# Posts by Damon

Total # Posts: 29,753

Math
12 marbles to start drew one yellow 4/12 then 11 marbles of which 3 are yellow 3/11 so 4/12 * 3/11 = 1/11

maths
cost = 1040 - 240 = 800 (240/800)100 = 30% profit 12 * 6.50

Stoichiometry
(75/1000).6 = .045 mol CaCO3 = 100 g/mol so 4.5 grams

Stoichiometry
CaCl2 + Na2CO3 ---> CaCO3 +2NaCl one to one in mols of each 75 *.6 = x * .4

maths
2400 * .15 2400 * 1.15 .8*2400 before VAT

maths
0.8 Liters * n = 36 Liters n = 38/0.8 = 45 cans ======================= b makes no sense to me. It is a typo I think.

Math
t/5 = (t-5)10 t = (t-5)50 t = 50 t -250 49 t =250 t = 250/49

Probablility
I assume you never use the same machine twice first cardio = 4/10 = 2/5 second = 3/9 =1/3 third = 2/8 = 1/4 fourth = 1/7 product = 2/5 *1/3*1/4*1/7 = 1/210 now weight first =6/10 = 3/5 second = 5/9 third = 4/8 = 1/2 fourth = 3/7 product = 3/5 * 5/9 * 1/2 * 3/7 =1/14 so 1/210...

Algebra
7-5.375 = 1.625 for left and right margins 1.625 - .3125 = 1.3125 for right margin do the vertical problem the same way

Algebra
75*20 + 95*30 = x * 50

Math
5 * 3/1 = 15

pre calculus
100(-.5 -.866i) - 50 - 50 sqrt3 i

pre calculus
we want r(cos T + i sin T) r = sqrt ((-2)^2 +2^2) =sqrt 8 =2 sqrt2 -2 = r cos T = 2 sqrt 2 cos T cos T =-sqrt 2 / 2 T = 3 pi/4 2 = R sin T = 2 sqrt 2 sin T sin T = sqrt2 /2 T = 3 pi/4 all right so z =2 sqrt 2[cos .75 pi+isin .75 pi]

AP Calculus
well lets think it might be like a hot stone cooling down to some room temperature Tf Google Newton's law of cooling T = Ts +(To-Ts)e^-(k t) To is your original 1900 time Ts is your final time in 2100 or whatever which is the fastest one can ever go k is a constant that ...

physics
Your second method is the right way to go.

pre calculus
I think you probably mean: e^(a+bi) =e^a e^bi = e^a (cosb+isinb) then e^i? = e^(0+i?) =(e^0)(cos pi+isinpi) = 1(-1 + 0) or e^i? = -1

R/5 - 6 = -1 add 6 to both sides R/5 +0 = 6 - 1 R/5 = 5 now multiply both sides by 5 (R/5)5 = (5)(5) R = 25

missing question
[f(x)-f(a)] /(x-a) = 7 as x-->a is the definition of the derivative f'(a) = 7

math
df/dx = 4 x^2/[x^3 +3] at x = -1 df/dx = 4/[2] = 2 so f(-1+dx) = f(-1) + 2 dx here dx = -.1 so f(-1-.1) = -3 +2(-.1) = -3 -.2 =-3.2

Physics
t is in seconds 40 t = 42(t-120)

math
sin ? = 0 slope = cos ? = -1 f(x) = sin(?) -1(x-?) = -(x-?)

science
global positioning systemhttp://www.safewise.com/blog/10-wearable-safety-gps-devices-kids/ ( of course I use GPS to get around the bleak ocean but that is old stuff:) sampling whale snot with drone http://shop.whale.org/pages/snotbot tidal power generation systems http://...

Electronics
http://www.electronics-tutorials.ws/rc/rc_1.html

Math
s^3 = 512 s = 512^(1/3) calculate s = 8 A = 6 (s^2) = 6 * 64

Calculus application of sin function
v = dh/dt = sin pi t then h = - (1/pi)cos pi t but h = A cos (2 pi t/T) so A = -1/pi pi = 2 pi /T so T = 2 so in the ean h =-(1/pi) cos pit = -(1/pi)cos(2 pi t/2) B) h =-(1/pi) cos pit v = dh/dt = sin pi t a = dv/dt = pi cos pi t C)1/pi D) cos 0 = 1 so at t = 0 , 1 , 2 etc E) ...

http://www.wolframalpha.com/widget/widgetPopup.jsp?p=v&id=8d8e2c27bcaa121d6ee0de4b98774bb4&title=Polar%20Graphs&theme=blue&i0=r%3D2(2-sin^2%C9%B5)^%C2%BD%20&i1=0&i2=Pi%2F2&podSelect=&showAssumptions=1&showWarnings=1

calculus
I suspect you mean: r=2(2-sin2?)^½ that makes me nervous that since you do not type exponents you might mean 2-sin^2 ? instead of what your typed. I will assume that first graph it here with sin 2? http://www.wolframalpha.com/widget/widgetPopup.jsp?p=v&id=...

Science
mass = 150/g or about 15 kg but who needs it? x = A sin w t v = Aw cos wt a = -Aw^2 sin wt = -w^2 x ============================= when x = .2 = A sin w t v = 5 = Aw cos w t a = +20=+Aw^2 sin w t = +w^2x =============================== so w^2 x = w^2(.2) = 20 w^2 = 200/2 = 100 ...

Maths
x^2 y = V G = 4x+y = 6 ================== y = 6-4x x^2 (6-4x) = V now do the complete the square thing like I did in your other problem to find the vertex of the parabola

Engineering
4 x = 800 x = 200 feet on a side square ========================= prove that square is max area A = x y P = 2 x + 2 y perimeter so x + y = P/2 A = x (P/2 - x) = -x^2 +P/2 x x^2 - (P/2) x = A find vertex,complete square x^2 - (P/2)x + P^2/16 = -A + P^2/16 (x-P/4)^2 = -(A-P^2/16...

math
s = standards d = deluxe 12 s +18 d = 360 ____divide by 6 s + d = 25 ________multiply by 2 2 s + 3 d = 60 2 s + 2 d = 50 -------------- d = 10 then s = 15

Physics
assume you mean 5 m/s^2 50 *1000/3600 = 13.9 m/s v = 13.9 - 5 t 0 = 13.9 - 5 t t = 13.9/5 average speed during stop = 13.9/2 d = (13.9/2) (13.9/5) or d = Vi t - .5 (5) t^2 d =13.9(13.9/5)-.5 (5) (13.9^2)/5^2 = .5 *13.9^2/5 the same

physics
ub^2 = .25 ua^2 average speed for initial slowing = .5(ua+ub) assume constant a t = .05/.5(ua+ub) = .1/(ua+ub) v = Vi +at ub = ua + a t ub-ua = a (.1)/(ua+ub) .1 a = -(ua^2-ub^2) .1 a = - (.75 ua^2) a = -7.5ua^2 now complete trip 0 = ua + a t t = ua/7.5ua^2 = 1/(7.5ua) d = Vi...

Math
There are lots of different ways. perhaps the easiest to understand uses the distributive property 12 = 10 + 2 13 = 10 + 3 (10 + 2) (10 + 3) = 10 (10+3) + 2 (10+3) = 100 + 30 + 20 + 6 = 100 + 50 + 6 = 156 ========================== You can shorten that by saying 10(13) + 2(13...

Physics
If there is no moment (torque) then there is no change of angular momentum [ I omega = constant] If they are not opposite in direction through the same point, they cause a moment, called a "couple"

algebra
n and 2 n 2 n - n = 20 n = 20 and so answer = 2n = 40

Gaussian Elimination Method
LOL, forgot the old easy stuff :)

Gaussian Elimination Method
to check, put it back in -4(-1) -(-2) = ? yes 6 12(-1) -2(-2) = ? yes -8

physics
m v^2/r horizontal m g down tan theta = mg/(mv^2/R)where theta is angle down from horizontal but cos theta = .7/2.8 so theta = 75.5 deg so tan theta = 3.87 so 3.87 = mg/mv^2/R = 9.81/(v^2/.7) v = 1.33 m/s m v^2/R = .4*1.77/.7 = 1.01 m g = .4*9.81 = 3.92 T^2 = 1.01^2 +3.92^2 T...

Math
9*10^-3 LY (5.88*10^12 mi/LY) = 52.92 * 10^9 mi = 5.292 * 10^10 mi

math!
q = first questions/min 2 q = final que/min t min for first ten 48 - t min for final 11 q t = 10 so t = 10/q q t + 2q(48-t) = 21 10 + 96q - 20 = 21 96 q = 31 q = 31/96 questions/min so twice that = 62/96 to finish ======================== check t = 960/31 = 30.97 min 48-t = 17...

Algebra 2
.75 x + .42 y = .5784 (100) x+y = 100 ============================ .75 x + .42 y = 57.84 .75 x + .75 y = 75 ---------------------- -.33 y = - 17.16 y = 52 x = 48 E

Physics
h f = 14.7 eV lambda = c T = c/f c about 3*10^8 m/s

Physiscs
well the length is L sqrt 13 but who cares? force up from floor = m g = 3g (because wall is smooth none up there) force sideways from wall = F thus force sideways at floor = F toward wall Now moments about center clockwise mg * 2L/2 = m g L counter clockwise F*1.5 L + F*1.5 L...

physics
80 km/hr * 1 hr/3600s * 1000 m/km = 22.2 m/s tan T = v^2/r / g = v^2/gr tan T = 22.2^2/(981) tan T = .502 T = 26 deg 39 min

Physics
rho g h 1000 * 9.81 * 20 = 196,200 Pascals = 1.94 atm gage (over 1 atm) or 2.94 atm absolute

Physics

Calculus
Oh, but I said where x = +/- infinity

Calculus
Oh, yes :)O

Calculus
Oh my, look around x = 0 and x = 1 and x = infinity and x = -infinity http://www.wolframalpha.com/input/?i=plot+1%2F(x(x-1))

Math
a) sin is + in I and II b) cos is - in II so there only c) hard to sketch here from origin up 7 distance 25 x^2 + 7^2 =625 and x is - x^2 = 625 - 49 = 576 x = -24 so point is at (-24,7) cos C = -24/25 tan C = -7/24

Math
cos /sin = -1 = cotan 90 + 45 360 - 45

Consider the linear programming problem
You are welcome.

Consider the linear programming problem
which we could have seen without doing the problem :) The potato seed costs less and the profit is more

Consider the linear programming problem
maximize 150 x + 50 y x + y <=70 20 x + 60 y <= 3000 x>= 0 y>= 0 x+y >=1 to fill in input form only http://www.wolframalpha.com/widget/widgetPopup.jsp?p=v&id=1e692c6f72587b2cbd3e7be018fd8960&title=Linear%20Programming%20Calculator&theme=blue result 10500 at (70,0)

Calculus
f' = 10 - 10/x^2 f" = 0 - 10 [ -2/x^3] = 20/x^3 I do not see anyplace where the curvature passes through zero except at x = +/- infinity

Linear Programming to Maximize Profit
You are welcome.

Linear Programming to Maximize Profit
Oh my heavens I have done so many linear programming problems tonight! s uses 6 plastic d uses 3 plastic so 6 s + 3 d </= 300 s uses 4 metal d uses 8 metal so 4 s + 8 d </= 608 s </=22 maximize 10 s + 2 d I get 332 at (22,56) using http://www.wolframalpha.com/widget/...

math
7x = 1.40 x = .20 2x = 0.40 4x = 0.80 5x = 1.00 7x = 1.40 sum = \$3.60

simplex method
For instructions using Simplex with pivots etc see http://en.wikipedia.org/wiki/Simplex_algorithm

doing with linear programming
http://www.wolframalpha.com/widget/widgetPopup.jsp?p=v&id=1e692c6f72587b2cbd3e7be018fd8960&title=Linear%20Programming%20Calculator&theme=blue max = 3220 at (12,50)

Calculus
This is a closed path check first if field is potential in which case integral is zero F = z^2 i + 2xy j + 3y^2k del cross F = 0 ???? nope no way so first line = 3 i + 0 j + 0 k F dot line = Fx *3 = 0*3 = 0 second line in x from 3 to 3 = 0 in y from 0 to 3 = 3 in z from 0 to 1...

Calc
or rather curl F

Calc
curve is ellipse at z = 11 and 5, y = 0 and x = +/-3 (-3 , 0 , 11) (+3 , 0, 5) at z = 8 , x = 0 and y = +/-3 The normal to that ellipse is in he x z plane and is perpendicular to the line joining(-3, 0 ,11)and (3,0,5) slope of that original line dz/dx = -6/6 = -1 remarkable so...

MITx

Calc
You doing an MITx subject?

Calc
curl of F over the surface curl is i j k d/dx d/dy d/dz fx fy fz is =(dFz/dy-dFy/dz)i +(dFx/dz-dFz/dx)j +(dFy/dx-dFx/dy)k here Curl F =(ex-9x)i +(y-ey)j +(9z-z)k

Calc
Flux = int over S of F dot [1i - (dz/dx)^2j -(dz/dy)^2k] F dot [i -4x^2 j - 4y^2 k] [xy - 4x^2yz -4y^2xz]dx dy now put in 2 -x^2-y^2 for z and do the integrals from 0 to 1

physics
if boy at 1 meter girl at (4/3) meter

physics
50 N * .2 m = 10 Nm

The Graphical Method
I get 40 of A, 0 of B for profit = 1000 maximize 25 x + 15 y constraints 5x+4y<=300 2x+3y<=108 x>=0 y>=0 x+y>=1 (phony to fill fields)

linear programming
http://www.wolframalpha.com/widget/widgetPopup.jsp?p=v&id=1e692c6f72587b2cbd3e7be018fd8960&title=Linear%20Programming%20Calculator&theme=blue try that while I look at your problem

f(x)/(x-a) = f(a) here a = -3 so we need f(-3) f(-3) =(-3)^4-9(-3)^3-5(-3)^2-3(-3)+4 = 81 + 9*27 - 45 +9 + 4 = 81 + 243 - 45 + 9 + 4

Linear Programming
note, to make the program format happy I put in max 180x+60y x+y</=60 20x+10y<=700 x>=0 y>=0 x+y>=1 phony but fills boxes

Linear Programming
a+b<=60 20 a + 10b </= 700 a and b >=0 maximize 180 a + 60 b intersections at 0,60 35,0 10,50 at a = 0, b = 60 180 (0) + 60 *60 = 3600 at a = 10, b = 50 180(10) + 60(50) = 4800 at a = 35, b = 0 180(35) = 6300 so plant 35 acres of a and zero of b. Use the whole \$700 ...

Linear Programming
http://www.wolframalpha.com/widget/widgetPopup.jsp?p=v&id=1e692c6f72587b2cbd3e7be018fd8960&title=Linear%20Programming%20Calculator&theme=blue

Gaussian Elimination Method
+5 -4 12 divide by 5 to get 1 -5 +3 +9 +1 -4/5 12/5 multiply by 5 and add -5 +3.0 +9 +1 -4/5 12/5 +0 -1.0 21 multiply by -1 +1 -4/5 12/5 +0 +1.0 -21 so y = -21 now multiply second eqn by 4/5 and add to first +1 -4/5 12/5 +0 +4/5 -84/5 +1 +0 -72/5 +0 +1 -21 x = -72/5, y = -21

Physics
sure, if you use a seesaw, you must be twice as far from the pivot point as the weight is. You must move twice as far down as the weight moves up. (draw geometry) You could use a pulley with one end of the line attached to the ceiling, then running down through the block on ...

Calculus
depth = h dV/dh = area of surface (draw it :) dV/dh = pi r^2 = surface area r = (2.7/4.3)h remember to use chain rule. for example dV/dt = 59.5 m^3/min but dV/dt = dV/dh dh/dt so dh/dt = 59.5/ (pi r^2) etc

Science
Now what American mammal is marsupial?

Science
eg: http://www.ucmp.berkeley.edu/mammal/marsupial/marsupial.html

Science

help me plz
I wish I knew what rt{t} meant but anyway we will need to do r of 9 and delta r for delta t at t = 9 r = t i + t^1.5 j + e^.25 t k dr/dt= i + 1.5 t^.5 j + .5 e^.25 t so dr (your delta r) = dt i + 1.5 t^.5 dt + .25 e^.25 t dt j Then r(9)= 9 i + 27 j+ 9.49 k dr = dt i + 4.5 dt j...

calculus
The DOMAIN is all real t HOWEVER the RANGE is only from -1 to +1 in i and -4 to + 4 in j and all real numbers in k

science
Senpai - buying books instead of borrowing from the library uses up trees (as well as a lot of other stuff like fuel).

science
Which do you think Jaden? Think of the effect of each answer on trash heaps and energy supplies and forests.

Science
initial momentum = 1 kg * 7 m/s - 2 kg * 7/6 m/s = = 14/3 kg m/s final momentum is the same 14/3 = 1 * V1 + 2 * V2 so V1 = 14/3 - 2 V2 initial Ke = (1/2)(1)(49) + (1/2)(2)(49/36) final Ke = .75*initial Ke = (1/2)(1)V1^2 + (1/2)(2)V2^2

force of gravity down slope = m g sin 30 = .5 m g force of friction up slope = FF use FF to get angular acceleration FF r = I alpha so alpha = FF r/I = FF r/(2/5 mr^2) alpha = 5FF/2mr FF = 2 m r alpha/5 a = r alpha so alpha = a/r and F = m a so m a = .5 m g - FF m a = .5 m g...

math
I do not know what your triangle looks like area outside triangle = circle area pi r^2 - triangle area

maths
volume of sphere = (4/3)pi r^3 pi R^2 h = (4/3) pi r^2 h = (4/3) r^2/R^2

maths

Physics- Equilibrium
If I had to pick one it would be c. Constant velocity means no acceleration which means no net force.

Physocs- Components of Resultant Vectors
A = 5 i - 3 j B = 5 i + 4 j --------------- C = 10i + 1 j

Physics- Accleration of a Falling Penny

Physics
Sorry for the long explanation. I am a naval architect and this subject is close to me :)

Physics
It is true if the body is floating. The force upward from the water is equal to the weight of the water displaced. If the body is floating, that water weight must be equal to the weight of the body and the body rises in the water until that is true. That is how ships float. If...

Physics- Baseball thrown upwards, accleration
THE ENTIRE TIME the acceleration is one g, about 9.8 m/s^2 downward. In other words yes, b

Statistics
http://davidmlane.com/hyperstat/z_table.html

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