# Posts by Damon

Total # Posts: 29,823

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) ...

second graph link not rights
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
google kangaroo, marsupial :)

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
just like your other problem, your turn

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

Physics-Tension Force
infinite

Physics
.4 N up 9.8*.145 down m a = .4 - 9.8*.145 that is about .4 - 1.4 or -1 a = -1/.145 = about -7 a

Science
I replied .

Math
9 3/4 = 39/4 39/4 / 3/4 = 39/4 * 4/3 = 39/3 = 13

TIP MATH!
well Ms Sue used the fact that 15% is halfway between 10% and 20% I used a tenth plus half of a tenth. same difference :)

TIP MATH!
10% + 5% = 15% 2.3 + half of that 2.3 + 1.2 = 3.50 ps the accurate answer is 3.49

Maths help asap please.
n (n+1) + n+1 n^2 + n + n + 1 n^2 + 2n + 1 = (n+1)(n+1)

Physics
d = speed * time d = (100 km/60 min) * 5 min d = 25/3

Science plsss help!
4) I suspect is B 5) .5^6 = .0156 = 1.6 % agree second number 5, really that fast?

Physics
one of those two speeds is negative

math
sin ? = 1/1.25 tan ? = sin ?/cos ? = 1/v

physics
sqrt (100 + 16) = sqrt 116 = srt (4*29) = 2 sqrt(29) tan angle above x axis = 4/10 |a| = (1/.5) *2 sqrt 29 = 4 sqrt 29 at same tan^-1(.4)

calculus antiderivation
Vi = 60 mi/h * 5280 ft/mi /3600 s/h Vf = 45 * 5280/3600 Vf = Vi - 11 t solve for t =========================== 0 = Vi - 11 T T = Vi/11 d = Vi T - 5.5 T^2

Math
1.5/6 = x/16 x = 16 * 1.5 / 6

Maths trigonometry
tan 30 = 150/x

factor of 2
for part b .5 m g (d+x) = .5 k (x)^2 + .5 m v^2 we know d from part a m v^2 = m g d + m g x - k x^2 m v dv/dx = m g - k x dv/dx = 0 at max v k x = m g

Physics
You are welcome.

Physics
Not that easy m g (d+.23) sin 30 = .5 k (.23)^2 sin 30 = .5 so m g (d+.23)= k (.23)^2 3.2 (9.8)(d+.23) = 443 * .23^2 =========================== for part b m g (d+x) = k (x)^2 + .5 m v^2 we know d from part a .5 m v^2 = m g d + m g x - k x^2 m v dv/dx = m g - 2 k x dv/dx = 0 ...

Physics
Slides (d + .23) total m g (d+.23) sin 30 = .5 k (.23)^2

The y intercept is where x = 0 so -12,000 is correct The x axis intercepts are when y, the profit, = 0 that is when x = 2 and z = 15 correct the 15 is from 6000 - 400 x = 0 x = 60/4 x = 15

Math Help
probability of no boys = .5^5 so probability of one or more than 1 = 1 - .5^5 = .969

calc
so displacement is zero and distance is 5.33 + 15.75 + 10.42 = 31.5 check my arithmetic !!!!

calc REPAIR of displacement
v = t^3 - 10 t^2 + 27 t - 18 integral = t^4/4-10t^3/3 +27t^2/2 -18t at 7 integral = -7.58 at 1 integral = -7.58 so displacement = 0

calc
I used this to do the numbers: http://www.mathportal.org/calculators/calculus/integral-calculator.php t = 1 to t = 3 int = +5.33 t = 3 to t = 6 int = -15.75 t = 6 to t = 7 int = +10.42 so distance = -21.5 this also says my answer for part 1 should have been 5.33 -15.75+10.42...

calc
(t-1)(t-3)(t-6) = 0 so 1 to 3 then 3 to 6 then 6 to 7

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