots, two or zero negative real roots 2. Which of the following is another representation of the polar coordinate P=(-9, -90 degrees) a. (-9, 90 degrees) b. (9, -90 degrees) c. (9, 90 degres) d. (9, 270 degrees) 3. A fire truck is en route to an address that is six blocks east and seven blocks south of the fire station. Using the fire station as the pole and the east direction as the polar axis, express the fire trucks destination in polar coordinates. Round the coordinates to the nearest unit. Express pheta in degrees a. (9, -49 degrees) b. (9, 49 degrees) c. (9, 41 degrees) d. (9, -41 degrees) 4. The letters r and phera represent polar coordinates. Write the following equation using rectangular coordinates (x,y) r =sin pheta + 2 cos pheta a. x^2 + y^2 + x + 2y =0 b. x^2 + y^2 -x -2y = 0 c. x^2 +y^2 - 2x -y =0 d. x^2 + y^2 + 2x y = 0 5. Write the following complex number in polar form. Express all angles in degrees rounded to the nearest tenth. 5 + 6i a. square root 61 ( cos 39.8 degrees + isin 39.8 degrees) b. square root 61 ( cos 50. 2 degrees + isin 50. 2 degrees) c. 61 (cos 50.2 degrees + isin 50.2 degrees) d. 61 (cos 39.8 degrees + isin 39.8 degrees) 7. Which type of conic section is represented in the equation: x^2 + (y-5)^2 = square root 10 a. circle b. parabola c. hyperbola d. ellipse 8. Change the exponential statement log base 3 (1/27) = x into an equivalent log statement a. x 1/27 = 3 b. (1/27)^-3 = x c. (1/27)^x = 3 d. 3^x = 1/27 9. Write the expression log base 3 square root 7x as the sum or difference of log. Express powers as factors. a. 1/2 log base 3 7x b. log base 3 square root 7 + log base 3 square root x c. log base 3 7- 1/2 log base 3 x d. 1/2 log base 3 7 + 1/2 log base 3 x 10. You want to make an invesment in continously compounding account over a period of ten years. What interest rate is required for your invesment to double in that time period? Round the log value and the answer to the nearest tenth. a. 0.7 percent b. 6.9 percent c. 14. 4 percent d. 1.4 percent 11. Find the sum of the first twelve arithmetic series An= 10n+9 a. 89 b. 170 c. 888 d. 531 12. Which of the following series diverges a. 2 + 4 + 8 +16 + 32 +... b. 3 +1 + 1/3 + 1/9 + 1/27 c. 16 +8 + 4 + 2 + 1 + ... d. 32 + 16 + 8 + 4 +2 + ... 13. Which of the following series converges? a. 1/8 + 1/8^2 + 1/8^3 + .... b. 1 + 4 + 9 + 16 + ... c. 4 +7 + 10 + 13 + ... d. 5^2 + 5^3 + 5^4 + 5^5 + .... 14. Find z * w. Leave your answer in simplified polar form. Express all angles in degrees rounded to the nearest tenth. z= 2(cos 140 degrees + isin 140 degrees) w= 7(cos 65 degrees + isin 65 degrees) PLEASE SHOW WORK. 15. Write the expression in a + bi form. [6(cos 60 degrees + isin 60 degrees)]^3 express your answer as a complex number in rectangular form. (show work) 16. Find the eccentricity of the ellipse x^2/25 + (y-7)^2/5 = 1 round to the nearest tenth. (show work) 17. The value of a particular invesment follows a pattern of exponential growth. You invested money in a money market account. The value of your invesment t years after your intitial invesment is given by the exponential growth model A= 2,600 e ^0.08 t. How much was initially invested in the account (show work) 18. Solve the equation 10^x = 1,000,000 (show work) 19. Write 10 + 6 + 2 + (-2) + (-6) + (-10) + (-14) in sigma notation. 1. Using Descrates' rule of signs, how many real roots does f(x)=8x^3 + x^2 -7x - 13 contain? a. No positive real roots, no negative real roots b. two or zero positive real roots, one or zero negative real roots c. one or zero positive real roots, two or zero negative real roots d. two or zero positive real roots, two or zero negative real roots 2. Which of the following is another representation of the polar coordinate P=(-9, -90 degrees) a. (-9, 90 degrees) b. (9, -90 degrees) c. (9, 90 degres) d. (9, 270 degrees) 3. A fire truck is en route to an address that is six blocks east and seven blocks south of the fire station. Using the fire station as the pole and the east direction as the polar axis, express the fire trucks destination in polar coordinates. Round the coordinates to the nearest unit. Express pheta in degrees a. (9, -49 degrees) b. (9, 49 degrees) c. (9, 41 degrees) d. (9, -41 degrees) 4. The letters r and phera represent polar coordinates. Write the following equation using rectangular coordinates (x,y) r =sin pheta + 2 cos pheta a. x^2 + y^2 + x + 2y =0 b. x^2 + y^2 -x -2y = 0 c. x^2 +y^2 - 2x -y =0 d. x^2 + y^2 + 2x y = 0 5. Write the following complex number in polar form. Express all angles in degrees rounded to the nearest tenth. 5 + 6i a. square root 61 ( cos 39.8 degrees + isin 39.8 degrees) b. square root 61 ( cos 50. 2 degrees + isin 50. 2 degrees) c. 61 (cos 50.2 degrees + isin 50.2 degrees) d. 61 (cos 39.8 degrees + isin 39.8 degrees) 7. Which type of conic section is represented in the equation: x^2 + (y-5)^2 = square root 10 a. circle b. parabola c. hyperbola d. ellipse 8. Change the exponential statement log base 3 (1/27) = x into an equivalent log statement a. x 1/27 = 3 b. (1/27)^-3 = x c. (1/27)^x = 3 d. 3^x = 1/27 9. Write the expression log base 3 square root 7x as the sum or difference of log. Express powers as factors. a. 1/2 log base 3 7x b. log base 3 square root 7 + log base 3 square root x c. log base 3 7- 1/2 log base 3 x d. 1/2 log base 3 7 + 1/2 log base 3 x 10. You want to make an invesment in continously compounding account over a period of ten years. What interest rate is required for your invesment to double in that time period? Round the log value and the answer to the nearest tenth. a. 0.7 percent b. 6.9 percent c. 14. 4 percent d. 1.4 percent 11. Find the sum of the first twelve arithmetic series An= 10n+9 a. 89 b. 170 c. 888 d. 531 12. Which of the following series diverges a. 2 + 4 + 8 +16 + 32 +... b. 3 +1 + 1/3 + 1/9 + 1/27 c. 16 +8 + 4 + 2 + 1 + ... d. 32 + 16 + 8 + 4 +2 + ... 13. Which of the following series converges? a. 1/8 + 1/8^2 + 1/8^3 + .... b. 1 + 4 + 9 + 16 + ... c. 4 +7 + 10 + 13 + ... d. 5^2 + 5^3 + 5^4 + 5^5 + .... 14. Find z * w. Leave your answer in simplified polar form. Express all angles in degrees rounded to the nearest tenth. z= 2(cos 140 degrees + isin 140 degrees) w= 7(cos 65 degrees + isin 65 degrees) PLEASE SHOW WORK. In polar form, the magnitude is 1.5 and phase angle is -141 15. Write the expression in a + bi form. [6(cos 60 degrees + isin 60 degrees)]^3 express your answer as a complex number in rectangular form. (show work) 16. Find the eccentricity of the ellipse x^2/25 + (y-7)^2/5 = 1 round to the nearest tenth. (show work) 17. The value of a particular invesment follows a pattern of exponential growth. You invested money in a money market account. The value of your invesment t years after your intitial invesment is given by the exponential growth model A= 2,600 e ^0.08 t. How much was initially invested in the account (show work) 2600 = 2600e (0.08*t) from the equation r/100 = 0.08 so r = 8 18. Solve the equation 10^x = 1,000,000 (show work) 19. Write 10 + 6 + 2 + (-2) + (-6) + (-10) + (-14) in sigma notation an =4 ( n1 )+ 10 \f1. Using Descrates' rule of signs, how many real roots does f(x)=8x^3 + x^2 -7x - 13 contain? a. No positive real roots, no negative real roots b. two or zero positive real roots, one or zero negative real roots c. one or zero positive real roots, two or zero negative real roots d. two or zero positive real roots, two or zero negative real roots 2. Which of the following is another representation of the polar coordinate P=(-9, -90 degrees) a. (-9, 90 degrees) b. (9, -90 degrees) c. (9, 90 degres) d. (9, 270 degrees) 3. A fire truck is en route to an address that is six blocks east and seven blocks south of the fire station. Using the fire station as the pole and the east direction as the polar axis, express the fire trucks destination in polar coordinates. Round the coordinates to the nearest unit. Express pheta in degrees a. (9, -49 degrees) b. (9, 49 degrees) c. (9, 41 degrees) d. (9, -41 degrees) 4. The letters r and phera represent polar coordinates. Write the following equation using rectangular coordinates (x,y) r =sin pheta + 2 cos pheta a. x^2 + y^2 + x + 2y =0 b. x^2 + y^2 -x -2y = 0 c. x^2 +y^2 - 2x -y =0 d. x^2 + y^2 + 2x y = 0 5. Write the following complex number in polar form. Express all angles in degrees rounded to the nearest tenth. 5 + 6i a. square root 61 ( cos 39.8 degrees + isin 39.8 degrees) b. square root 61 ( cos 50. 2 degrees + isin 50. 2 degrees) c. 61 (cos 50.2 degrees + isin 50.2 degrees) d. 61 (cos 39.8 degrees + isin 39.8 degrees) 7. Which type of conic section is represented in the equation: x^2 + (y-5)^2 = square root 10 a. circle b. parabola c. hyperbola d. ellipse 8. Change the exponential statement log base 3 (1/27) = x into an equivalent log statement a. x 1/27 = 3 b. (1/27)^-3 = x c. (1/27)^x = 3 d. 3^x = 1/27 9. Write the expression log base 3 square root 7x as the sum or difference of log. Express powers as factors. a. 1/2 log base 3 7x b. log base 3 square root 7 + log base 3 square root x c. log base 3 7- 1/2 log base 3 x d. 1/2 log base 3 7 + 1/2 log base 3 x 10. You want to make an invesment in continously compounding account over a period of ten years. What interest rate is required for your invesment to double in that time period? Round the log value and the answer to the nearest tenth. a. 0.7 percent b. 6.9 percent c. 14. 4 percent d. 1.4 percent 11. Find the sum of the first twelve arithmetic series An= 10n+9 a. 89 b. 170 c. 888 d. 531 12. Which of the following series diverges a. 2 + 4 + 8 +16 + 32 +... b. 3 +1 + 1/3 + 1/9 + 1/27 c. 16 +8 + 4 + 2 + 1 + ... d. 32 + 16 + 8 + 4 +2 + ... 13. Which of the following series converges? a. 1/8 + 1/8^2 + 1/8^3 + .... b. 1 + 4 + 9 + 16 + ... c. 4 +7 + 10 + 13 + ... d. 5^2 + 5^3 + 5^4 + 5^5 + .... 14. Find z * w. Leave your answer in simplified polar form. Express all angles in degrees rounded to the nearest tenth. z= 2(cos 140 degrees + isin 140 degrees) w= 7(cos 65 degrees + isin 65 degrees) PLEASE SHOW WORK. In polar form, the magnitude is 1.5 and phase angle is -141 15. Write the expression in a + bi form. [6(cos 60 degrees + isin 60 degrees)]^3 express your answer as a complex number in rectangular form. (show work) 16. Find the eccentricity of the ellipse x^2/25 + (y-7)^2/5 = 1 round to the nearest tenth. (show work) 17. The value of a particular invesment follows a pattern of exponential growth. You invested money in a money market account. The value of your invesment t years after your intitial invesment is given by the exponential growth model A= 2,600 e ^0.08 t. How much was initially invested in the account (show work) 2600 = 2600e (0.08*t) from the equation r/100 = 0.08 so r = 8 18. Solve the equation 10^x = 1,000,000 (show work) 19. Write 10 + 6 + 2 + (-2) + (-6) + (-10) + (-14) in sigma notation an =4 ( n1 )+ 10 \f