Splash Screen

Perform the operation below: 4+ 8𝑖 2 −(4−8𝑖) EOC Review Problem 1 Perform the operation below: 4+ 8𝑖 2 −(4−8𝑖) What is the resulting value? −8 1−𝑖 8 1+𝑖 8(1−𝑖) 8+1 Concept

EOC Review Problem 2 Jack is dealing with two dependent events: A and B. He wants to determine the conditional probability of A given B. Which of these equations will Jack need to uses to calculate that probability? P 𝐴 𝐵 = 𝑃(𝐴) 𝑃(𝐵) P 𝐴 𝐵 = 𝑃(𝐵) 𝑃(𝐴) P 𝐴 𝐵 = 𝑃(𝐴 𝑎𝑛𝑑 𝐵) 𝑃(𝐴) P 𝐴 𝐵 = 𝑃(𝐴 𝑎𝑛𝑑 𝐵) 𝑃(𝐵) Concept

In the formula 𝑡=0.5 ℎ , which variable appears in the radical? When you jump, the time that you are in the air is your hang time. Hang time can be calculated in seconds t if you know the height h of the jump in feet. The formula for hang time is 𝑡=0.5 ℎ . Michael Jordan had a hang time of about 0.98 second. How would you calculate the height of Jordan’s jump? In the formula 𝑡=0.5 ℎ , which variable appears in the radical? What is the value of t if h = 4? Looking at your answer to the previous question, how is t affected if h is multiplied by 4? Concept

You solved polynomial equations. Solve equations containing radicals. Solve inequalities containing radicals. Then/Now

radical equation extraneous solution radical inequality Vocabulary

Concept

Add 1 to each side to isolate the radical. Solve Radical Equations A. Solve . Original equation Add 1 to each side to isolate the radical. Square each side to eliminate the radical. Find the squares. Add 2 to each side. Example 1

Answer: The solution checks. The solution is 38. Solve Radical Equations Check Original equation Replace y with 38. ? Simplify.  Answer: The solution checks. The solution is 38. Example 1

B. Solve . Original equation Square each side. Find the squares. Solve Radical Equations B. Solve . Original equation Square each side. Find the squares. Isolate the radical. Divide each side by –4. Example 1

Evaluate the square roots. Solve Radical Equations Square each side. Evaluate the squares. Original equation Check Replace x with 16. Simplify. Evaluate the square roots.  Answer: The solution does not check, so there is no real solution. Example 1

Solve the equation (𝑥−5) 1 3 −4=−2 Concept

The organizers of a concert are preparing for the arrival of 50,000 people in the open field where the concert will take place. Each person is allotted 5 square feet of space, so the organizers rope off a circular area of 250,000 square feet. Using the formula 𝐴=𝜋 𝑟 2 , where A represents the area of the circular region and r represents the radius of the region, find the radius of this region. Concept

A. Solve . A. 19 B. 61 C. 67 D. no real solution Example 1

B. Solve . A. 2 B. 4 C. 9 D. no real solution Example 1

Subtract 5 from each side. Solve a Cube Root Equation In order to remove the power, or cube root, you must first isolate it and then raise each side of the equation to the third power. Original equation Subtract 5 from each side. Cube each side. Evaluate the cubes. Example 2

Subtract 1 from each side. Solve a Cube Root Equation Subtract 1 from each side. Divide each side by 3. Check Original equation Replace y with –42. Simplify. The cube root of –125 is –5.  Add. Answer: The solution is –42. Example 2

A. –14 B. 4 C. 13 D. 26 Example 2

Solve a Radical Equation A m = –2 B m = 0 C m = 12 D m = 14 Example 3

Raise each side to the sixth power. Solve a Radical Equation Original equation Add 4 to each side. Divide each side by 7. Raise each side to the sixth power. Evaluate each side. Subtract 4 from each side. Answer: The answer is C. Example 3

A. 221 B. 242 C. 266 D. 288 Example 3

Concept

Solve a Radical Inequality Since the radicand of a square root must be greater than or equal to zero, first solve 3x – 6  0 to identify the values of x for which the left side of the inequality is defined. 3x – 6  0 3x  6 x  2 Example 4

Answer: The solution is 2  x  5. Solve a Radical Inequality Original inequality Isolate the radical. Eliminate the radical. Add 6 to each side. Divide each side by 3. Answer: The solution is 2  x  5. Example 4

Only the values in the interval 2  x  5 satisfy the inequality. Solve a Radical Inequality Check Test some x-values to confirm the solution. Let Use three test values: one less than 2, one between 2 and 5, and one greater than 5. Only the values in the interval 2  x  5 satisfy the inequality. Example 4

Solve the inequality 𝑑+3 + 𝑑+7 >4 Concept

A. B. C. D. Example 4

Exit Slip The radius r of the orbit of a satellite is given by the formula 𝑟= 3 𝐺𝑀 𝑡 2 4 𝜋 4 , where G is the universal gravitational constant, M is the mass of the central object, and t is the time it takes the satellite to complete one orbit. Solve this formula for t. Concept

Glencoe Algebra 2 Common Core Homework Glencoe Algebra 2 Common Core pages 432 – 434 # 1, 2, 6, 15 – 20, 29 – 36, 62, 63, 67, 72, 73 Concept

End of the Lesson