The only solutions are x = 0, x = 1, x = 32, x = 243, and x = 1024. --- Suppose that x is a solution to this equation. Then, since floor((3x)^(1/5)) is always an integer, then x^(1/5) must be an integer; which in turn means that x must be a 5th power. So we have ruled out all x which are not 5th powers. --- By trying small 5th powers, we see that * x = 0^5 = 0 is a solution * x = 1^5 = 1 is a solution * x = 2^5 = 32 is a solution * x = 3^5 = 243 is a solution * x = 4^5 = 1024 is a solution and that no larger 5th powers appear to work, and no negative 5th powers appear to work. Let us try to prove that the above five values are the only solutions. --- Suppose that x < 0 and x is a 5th power. Since x < 0, then we have 3x < x Since the function f(x) = x^(1/5) is increasing, then applying it to both sides of the inequality preserves the inequality, so we have (3x)^(1/5) < x^(1/5) Now, x^(1/5) is an integer, because x is a fifth power; thus, floor((3x)^(1/5)) must be a smaller integer, because (3x)^(1/5) is less than x^(1/5). So x cannot be a solution when x < 0. --- It remains to show that x cannot be a solution when x = k^5, where k is an integer greater than 4. To show this, I will first show by induction that if k is an integer greater than 4, then 3^(1/5) * k k + 1. Base case: 3^(1/5) * 5 5 + 1 by a calculator. Inductive step: Suppose that 3^(1/5) * n n + 1. Clearly also 3^(1/5) 1. Adding these two inequalities gives 3^(1/5) * n + 3^(1/5) n + 2. Factoring the left and rewriting the right gives 3^(1/5)(n + 1) (n + 1) + 1, which is what we wanted to show. --- Now, suppose that x = k^5, where k is an integer greater than 4. Then (3x)^(1/5) = 3^(1/5) * x^(1/5) = 3^(1/5) * (k^5)^(1/5) = 3^(1/5) * k, and x^(1/5) = (k^5)^(1/5) = k. But by the induction above, 3^(1/5) * k k + 1, so (3x)^(1/5) x^(1/5) + 1, which means that floor((3x)^(1/5)) x^(1/5). So x cannot be a solution to the equation.
Q:Anyone know how to fix a squeeky floor?
A squeak in hardwood flooring is caused by two pieces of wood rubbing against one another. One way to stop the sound is by reducing the friction of the moving pieces using a lubricant. I’m not talking oil here, but rather a dusting with ultra-fine graphite powder. This is available at your local hardware stores, and for the most part it’s used to free lock mechanisms. But if you pour a tiny bit of it on the floor so that it can work its way into the squeaking boards, it could very well reduce or eliminate the sound. If that fails, you can always try a pair of well-placed nails. You first need to pre-drill some slender holes into the wood, angled slightly towards one another. Then drive the nails in, being careful not to bang up the hardwood floor with the head of the hammer.
Q:how to take the vinyl floor out.?
Chances are under your vinyl floor will be 1/4 inch luan plywood under that will be your subfloor. You will have to remove and replace the luan and the vinyl. The other solution for your floor will be to skim coat the existing vinyl and install your new vinyl on top. Only up to 2 layers before you will need to remove the 2 layers and the luan again. These installation methods are approved by the vinyl floor manufacturers. Ask for an installation guideline sheet. If they don't have one or can't get it for you. Run. Good luck with your project.
Q:Repairing & Replacing Flooring?
Q:Laundry: What type of vinyl flooring?
If your concrete floor isn't completely smooth, any kind of vinyl will show the bumps and dips in it. If you can live with that until you rebuild the room, I'd use Trafficmaster Allure vinyl planks from Home Depot. They stick to each other but not the floor and are very easy to DIY. If you really want a smooth surface you'll have to use underlayment for any vinyl, or check at the store and see if there's anything you can use to skim coat the floor to make it smoother. Embossing leveler might work.
Q:Underlayment over concrete floor?
Leveler is usually enough, but with vinyl tile it will show any small imperfection or bump. But if you properly apply a leveler and maybe a little thin- set where needed you can make your smooth. You might want to use the mastic type of tiles verses the peel and stick variety, but both types should work just fine.
Q:how to clean parkay floors?
it's not parkay, it's butter
Q:How does sea-floor spreading account for the age of sea floor?
Here ya go.
Q:Is the color of the angle to be the same as the door or the floor?
This is not exactly the same as the color of the floor and the floor of the color of the room to see your main colors and your preferences also include your lifestyle, each interior design is based on personal habits and personal preferences and made a unique, Recommended when the color comparison with the comparison,
Q:Cleaning Laminate floors?
I can only tell you how I do mine, I use Mr. clean lemon scent and a micro fiber flat mop. I wash the whole floor and them rinse the mop head real well and then again go over the floor with clean warm water. That's it.