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The solution is
Square both sides.
This equation has two solutions, and The is an extraneous solution since it does not check in the original equation:
Solve each square root equation.
The symbol,
, signifies the
positive square root and not the negative square root.
Solve each square root equation.
For the following problems, solve the square root equations.
At a certain electronics company, the daily output
is related to the number of people
on the assembly line by
(a) Determine the daily output if there are 44 people on the assembly line.
(b) Determine how many people are needed on the assembly line if the daily output is to be 520.
At a store, the daily number of sales
is approximately related to the number of employees
by
(a) Determine the approximate number of sales if there are 19 employees.
(b) Determine the number of employees the store would need to produce 310 sales.
The resonance frequency
in an electronic circuit containing inductance
and capacitance
in series is given by
(a) Determine the resonance frequency in an electronic circuit if the inductance is 4 and the capacitance is
. Use
(b) Determine the inductance in an electric circuit if the resonance frequency is
and the capacitance is
. Use
If two magnetic poles of strength
and
units are at a distance
centimeters (cm) apart, the force
of repulsion in air between them is given by
(a) Determine the force of repulsion if two magnetic poles of strengths 20 and 40 units are 5 cm apart in air.
(b) Determine how far apart are two magnetic poles of strengths 30 and 40 units if the force of repulsion in air between them is
.
The velocity
in feet per second of outflow of a liquid from an orifice is given by
where
is the height in feet of the liquid above the opening.
(a) Determine the velocity of outflow of a liquid from an orifice that is 9 feet below the top surface of a liquid (
is in feet/sec).
(b) Determine how high a liquid is above an orifice if the velocity of outflow is 81 feet/second.
The period
in seconds of a simple pendulum of length
in feet is given by
(a) Determine the period of a simple pendulum that is 2 feet long. Use
(b) Determine the length in feet of a simple pendulum whose period is
seconds. Use
The kinetic energy
in foot pounds of a body of mass
in slugs moving with a velocity
in feet/sec is given by
(a) Determine the kinetic energy of a 2-slug body moving with a velocity of 4 ft/sec.
(b) Determine the velocity in feet/sec of a 4-slug body if its kinetic energy is 50 foot pounds.
( [link] ) Classify as an identity, a contradiction, or a conditional equation.
(
[link] ) Supply the missing words. In the coordinate plane, lines with
positive; negative
( [link] ) Simplify
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