example 4 using a square root equation amusement parks on an amusement park ride, riders stand...
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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 AnswerDisplay
a. –7.5
b. 2.8
c. –35.4
EXAMPLE 4 Using a Square Root Equation
SOLUTION
The speed should be about 8 meters per second.
ANSWER
rs = 4.95
= 4.95 2.61
= 8.019
Write equation for speed of the ride.
Substitute 2.61 for r.
Approximate the square root using a calculator.
Multiply.
4.95 (1.62)
EXAMPLE 5 Solving Equations Using Square Roots
Original equation
Definition of square root
Evaluate square roots.
ANSWER
The solutions are 8 and –8.
2 =x 64
=x +– 64
=x +– 8
2 =a. x 64
EXAMPLE 5 Solving Equations Using Square Roots
Original equation
Subtract 14 from each side.
Simplify.
Definition of square root
Approximate square roots.
ANSWER
The solutions are about 2.4 and –2.4.
= 62z
b.
=2z 14+ 20
=2z + 14 –14 20 – 14
6z +–=
z ≈ +– 2.4
=2z 14+ 20
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
+–y 5=
15.
=2y 15– 10
ANSWER
GUIDED PRACTICE for Examples 3, 4 and 5
16.
=2x 7+ 16
x +– 3=
ANSWER