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EXAMPLE 4

r. The model s = 4.95 gives the speed needed to keep riders pinned to the wall. In the model, s is the speed in meters per second and r is the radius of the ride in meters. Find the speed necessary to keep riders pinned to the wall of a ride that has a radius of 2.61 meters. EXAMPLE 4.

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EXAMPLE 4

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  1. r The model s = 4.95 gives the speed needed to keep riders pinned to the wall. In the model, sis the speed in meters per second and ris the radius of the ride in meters. Find the speed necessary to keep riders pinned to the wall of a ride that has a radius of 2.61 meters. EXAMPLE 4 Using a Square Root Equation Amusement Parks On an amusement park ride, riders stand against a circular wall that spins. At a certain speed, the floor drops out and the force of the rotation keeps the riders pinned to the wall.

  2. – – 8 a. 56.25 1256 b. c. SOLUTION Display Answer Keystrokes a. b. c. EXAMPLE 3 Using a Calculator Evaluate the square root. Round to the nearest tenth, if necessary. –7.5 2.8 –35.4

  3. s 4.95 = r 4.95 = 4.95 (1.62) 8.019 2.61 = ANSWER The speed should be about 8 meters per second. EXAMPLE 4 Using a Square Root Equation SOLUTION Write equation for speed of the ride. Substitute 2.61 for r. Approximate the square root using a calculator. Multiply.

  4. a. x 64 64 = 2 + + x = – – x 8 = x 64 2 = ANSWER The solutions are 8 and –8. EXAMPLE 5 Solving Equations Using Square Roots Original equation Definition of square root Evaluate square roots.

  5. b. z z z 14 14 20 20 + + = = 2 2 2 + + – 14 14 20 – 14 = + – – 6 z 6 = 2 z = z ≈ 2.4 ANSWER The solutions are about 2.4 and –2.4. EXAMPLE 5 Solving Equations Using Square Roots Original equation Subtract 14 from each side. Simplify. Definition of square root Approximate square roots.

  6. 9. 236 ANSWER 15.4 for Examples 3, 4 and 5 GUIDED PRACTICE Use a calculator to evaluate. Round to the nearest tenth.

  7. 11 10. ANSWER 3.3 for Examples 3, 4 and 5 GUIDED PRACTICE Use a calculator to evaluate. Round to the nearest tenth.

  8. – 11. ANSWER 20.96 –4.6 for Examples 3, 4 and 5 GUIDED PRACTICE Use a calculator to evaluate. Round to the nearest tenth.

  9. – 12. ANSWER 3590 –59.9 for Examples 3, 4 and 5 GUIDED PRACTICE Use a calculator to evaluate. Round to the nearest tenth.

  10. t2 36 13. = ANSWER t = 6 _ + for Examples 3, 4 and 5 GUIDED PRACTICE

  11. k 121 = 14. 2 + – ANSWER x 11 = for Examples 3, 4 and 5 GUIDED PRACTICE

  12. 15 15. y 10 – = 2 + – y 5 = for Examples 3, 4 and 5 GUIDED PRACTICE ANSWER

  13. 7 16. x 16 + = 2 + – x 3 = for Examples 3, 4 and 5 GUIDED PRACTICE ANSWER

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