If g left parenthesis x right parenthesis equals 36 x squared minus 36 and h left parenthesis x right parenthesis equals 65 x,
then solve g left parenthesis x right parenthesis greater than h left parenthesis x right parenthesis .
1 answer:
Given
g(x) = 36x² -36
h(x) = 65x
Find
x such that g(x) > h(x)
Solution
We can start by substituting the given information into the required relation.
36x² -36 > 65x
Subtracting the right side and factoring gives
36x² -65x -36 > 0
(9x +4)(4x -9) > 0
The product of these factors will be greater than zero when both factors are negative or both are positive. They change sign at x = -4/9 and x = 9/4. Hence, the solution is
x < -4/9 or 9/4 < x
g(x) = 36x² -36
h(x) = 65x
Find
x such that g(x) > h(x)
Solution
We can start by substituting the given information into the required relation.
36x² -36 > 65x
Subtracting the right side and factoring gives
36x² -65x -36 > 0
(9x +4)(4x -9) > 0
The product of these factors will be greater than zero when both factors are negative or both are positive. They change sign at x = -4/9 and x = 9/4. Hence, the solution is
x < -4/9 or 9/4 < x
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After 4 interval of six months, Joe to earn same hourly rate as Blaine
<em><u>Solution:</u></em>
Given that,
Amount earned by Joe = $ 14 per hour
Amount earned by Blaine = $ 18 per hour
Lets assume the number of six month intervals be "x"
<em><u>Joe receives a raise of $1.75 every six months</u></em>
Therefore,
Joe earning: 14 + 1.75(number of six month intervals)
Equation for Joe earning: 14 + 1.75x ------- eqn 1
<em><u>Blaine receives a raise of $0.75 every six months</u></em>
Therefore,
Blaine earning: 18 + 0.75(number of six month intervals)
Equation for Blaine earning: 18 + 0.75x ------------ eqn 2
The number of six-month intervals it will take Joe to earn the same hourly rate as Blaine,
Eqn 1 must be equal to eqn 2
Thus after 4 interval of six months, Joe to earn same hourly rate as Blaine.