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x^4 - 46x^2 + 45 = 0

Let u = x^2

u^2 - 46u + 45 = 0

This factorises;  (u - 1)(u - 45) = 0

So 1)  u = 1       2) u = 45

Hence 1) x^2 = 1   so  1a) x = 1    and   1b) x = -1

and      2) x^2 = 45   so  2a)  x = sqrt(45) , x = sqrt(9*5),  x = 3sqrt(5)   and   2b)  x = -3sqrt(5)

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10000 - 5 = 9995

Watch this :)

You can shove your spam far up yourass

You can shove your spam up yourass

Guest, I understand your reasoning. I tend to think of equations like this when I see elementary posts:

\(\hspace {.1em} \lim_{\Delta t \to 0^+} \int_{\Delta t}^{T} \int_{\Omega}D(t_1,x) \frac{\phi(t_1-\Delta t,x)-\phi(t_1,x)}{(-\Delta t)} dx \,dt_1 \\ \hspace {3em} =\lim_{\Delta t \to 0^+} \int_{0}^{T} \! \int_{\Omega} D(t_1,x) \frac{\phi(t_1-\Delta t,x)-\phi(t_1,x)}{(-\Delta t)} \chi_{(\Delta t,T)}(t_1) dx \, dt_1 \\ \hspace {3em} = \int_{0}^{T} \! \int_{\Omega} D(t_1,x) \frac{\partial\phi}{\partial t_1}(t_1,x) dx \; dt_1 \\ \)

This is the simplified version and it easily conveys the point in basic terms. 

BTW, you mangled your mathematical presentation (Buggered it up, in case you don’t know what that means).

4 above 3 plus 4 above 5 is this:

\(3^{(4 + 5^4)} \\ = 3^{(4 + 625)} \\ = 3^{(629)}\\ = 1.28608... \times 10^{300}\)

We don’t want to send students down the wrong path. 

2x+34=0 <=> 2x=-34 <=> x=-34/2 <=> x=-17

18/18 = 1

Any number, except 0, divided by itself = 1

Yes! Thank you

\((3x^{\frac13})\cdot(8x^2) \\~\\ =3\cdot x^{\frac13}\cdot8\cdot x^2 \\~\\ =3\cdot8\cdot x^2\cdot x^{\frac13} \\~\\ =24\cdot x^{2+\frac13} \\~\\ =24\cdot x^{\frac73}\)

And x^(7/3) is the same thing as the cube root of ( x⁷ ) ....

\(=24\sqrt[3]{x^7}\)

Does that answer the question ?  

\(10=4+4+4-\sqrt4 \)

\(11=\frac{44}{\sqrt4^{\sqrt4}}\)

\(12=\sqrt4(\sqrt4+\sqrt4+\sqrt4)\)

There are 3! (3*2*1), or 6 ways to plan the family vacation. The factorial function would be useful here, as you wouldn't have to list all the possibilities, but instead calculate 3!.

Ah okay..thanks for the explanation!  

Here's a 7, 8, and 9...(...These ones seemed a little too easy  )

\( 7=4+4-\frac44 \\~\\ 8=4+4*\frac44 \\~\\ 9=4+4+\frac44\)

use the 2nd button

I do not know if this will satisfy you but

\(e^{i\theta}\quad \text{can be written as }cos\theta+isin\theta\\ so\\ e^{\pi i}=cos\pi +isin\pi = -1+i*0 = -1\)

Good job, hectictar!

Concatenation means the action of linking together. For example, 44 is a concatenation, or a link, of a 4 and another 4. Makes sense, no? It's an easier concept to explain than to say the vocab word...

Anyway, here comes the next few.

\(5=\sqrt4+\sqrt4+\frac{4}{4}\)

\(6=\frac{4!}{4+4}*\sqrt4\)

\(Area=1456ft^2\)

First, let's look at the given info. We know that there is 155 feet of fence. 155 feet of fence is referring to the entire perimeter. 45.5 feet is referring to only one side length. In a rectangle, however, opposite sides are congruent. The formula for finding the perimeter is 2(l+w).

Let w= width 

\(155=2(45.5+w)\)      Substitute the values in that we know from given info.

\(155=91+2w\)      Distribute the two into the parentheses.

\(64=2w\)      Subtract 91 from both sides

\(w=\frac{64}{2}=32\)      Divide 2 from both sides to isolate the width.

Although we have found the width, this is not the final answer because the question is asking for the entire area of the fenced area. The formula is A=lw. w=32.5 and l=45.5

\(A=32*45.5=1456ft^2\)Of course, include units in your final answer.

I am not very good at these.....but here's ones for 2 and 3 and 4:

2 = \(\frac{4*4}{4+4}\)

3 =  \(\sqrt{4}+\sqrt4-\frac44\)

4 = \(4! - 4*4 - 4\)

Also...what do you mean by concatenation?

I looked it up but I still don't really know what it is

*edit*

I accidentally put 5 fours for 2...thanks to geno for letting me know!! 

Find the volume of a grain silo with a half sphere on one end that has the diameter of 6ft and a cylinder height 35 ft.

The radius is a half or the diameter

You have half a sphere with diameter 6'

and you have a cylinder with diameter 6' and length 35'

Volume of sphere is  4/3pi r^3

Volume of cylinder is   pi*r^2*h

Work the 2 out and add them together :)

Much help thanks very much

Thanks

4 above 3 + 4 above 5

\(\frac{4}{3}+\frac{4}{5}\\ =\frac{4}{3}*\frac{5}{5}+\frac{4}{5}*\frac{3}{3}\\ =\frac{20}{15}+\frac{12}{15}\\ =\frac{32}{15}\\ =2\frac{2}{15}\)

Im not sure what you mean by "above," but this is my interpretation of that. I apologize if this is incorrect:

\(4^{{3+4}^5}={4^{7^5}}={4^{16807}}\approx{6.64162344 × 10^{10118}}\)

can anyone help answers these?