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Think i worked it out. I used , instead of .

Anyone want to help still? I am really s**t at illustrating stuff like this.

Need a prog/site that makes it easy to copy/paste it into a word doc.

And ye catch h (y-axis) vs effort E (x-axis)

You have two = signs!!

What do you want to plot against what (h vs E?)? 

3x + 1/19 is the simplified answer, the z on the top and bottom cancel each other out because no matter what number z is you will have a number being divided by itself and that is always going to equal 1.

tan^2 30 - cos^2 45 ?

=-1/6

Factor the following:
3 x^5+2 x+5

The possible rational roots of 3 x^5+2 x+5 are x = ±1/3, x = ±5/3, x = ±1, x = ±5. Of these, x = -1 is a root. This gives x+1 as all linear factors:
((x+1) (3 x^5+2 x+5))/(x+1)

 |  |
x | + | 1 |  | 3 x^4 | - | 3 x^3 | + | 3 x^2 | - | 3 x | + | 5
3 x^5 | + | 0 x^4 | + | 0 x^3 | + | 0 x^2 | + | 2 x | + | 5
3 x^5 | + | 3 x^4 |  |  |  |  |  |  |  |
 |  | -3 x^4 | + | 0 x^3 |  |  |  |  |  |
 |  | -3 x^4 | - | 3 x^3 |  |  |  |  |  |
 |  |  |  | 3 x^3 | + | 0 x^2 |  |  |  |
 |  |  |  | 3 x^3 | + | 3 x^2 |  |  |  |
 |  |  |  |  |  | -3 x^2 | + | 2 x |  |
 |  |  |  |  |  | -3 x^2 | - | 3 x |  |
 |  |  |  |  |  |  |  | 5 x | + | 5
 |  |  |  |  |  |  |  | 5 x | + | 5
 |  |  |  |  |  |  |  |  |  | 0:
Answer: |  3 x^4-3 x^3+3 x^2-3 x+5 (x+1)

no, 100 * 100% = 100

because PERCENT (%) is meusured in .01.

so YOU try multiply by 100% to get it, but if you multiply by 100%, you are just multiplying by 1.

Thanks,  Landry.......here's another formula....if we know the side length

We have 5 equal isoceles triangles.......each with an apex angle of 72°

If we know the side length, the height of each triangle can be found, thusly:

tan (36) = (1/2)s / h

h = s / [2 tan 36]  =  (1/2)s*cot36

So....the area of one triangle =

(1/2)s * (1/2)s * cot 36  =

(1/4)s^2 * cot(36)

So....the total area =

(5/4)s^2*cot(36)  =

(5/4)s^2 * tan(54)

Actually, you are multiplying by 100 %, not 100.

As 100 = 100 * 100 % = 10 000%

Thanks Alan :)

Melody,

These are quite well known summations, though I can't think, offhand, exactly how to do them!

5*4*3*2*1 = 120

I think this is what you mean:

3/7=0.428571.... x 100=42.8571%

log_3⁡〖[(100x^3 ∛(5-x))/(27(x+7)^4 )]〗 needs expantion

\(log_3⁡\frac{100x^3 \sqrt[3]{5-x}}{27(x+7)^4 }\\ =log_3⁡ [100x^3 \sqrt[3]{5-x}]\quad-\quad [log_327(x+7)^4] \\ =log_3⁡ [100]+log_3⁡ [x^3 ]+log_3⁡ [\sqrt[3]{5-x}]\quad-\quad [log_327+log_3(x+7)^4] \\ =log_3⁡ [100]+log_3⁡ [x^3 ]+log_3⁡ [\sqrt[3]{5-x}]\quad-\quad log_327-log_3(x+7)^4 \\ =log_3⁡ [100]+3log_3⁡ [x ]+\frac{1}{3}log_3⁡ (5-x)\quad-\quad log_33^3-4log_3(x+7) \\ =log_3⁡ [100]+3log_3⁡ [x ]+\frac{1}{3}log_3⁡ (5-x)\quad-\quad 3-4log_3(x+7) \\ \mbox{I am going to stop here because this is not going anywhere.}\)

It is thought by astronomers and comologists that only 1 in a billion, or one in 10^9,  particles of matter remained in the early Universe.

Thanks Alan, am I right in thinking you just already knew those equivalent expressions. ??

I thought there might be a way of determining them without pre-knowledge ://

If a>0 and n is whole number ,then(2^n/(1+a^(2^n))

\(\frac{2^n}{1+a^{2^{n}}}\)

I don't see how this can be simplified :/// 

Maybe someone else can though ?

In a cone, the radius is 8 cm and the lateral surface area is 136pi cm^2.

1. find the slant height of the cone.

2.Find the height of the cone.

3.Find the volume of the cone, in terms of pi.

The lateral surface area of a cone is given by the formula  pi*r*L   where L is the slant height.

\(Lateral\; Surface\; area=\pi rl\\ 136\pi = \pi \times 8 \times l\\ 136=8 \times l\\ 17=l\\ slant\;height=17\;cm \)

The radius is 8cm and the slant height is 17cm

so

\(h^2=17^2-8^2\\ h^2=289-64\\ h^2=225\\ h=15\; cm\)

A cone is a circular pyramid and the volume of any pyramid is   V = (1/3) * area of base * perpendicular height

\(Area \;of \;base = \pi*r^2 = \pi * 8^2 = 64\pi\)

\(V=\frac{1}{3}*64\pi*15\\ V=64\pi*5\\ V=320\pi\;\;cm^3\\\)

pmcc = Pearson product moment correlation coefficient.

See:  https://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient for example

This can be expressed as follows:

As Melody noted, it is not an Arithmetic Progression, which has a constant difference between successive terms.

.

Not as a general rule. 

Well, here's an exponential decay and an exponential decay shifted up by 7 units:

.

Undefined.

limit as x → 0  of  0^x is 0

limit as x → 0 of x^0  is 1

.