EXAMPLE 4 Using a Square Root Equation Amusement Parks

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Presentation transcript:

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. 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. r

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

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

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

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

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

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

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

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

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

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

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

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