/sci/ - Science & Math

u = 2
v = 3

or

u = 1.5
v = 4
u = 6/v. substituting into OP
12/v + v = 7
12 + v^2 = 7v
v^2 - 7v +12 = 0
(v-3)(v-4) = 0
v = 3 or 4

substitute into OP and u becomes obvious.
k-thnx-bai.

>>3160775
the gene for antibiotic resistance will be within the plasmid, it is the plasmid that is transformed.
only bacteria with that specific transformed plasmid will be able to survive exposure to the antibiotic, all otehr bacteria will be killed by the antibiotic, so you have a pure sample and know that every single individual bacterium in teh colony MUST have the plasmid with the resistance gene in it.
Then you can lyse the bacteria allowing the plasmid to be isolated and collected.

>>3101422
sorry, was away. very busy today.
erm, shortest possible will be SQRT[748], and the garden will be square,
longest is 34 meters.
gotta go.
xxx

>>3063627
hmm, yes. better to teach him the method, than give him the answer i think.
here was to do:
if you are factoring a quadratic in the form x^2+bx+c
then the answer will be (x+p)(x+q)
where c = (pq) and b = (p+q)
so all i had to do was find 2 numbers that multiply together to make 26, and add together to make 15.
13 and 2 jumped straight into my mind...you can just keep trying all different combinations until you get one that works for both.

>>2977055
there was a whole thread about this before. notice that on OP's picture the 'plank' is a very thin rod of wood,
so it isnt a flat square board like you are imagining.

secondly, you can invent an infinite ways to make smaller cuts and make more pieces. on your square board analogy you could cut off a tiny segment from one of the corners, and you would have made an extra piece, in not much time at all.

presuming that all cuts are the same length, (so you cut the width of the board, and then the width of the board again) then the answer is 20 minutes.

>>2932320
<span class="math"> t = (v-u)/a [/spoiler]

the brackets are important here.

43,156.1 - 42,876.1 = 280 miles
at 35 miles per gallon thats 8 gallons

$34.24 / 8 = $4.28 per gallon

(x^2+4x+3)(x-2)
x^3+4x^2+3x-2x^2-8x-6
x^3+2x^2-5x-6

(x^2+4x+3)(x-2)
x^3+4x^2+3x-2x^2-8x-6
x^3+2x^2 -x-6

in your equation, multiply both sides by 1 - sinx to get:

<span class="math"> (1+sinx)(1-sinx) = cos^2x [/spoiler]
<span class="math">1 - sin^2 x = cos^2x [/spoiler]

we know [sin^2x+cos^2x = 1] so we get:
<span class="math"> sin^2x+cos^2x - sin^2 x = cos^2x [/spoiler]
<span class="math"> cos^2x = cos^2x [/spoiler]
yes it does.
awesome.

odds for box B are 7/10
odds for box A are 2/10

odds that box B was picked is (7/10)/(7/10 + 2/10)

=7/9

i just realised this will probably need some explanation...im aleady starting to feel a bit high so please bear with me.

1. chance of F being at the start is 1/9, when this occurs, the chance of S being at the end is 1/8 (after F is placed, there are 8 letters left to place, and the end letter has 1/8 chance of ebing any of them)
multiplying these probabilities gets 1/72.

for 2, the 4 maths books arranged together in a cell of 4, can be done in 24 different ways (thats 4!) and after considering this, we can treat them as 1 cell.
so thats the cell of math books, + the 8 unplaced english books, so we have to consider 9 combinations now that we already have this cell, and that means 9!
so the answer will be 4! X 9!

for 3, its easier to consider the odds of the 2 i's being together, and do the 100% - this to find the cases where it isnt. and this is 10! as we treat the 2 i's as 1 cell, so there is 11 letters all together, but we do 10! as we treat 2 i's as 1 here.
so chance of 2 is togetehr is 10!/11!
therefore the chance of 2 i's NOT together will be 1 - (10!/11!)

kk, this stumped me originally, until i realised its 5 vowels and 5 consonants.
ok, first of all there is a multiplication factor of 2 outside the brackets because it can eitehr go AVAVAVAVAV or VAVAVAVAVA

ijn any of these cases, treat it as 2 different cells of 5, now that they all have their place and are seperated, and this means 5! for the vowels, and 5! for the consonants.
this gives 2X5!X5! and to find teh probability, we just have to divide this by the nu,ber of total combinations in teh system, which is 10! (as there are 10 letters all together. this means probability will be (2X5!x5!)/10!

if explanation is hard to follow, its coz im a little high right now.

weight isnt a factor here, as already previously stated this is a matter of equating kinetic energy with potential energy

H is he height, which is 0.4 X 2, seeing as the diameter of the loop is the height, not the radius. so H = 0.8

potential energy = MGH = MX9.8X0.8 = 7.84M
kinetic energy = 0.5MV^2

0.5MV^2 = 7.84M
the M's cancel, so we have
0.5V^2 = 7.84
V^2 = 15.68
V = 3.96 m/s to 3SF

weight isnt a factor here, as already previously stated thsi is a matter of equating kinetic energy with potential energy

H is he height, which is 0.4 X 2, seeing as the diameter of the loop is the height, not the radius. so H = 0.8

potential energy = MGH = MX9.8X0.8 = 7.84M
kinetic energy = 0.5MV^2

0.5MV^2 = 7.84M
the M's cancel, so we habe
0.5V^2 = 7.84
V^2 = 15.68
V = 3.96 m/s to 3SF

Hi there OP.
this stumped me for a long time, but i think ive got it.

okay, for the box we have dimensions <span class="math"> yx^2 [/spoiler]because the bottom is a square (so 2 dimensions are the same, hence the x's) and we have the height, y.

the equation for volume is: <span class="math"> 12500 = yx^2 [/spoiler]

now we need an equation for cost.
<span class="math"> C = 0.06x^2 +0.08xy [/spoiler]

this requires some explanation i think.
the bottom is 0.05 per cm^2, and the top is 0.01cm^2 (only the base is more costly) so adding these together, this is the price to pay for 1 cm^2 in the x^2 plane.
now the other plane is up the side of the box, this is xy, because it is the height, times the length.
the price for this is 0.08, because OP, specified we double pack the sides, so it is 0.01, X 4 sides X 2 (for doublepack) = 0.08.

now, by using simultaneous equations, i rearange the volume equation to get <span class="math"> y = 12500/x^2 [/spoiler]

putting this into the cost equation we get <span class="math"> C = 0.06x^2 + 0.08x(12500/x^2) [/spoiler]
<span class="math"> = 0.06x^2 + 1000/x [/spoiler]

plugging that into wolfram alpha, it gives a minimum value of x as 20.274.
http://www.wolframalpha.com/input/?i=C+%3D+0.06x^2+%2B1000%2Fx
plug that into the equation <span class="math"> yx^2 = 12500 [/spoiler] and you get
<span class="math"> 411.035y = 12500 [/spoiler]
<span class="math"> y = ~30.411 [/spoiler]

so these are the dimensions for minimum cost.

very hard question... i am not often stumped, but i took a while on this one.

if somebody else already posted the answer...fair play.

<span class="math"> x^3 -2x^2 + x [/spoiler]

first off, 'x' can be seen as a common factor by observation, so lets take that out first.

<span class="math"> x(x^2-2x+1) [/spoiler]

next, by EK's shortcut faggotry rule, we need 2 numbers that multiply to make 1, and add together to make -2.
by observation, oh will you look at that! '-1' works perfectly (by observation). and seeing as it is the same number, instead of 2 brackets, we will just have 1 squared.
so it will be
<span class="math"> x(x+1)^2 [/spoiler]

12: 0.023X(230-170)/2.0

= 0.69 m/s
(also, is that 2.0 kg block of wood, or 20 kg block of wood, i honestly cant tell if i am imagining a decimal point there... if i am, then its a 20 KG block of wood, and the answer is 0.069.

15. I = m(v-u) = 0.045X45 = 2.025.

force = impulse/time = 2.025/3.5X10-^3 = 578.57N to 2dp.

>>2389482
actually i may be wrong... the amount of water displaced by the boat is dependent on the mass of the boat and everything it occupies, therefore, a heavier anchor means the boat is lower in the water and displaces more of the water.
however, if the anchor is thrown overboard then as long as it is heavy enough to sink, its VOLUMe not mass, determines how much water is displaced.
so if we have a very light anchor, made of carbon fibre that is very big, when thrown overboard, the water level will increase as it displaces a lot of water.
if a very small but heavy lead anchor is used, when throw overboard the water level will decrease, as the boat is signicantly lighter, and so higher in the water, but the anchor doesnt displace much water.
also, i suspect someone may have beaten me to this point while i am writing this. if so, brofist.
that is all.

2091.5 = 4.175w

so just divide both sides by 4.175 to find out what w is.