Melody

use pythagoras's theorum

\(d^2=l^2+b^2\)

Hello, I have a recipe that comes in a three-part solution 1000ml of A, 500ml of B, and 250ml of C which makes a 1750ml solution kit, how do you solve this if i need 300ml of solution in total, how do i calculate whats needed for parts A, B and C. Thanks Nigel

We are not here to do your homework for you.

ok :)

\(k=2^p-1\\ N=k^2-1\\ N=(2^p-1)^2-1\\ N=2^{2p}-2*2^p+1-1\\ N=2^p*2^p-2*2^p\\ N=2^p(2^p-2)\\ N=2^{p+1}(2^{p-1}-1)\\ so\\ 2^{p+1}\text{ is a factor of }N\)

So I have shown that  2^(p+1) is a factor of N

Which is the other way around from what you asked.

what a strange question.

4(sin^4 30^o+cos^4 60a^o)-2(cos^2 45^o-sin2 60^o)  -    [4(sin^4 30^o+cos^4 60a^o)-2(cos^2 45^o-sin2 60^o)] =0

perhaps you want to know what the value is ...

\(4(sin^4 30^o+cos^4 60a^o)-2(cos^2 45^o-sin2 60^o)\\ =4(\frac{1}{2^4}+cos^4 60a^o)-2(\frac{1}{2}-sin2 60^o)\\ \text {interpretation of meaning (possible errors)}\\ =4(\frac{1}{2^4}+cos^4 60^o)-2(\frac{1}{2}-sin^2 60^o)\\ =4(\frac{1}{2^4}+\frac{1}{2^4})-2(\frac{1}{2}-\frac{3}{4})\\ =4(\frac{2}{2^4})-2(\frac{-1}{4})\\ =\frac{1}{2}+\frac{1}{2}\\ =1 \)

so

4(sin^4 30^o+cos^4 60^o)-2(cos^2 45^o-sin^2 60^o) -1 =0

Hi Tetre,

The word trapezoid means different things in different countries, could you plase give a definition that we should use?

I'll just tell what I think you mean.

AB and DC are parallel.  

This means that AEB and DEC are similar triangles 

so

the ratio of the height of ABE and DEC will be   8:17

so  Area of  AEB = 0.5*8*8k       and area of DEC = 0.5*17* 17k    

and area of  ABCD = 0.5*17* 17k  -   0.5*8*8k

ratio of the area of triangle EAB  to the area of trapezoid ABCD

\(=\frac{0.5*8*8k}{0.5*17*17k\;-\;0.5*8*8k}\\ =\frac{8*8k}{17*17k\;-\;8*8k}\\ =\frac{8*8}{289\;-\;64}\\ =\frac{64}{225}\\\)

Yes, there is a loop :)

\(\int e^{5x}sin(3x)dx=[\frac{e^{5x}}{5}\cdot sin(3x)]-\int \frac{e^{5x}}{5}\cdot3cos(3x)dx\\ \int e^{5x}sin(3x)dx=\frac{e^{5x} sin(3x)}{5}-\frac{3}{5}\int e^{5x}cos(3x)dx\\ \int e^{5x}sin(3x)dx=\frac{e^{5x} sin(3x)}{5}-\frac{3}{5}\left[(\frac{e^{5x}cos(3x)}{5})-\int \frac{-3}{5} e^{5x}sin(3x)dx\right]\\ \int e^{5x}sin(3x)dx=\frac{e^{5x} sin(3x)}{5}-\frac{3e^{5x}cos(3x)}{25}- \frac{9}{25}\int e^{5x}sin(3x)dx+c\\ \int e^{5x}sin(3x)dx+ \frac{9}{25}\int e^{5x}sin(3x)dx=\frac{e^{5x} sin(3x)}{5}-\frac{3e^{5x}cos(3x)}{25}+c\\ \frac{34}{25}\int e^{5x}sin(3x)dx=\frac{5e^{5x} sin(3x)}{25}-\frac{3e^{5x}cos(3x)}{25}+c\\ \int e^{5x}sin(3x)dx=\frac{5e^{5x} sin(3x)}{34}-\frac{3e^{5x}cos(3x)}{34}+c\\ \int e^{5x}sin(3x)dx=\frac{e^{5x} (5sin(3x)-3cos(3x))}{34}+c \)

Hi :)

I always like to see people thinking about numbers the way you do but infintiy^2 has no real meaning. I mean it is no bigger than infinity.  You can square huge numbers and get an even bigger number but infinity is not a huge number. It is a concept. 

Hi Geno,

This still does not make sense to me.

Ther must be more teams playing or else the percentages do have to add to 100% and if other teams are playing and there are 180 games in total then no team will actually get to play 180 games will they. 

So like i said, id does not make sense to me :/

2y^2-12y-17=x

This is a sideways parabola (because it is the y that is squared)

it opens out in the positive direction because   the number in front of the y^2 is positive (+2)

When y=0, x=-17

So it must have 2 real roots, if you sketch what I have said so far you will see why.

\(\triangle = b^2-4ac = 144-136=8\)

8 is not a perfect square so there are 2 irrational roots.

The axis of symmetry is   y=-b/2a = 12/4 = 3

So the roots, (y intercepts), are,    

\(x=\frac{--12\pm\sqrt8}{4}\\ x=\frac{12\pm2\sqrt2}{4}\\ x=\frac{6\pm\sqrt2}{2}\\ \text{So it is a sideways parabola that passes through}\\ (\frac{6+\sqrt2}{2},0),\;\;\;(\frac{6-\sqrt2}{2},0),\;\;\;and \;\;\;(-17,0)\)

At the vertex y=3 sub that in to get the value of x