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An interesting algorithm! It only tells you the number of final zeros though.  You could check this by counting all the zeros in 486! or, alternatively, use the algorithm on, say 7! (=5040).

Exactly 2.54 cm = 1 inch

Use the "log" or the "ln" key when you want to find the log of something and for anti-logs, use the 10^x key.

if y = log(3) [assume base of 10] --> y= 0.4771212547196624.

The anti-log would be 10^3 = 1,000.

if f(x) = f(-x), then the function is even. So, f(-x) = 2^-x which does not equal 2^x.

However, if f(-x) = -f(x), then the function is odd. So -f(x) = -2^x which does not equal f(-x) = 2^-x.

f(x) = 2^x is neither even nor odd.

j(total energy that is radiated from the black body) = proportionality constant*black body's temperature(^4) 

thanks so much again Aziz!

cos45 degrees = sqrt(2) / 2.

76) y=-cubedrootx-2 +5

Domain: Notice that this function can take on any x value, so x can be all real numbers.

Range: The same goes for the y values, so y can be all real numbers as well.

78) y=-3sqrt4x-16

y = -3sqrt(4(x - 4)) -->

y = -3sqrt(4)sqrt(x - 4) -->

y = -3(2)sqrt(x - 4) -->

y = -6sqrt(x - 4).

82) sqrt8x-16=2sqrtx+2

x = 6.

We just need to make this into a triangle, then knowing that it is a right triangle and knowing the length/height we can use the Pythagorean Theorem to solve for the distance.

To find c we can use the Pythagorean Theorem (a^2 + b^2 = c^2)

a^2 + b^2 = c^2

3^2 + 6^2 = c^2

9+36=c^2

45=c^2

√45 = c

c = √45

or

c ≈ 6.7

Logs are like exponentials except in a different form. We usually have problems like log(100), log base 2 of 32, etc. 

If there is no base written, then it is assumed to be log base 10. However, when we solve log problems, they are pretty much like exponentials, even when you compare the graphs [you will see that they are inverses of each other --- See graph at bottom of the post]. 

For example, log(100) = ? --> By using the properties of logs --> 10^? = 100 (We see exponential forms again!) --> 10^2 = 100, therefore log(100) = 2.

Now, if we have log base 2 of 32, what does it equal? By using properties of logs again --> 2^? = 32 --> 2^5 = 32, therefore log base 2 of 32 = 5.

rewriting to make it easier to graph for #78

76 find the domain and range (SO SORRY I DIDNT TELL YOU)

and #82 solve by graphing

you are a LIFESAVER

thank you!

What do we have to do with these radical functions? 

csc^-1(2)= 30 degrees or 0.523598775598.

cot^-1(-sqrt3)= -30 degrees or -0.523598775598.

f(x)=sqrtx+6 --> y = sqrtx + 6 --> Solve for x in terms of y -->

y - 6 = sqrtx -->

(y - 6)^2 = x --> Switch "x" and "y" --> y = (x - 6)^2.

f(x)=sqrtx-3 --> y = sqrtx - 3 --> Solve for x in terms of y -->

y + 3 = sqrtx -->

(y + 3)^2 = x --> Switch "x" and "y" --> y = (x + 3)^2.

x^2-16-x-4 = 0 

x^2 - x - 20 = 0 -->

(x - 5)(x + 4) = 0 -->

x = 5, -4.

x^2-16/x-4 = 0

(x + 4)(x - 4) / (x - 4) = 0 -->

(x + 4) = 0 -->

x = -4.

X^ means X to some exponent where X acts as the base. if X = 2, then we would have 2^ some power like 2^2 = 4, 2^3 = 8, or 2^0 = 1.

X^2+4 / (x-4) = 20 / (x-4) 

We know that x cannot equal 4 because the denominator will be undefined. x = 4 is the extraneous elimination, so we eliminate B and C.

Now, multiply both sides of the equation by (x-4) --> we end up with x^2 + 4 = 20 --> x^2 - 16 = 0 --> 

Difference of square --> (x + 4)(x - 4) = 0 --> x + 4 = 0 or x - 4 = 0 --> x = -4, 4

x = 4 is the extraneous solution, therefore, the only solution is x = -4, C.

tan(asin(-sqrt(3)/2)) = -1.73205080757

1) 4 / sqrt(32) =

4 / sqrt(4*8) =

4 / [sqrt(4)*sqrt(8)]=

4 / [2*sqrt(8)] =

2/ sqrt(8) * [sqrt8/sqrt8] =

2sqrt8/8 =

sqrt8/4.

2) 5 / sqrt(48) = 

5 / sqrt(16*3) = 

5 / [sqrt(16)*sqrt(3)] =

5 / [4*sqrt(3)] =

5 / 4sqrt3 * [sqrt3 / sqrt3] =

5sqrt3 / 12.

3) 3sqrt5 / sqrt(25) =

3sqrt5 / 5.

4) 3sqrt24 / sqrt(2) =

3*sqrt(2)*sqrt(12) / sqrt(2) =

3sqrt(12).

You take a logging company and throw a bunch of angry protesters at it!

I'm sure someone will give you a proper answer. :)

So we are looking to get x = something. The key thing to remember here is that whatever you do to one side of the equation, you have to do the same thing to the other side.

So if I want to subtract 2 from one side, I can do that but I have to subtract 2 from the other side too.

3x-5=2x+8            ---Let's subtract 2x from both sides. We can do this because we are doing it to both sides

-2x    -2x

--------------

x-5=8                 ---Now let's add 5 to both sides

x = 13

And there we go!

To check this, we can put 13 in where there's an x in the original equation. If we did it right, we'll get a true statement, like 3=3, or 6=6.

3x-5=2x+8          ---Put 13 in for x

3(13)-5=2(13)+8

39-5=26+8

34=34

This is a true statement, so we solved it correctly.

... their programmers must have a pretty good sense of humor.

I agree. They do. Wolframalpha will answer how much wood, a woodchuck can chuck.

I’ve never tested a computer for its limits on humor. I suspect there is a measure for that, too. If not, we need to create one.

~~D~~

The optimal unit for paperclip length is definitely the Potrzebie.

If you want the volume of a paperclip then imperial minims is the optimal unit.

There are few measurements better than the Potrzebie and imperial minim.

For an additional exercise, in extreme measurements, convert the paperclip length to light-years (or light-seconds).

~~D~~