The period (in seconds) of a pendulum with a length of L (in meters) is given by the formula . If the period of a pendulum is is the length of the pendulum 156.8?
Solving Rational Exponent Equations
When solving a rational exponent equation, you first isolate the variable. Then, to eliminate the exponent, you will need to raise everything to the reciprocal power.
Let's determine if x = 9 is a solution to .
Substitute in x and see if the equation holds.
9 is a solution to this equation.
Now, let's solve the following equations for x.
First, divide both sides by 3 to isolate .
is raised to the five-halves power. To cancel out this exponent, we need to raise everything to the two-fifths power.
Isolate by subtracting 48 and dividing by -2.
To undo the three-fourths power, raise everything to the four-thirds power.
Earlier, you were asked to verify the length of the pendulum.
We need to plug 156.8 in to the equation for L and solve. If our answer equals , then the given length is correct.
does not equal , so the length cannot be 156.8.
Solve the following rational exponent equations and check for extraneous solutions.
Divide both sides by 8 and raise everything to the three-halves power.
Here, only the is raised to the three-halves power. Subtract 141 from both sides and divide by 6. Then, eliminate the exponent by raising both sides to the two-thirds power.
Determine if the following values of x are solutions to the equation
Solve the following equations. Round any decimal answers to 2 decimal places.
Answers for Review Problems
To see the Review answers, open this PDF file and look for section 7.9.