Math Is Fun Forum

The sum means the addition of all the numbers. So just add:
  128
  145
+106
-------

I thought about the first one for a while and couldn't conjure up an answer. Mind posting the results in hidden text?

Particularly, you should know the multiplication tables by heart for all numbers up to at least 12. When I was a bit younger, I used to do tons of multiplication in my head before falling asleep and now it's permanently set in there. Knowing them directly will help you a lot in the future in math where you have to start factoring and such.

Good luck.

Thanks for the link. I guess apart from knowing the different identities, it's experience that will allow one to decide while identity to use.

And if that doesn't work, I gotta go all the way back and try a new one.

I'll keep trying different examples, it'll help during exam time.

Normally when then the textbook says solve graphically, it means graph it on a graphing calculator or some applet like this: http://www.mathsisfun.com/data/graph.html

And you see for what value of x, y is equal to 0 by looking at the x-intercepts of the graph. That is how you would go about solving it.

Nevermind, I thought of it quite a bit and I think I've got the concept.

But just to make sure:

First 100 km/h is converted into 2777.78 cm/s. That is the speed at which the tire travels. So basically, every second, it moves 2777.78 cm. This would make it the arc length.

Now we have to look at it in a perspective of ONE SECOND intervals.

So Θ = a/r
Θ = 77.16 is the value of the angle in radians but for ONLY ONE SECOND.

Then we must find out how many times it rotates in one second or how many revolutions it has so we divide that number by 2pi.

Is my understanding correct?

That is the point. You CANNOT use synthetic division unless the divisor is linear.

Note that when you expand the divisor, it has a degree of 9. So in the end the divisor is two degrees higher than the dividend. I'm still relatively inexperienced in math so I may be incorrect but I don't think you can perform that division.

I guess you can just leave the answer as (4x^7 - 8x^6 + 4x^5 - 5x^3 + 2x^2 +3) / (2x^3 + x + 1)^3 .

I think you're assuming that for any value of x, the first equation holds true.

Let's say

So that means only when x is equal to 8, does the left side equal to the right side.

When you put in a random number, it does not work out. Ex. when we substitute in 5 for x:

Obviously, that is not the case.

I worked it out visually as well for the page Bobbym linked.

Nationality:        Norwegian          Dane          Brit          German          Swede
Pet:                  Cats                  Horses        Birds        ---------           Dogs
Color:               Yellow                Blue           Red          Green             White
Sport:               Hockey              Baseball      Polo         Soccer            Billiards
Drink:               Water                Tea             Milk         Coffee             Beer

This leaves us with one blank missing and since we were given no information about the fish, we could not determine where it belonged.
Since the only spot left is for Germany, the fish would have to belong to the German.

You have to flip the signs when you multiply/divide both sides by a negative number. I'm just posting the above to show you that, but my process is not right.

The correct answer should be -1/10 < x < 0 OR 0 < x < 1/10. Plug in values and you will see that my answer is correct. For instance if what the text says about x having to be less than 1/10 was true, then that means we can sub a value like -2/10 in for x.

Which obviously is not correct.