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3-5-14(B) & 3-6-14(A) AM2.3c To Solve Radical Equations

3-5-14(B) & 3-6-14(A) AM2.3c To Solve Radical Equations Chapter Test: Fri, 3/14 (A) & Mon, 3/17 (B). TOWERS OF HANOI

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3-5-14(B) & 3-6-14(A) AM2.3c To Solve Radical Equations

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  1. 3-5-14(B) & 3-6-14(A) AM2.3c To Solve Radical Equations Chapter Test: Fri, 3/14 (A) & Mon, 3/17 (B) TOWERS OF HANOI Legend has it that there is a great temple in Benares with a dome that is considered the center of the world. Under this dome, there is a brass platform with three diamond needles…

  2. TOWERS OF HANOI Legend has it that there is a great temple in Benares with a dome that is considered the center of the world. Under this dome, there is a brass platform with three diamond needles. 64 golden disks, of diminishing sizes, are stacked on these needles. These are continuously being moved by the priests. One at a time, about one second between each move. No larger disk is placed on a smaller disk. It is said that when all disks are moved, that will signal the END OF THE WORLD! How long will it take? http://www.mathsisfun.com/games/towerofhanoi.html

  3. The formula for the number of moves is: So, if we used 3 disks, it took 7 moves, which is 23 – 1. Why 2? Because every time you add a disk, you double the number of moves Now, their legend says the end of the world will occur when they have finished moving the 64 disks. How long will that take? 264 – 1 seconds. Converting seconds to minutes to hours to days to years, it will take….. About 580 billion years!

  4. Active Learning Assignment Questions?

  5. Lesson: • To Solve with Radicals: • Find the domain restrictions. • ( Means set radicand ≥ 0) • (Only needed for even roots) • Use powers to clear the radical. *

  6. LESSON: Find domain restrictions. Solve and check for extraneous solutions It passes the domain restrictions, now, check for 3: Domain: 4x – 2 ≥ 0 3x + 1 ≥ 0 4x ≥ 2 3x ≥ -1 x ≥ 1/2 x ≥ -1/3 2 2 ü

  7. Solve and check for extraneous solutions (it has an odd root, so there are no domain restrictions.) Check for – 41 : ü

  8. Solve and check for extraneous solutions. ***EVEN ROOT*** Which gives: Now, raise both sides to a power that will be an inverse to the exponent. Maybe, now, check!

  9. ü ü

  10. Find domain restrictions, solve, and check answers: Check: Domain: x ≥ 0 *Now, you have an odd root ü

  11. Find domain restrictions, solve, and check answers: Domain Restrictions? Set x + 1 ≥ 0 Thus: x ≥ -1 (Square both sides) (Express squares) (Multiply, FOIL, or distribute) (Set equal to zero) (Factor) 0 = (x – 8)(x – 3) Either x – 8 = 0 or x – 3 = 0 (Set factors equal to zero & solve) x = 8 or x = 3 Are we finished?

  12. Find domain restrictions, solve, and check answers: Check x = 8: ... x = 8 or x = 3 ü Thus, both x = 8 and x = 3 work! Now, check x = 3: ü

  13. Find domain restrictions, solve, and check answers: → Domain: 2x + 7 ≥ 0 x ≥ -7/2 Which gives: (Zero out one side) (Domain is OK, let’s check 1 & -3) (Factor)

  14. No ü Yes

  15. Solve and check for extraneous solutions. Which gives: (Zero out one side) (Factor) (Now, check)

  16. ü Yes No

  17. Active Learning Assignment: H/O AM2.3c Column 2, & #24 Chapter Test: Fri, 3/14 (A) & Mon, 3/17 (B)

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