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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Before going to the question, let's review what range is:
Range is the difference between the greatest number and the least number in a data set. Finding range is pretty easy. All you need to do is find the greatest number and lowest number, and find the difference.
In this data set, you have the following numbers:
The greatest number is 11. The lowest number is 2. That means that the range is equal to:
Subtract:
★ The range is 9 ; range = 9
<em>If you have any questions, feel free to ask in the comments! :)</em>