The speed of a roller coaster as it travels through a loop
depends on the height of the hill from which the coaster has just descended.
The equation 
gives the speed
s in feet per second where h is the height of the hill and r is
the radius of the loop.
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Suppose the owner of an amusement park wants to design a
roller coaster that will travel at a speed of 40 feet per second as it goes
through a loop with a radius of 30 feet. How high should the hill be? This problem will be solved in Example 5.
Equations like that contain radicals
with variables in the radicand are called radical equations. To solve these equations,
first isolate the radical on one side of the equation. Then square each side of
the equation to eliminate the radical.
Solve each equation. Check your solution.
Alternative
Solutions:
The
solution is 9.
Alternative Solutions:
The
solution is 13.
You can use a graphing calculator to
solve radical equations.
Squaring each side of an equation may
produce results that do not satisfy the original equation. So, you must
check all solutions when you solve radical equations.
Example
Solve each equation. Check your solution.
Alternative Solutions:
Since
2 does not satisfy the original equation, 7 is the only solution.
Alternative Solutions:
Since
3 does not satisfy the original equation, 10 is the only solution.
Radical equations are used in many
real-life situations.
Engineering
Link
5. Refer to the application at the beginning of the lesson. How high should the hill be?
Alternative Solutions:
Sumber
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