Slove the inequality for n 24 > 18 + 2n
2 answers:
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Answer:
- g(20) > f(20)
- g(x) exceeds f(x) for any x > 4
Step-by-step explanation:
As with most graphing problems not involving straight lines, it works well to start with a table of values. Pick a few values of x and compute f(x) and g(x) for those values. Plot the points and draw a smooth curve through them.
As in the attached, your table will show that there are two points of intersection between f(x) and g(x), and that for values of x more than 4, g(x) becomes much greater very quickly. Both curves rapidly reach the top of your graph space.
To find whether f(20) or g(20) is greater, you can evaluate the functions for that value of x.
f(20) = 20² = 400
g(20) = 2²⁰ = 1,048,576
Clearly, g(20) has a greater value.
I would compute sqrt(1 + 160pi^2) first to get approximately 39.75093337
Add this to 1 and we have 40.75093337
Then divide over 2pi to get a final approximate result of 6.48571248
So x = 6.48571248 is one approximate solution
In short, I computed only focusing on the plus for now.
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If you were to compute you should get roughly -6.167402596 as your other solution. Each solution can then be plugged into the original equation to check if you get 0 or not. You likely won't land exactly on 0 but you'll get close enough.