# Posts by Damon

Total # Posts: 30,065

**precalculus**

hyperbola opening right and left center at (0,0) crosses x axis at -1 and +1 slopes at corners = +/- 2

**linear programming**

maximize p p = 6s+5b s+b</=70 b>/=20 s>/=10 sketch a graph there are two intersections to check (s,b) = (10,60) here p= 60+300 = 360 and (s,b) = (50 ,20) here p=300 + 100 = 400 (winner)

**physics**

Fup = 400 Fdown = 9.81*50 =491 so accelerating down a down = 91/50 m/s^2

**Science-y Math-y Stuff**

0.8 x = 4,000

**Science**

There was this guy in Sicily , Archimedes: http://www.math.nyu.edu/~crorres/Archimedes/Lever/LeverIntro.html http://en.wikipedia.org/wiki/Lever

**Physics**

alternatively you can use conservation of energy kinetic energy at bottom = potenial energy at top (1/2)mVi^2 = m g h so Vi^2 = (2 g h) h = Vi^2/2g

**Physics**

get vetical component of velocity up at ground, call it Vi. If shot at angle A up from horizontal then Vi = V sin A during flight acceleration = -g or 9.8 m/s^2 down or 32 ft/s^2 down speed up = v = Vi - g t = Vi -9.8 t or = Vi -32 t at top, v = 0 so t = Vi/9.8 or t = Vi/32 ...

**Physics**

average speed during initial slowdown = (80+40)/2 = 60km/h 60 km/h * t = 0.5 km t = 5/600 hours = (1/120)hr (1 hr/120)(60min/hr)(60s/min) = 30 seconds so a = change in speed/time = -40 km/hr /30 s = (-40 * 1000 m/3600s)/30s = -(4/3)/3.6 m/s^2 so Vi = (40/3.6) m/s final v = 0 =...

**I THINK I FIGURED IT OUT!**

8 works if you reverse order

**Math**

2/5 = 10/x x = 25

**Pre-Calculus**

well if you mean (x^2-1) it is D but if you really mean (lim x^2) -1 which is what you typed it is A

**Algebra**

9(r-2)<-73 or 9(-r+2)<-73 first one: 9 r -18 < -73 9 r < -55 r < -55/9 sure looks like a solution second one: -9 r + 18 <-73 9 r -18 > 73 9 r > 91 r >91/9 so second solution

**pre-calculus**

square :) side = 50/4 = 25/2 A = x y P = 2x+2y = 50 so y = (25-x) A = x(25-x) = 25 x - x^2 x^2 -25 x = -A x^2 - 25 x + (25/2)^2 = -A + 625/4 x = 25/2 sure enough so y = 25/2 and A = 625/4 = (25/2)^2

**Algebra**

1. 8 is a factor of 12?? 12/8 = 3/2 = 1.5 2 55/5 = 11 3. You said what P was 4 and 5 are incomplete problem statements both A and B are subsets of U 2 is the intersection of A and B

**physics**

suspect 1000 kg not 100 kg but anyway gravity down = 9.81 *100 = 981 N acceleration down = v^2/r Up force = F so 981 - F = ma = 100 v^2/r so F = 981 - 100 (400)/200 = 781 N but as you know if it is a real car I think 7810 N

**Physics**

I will guess that you mean the current leaves the battery and runs through r2 then splits and runs through r1 and r3 in parallel then joins again and runs through r4 back to the battery. If I guess right then r1 and r =3 in parallel are r1 r3 /(r1+r3) = 90*40/(130) = 3600/130...

**SS HEEELLLPP!!!**

I think that is a matter of opinion, not history. Check your text for what they say. I am not sure the Great Wall was such a success militarily. There seem to have been plenty of intruders from the north after. My own opinion is that the most important thing was the ability of...

**Physics**

x momentum = 16*30 = 480 g cm/s -x momentum = 4*50 = -200 g cm/s total x momentum = +280 g cm/s That will NOT CHANGE ! new mass = 16 + 4 = 20 g so 20 * Vx = 280 Vx = 14 cm/s

**8TH GRADE MATH**

60 sqrt 2 hypotenuse = sqrt (60^2+60^2) = sqrt (2 * 60^2) = 60 sqrt 2 = 84.85

**physics**

Vi = 30 sin 30 = 15 = initial speed UP u = 30 cos 30 = 26 = horizontal speed until caught v = Vi - 9.81 t at top v = 0 (First answer) so at top t = 15/9.81 = 1.53 seconds upward bound THE ACCELERATION IS -9.81 m/s^2 the ENTIRE TIME that it is airborne

**check for typo**

The way you wrote it k x^2 = (3k-5) x = +/- sqrt(3 - 5/k) but I wonder if you mean kx^2 -3kx+5 which would be x = [3k +/- sqrt(9k^2-20k) ]/2k

**Chemistry**

k m/r^2 so (3/4)(804)

**algebra**

I guess maybe you mean 6/ (?3 + 2 ) if so then [ 6/(?3+2)] * [(?3-2)/(?3-2)] 6(?3-2)/[3-4] -6?3 + 12 which is B

**Physics**

Archimedes said Force up = weight of fluid displaced. It displaced 6.4-5.6 = 0.8 kg of water so its volume is V = .8 kg (m^3/1000kg) = 8*10^-4 m^3 so its density is (6.4 /8)10^4 kg/m^3 =8000 kg/m^3 might be iron

**physics**

suspect STATIC is 0.68 .68 m g = starting Force .55 m g = constant velocity Force

**Algebra**

1-4k >= -11 and -1+4k >=-11 -4k >= -12 _and ___4k>=-10 4 k <= 12 __and_____k>=-2.5 k <= 3 note arrow reverse when signs changed so in the end between -3and +3 -2.5 <= k <= 3

**Physics**

You could have done that, patience :)

**Physics**

Total force up =100(9.81) = T1 sin37 + T2 sin 53 Total horizontal force = 0 = T1 cos 37 - T2 cos 53 use that to get T1 and T2 now for example moments about left end T2 sin 53 *5 = 100*9.81* X

**Math**

3(-2)(-2) -2(-2)(3) + 10 12 + 12 + 10 34

**system of equations**

Oh, and you might want to click on "very detailed solution" :)

**system of equations**

Click on Gauss Jordan there of course.

**system of equations**

5 -3 -34 10 -5 -65 (-5, +3) see http://matrix.reshish.com/gaussSolution.php

**whoops sorry**

xp = 100 +/- 50sqrt2 so about 30 (NOT 70 AS I SAID) if xp = 30 yp = .01x^2 = 9

**Calculus**

y = a x^2 100 = a(10,000) a = .01 so our parabola is y = .01 x^2 now a tangent to that parabola must pass through (100,50) slope = .02 xp at parabola y = (.02xp)x + b 50 = 2 xp + b b = 50-2xp but yp = .01 xp^2 and yp =.02xp^2 +50-2xp .01 xp^2 = .02xp^2 + 50 - 2 xp .01 xp^2 -...

**where is the equation?**

I might be able to solve for x given that y is 15 if I had any idea what the equation was.

**la**

Well I suppose your own :)

**math help**

3 < 4 three is less than four 4 > 3 four is greater than three and by the way 4<=4 four is either less than or equal to four

**physics**

31 cos 35

**work and energy PHYSICS**

at O where h = 0, all kinetic, E= (1/2)m Vi^2 + 0 at Q, not moving any more E =0 + m g Q Total energy during whole trip E = (1/2)m v^2 + m g h as h goes up to Q, v goes down to 0 using the start and finish points (1/2) m V^2 = m g Q Vi^2 = 2 g Q Vi = sqrt(2gQ)

**Physics - studying for finals**

for the second part, out in a phase angle .05 sin[(2pi/.75)(x+.375t) -PHI] (2pi/.75)(0.50) -PHI = 0 PHI = 2 pi (.5/.75)

**Physics - studying for finals**

A =0.0500 m L = 0.750 m T = 1/5 = 0.2 goes .75 m in .2 s so v=.75/2 = .375m/s for constant phase (x+vt) the+vt makes it left to make it go 2pi for every wavelength l or time T sin [2 pi (x+vt)/L] now the size .05 sin[(2pi/L)(x+vt)] more numbers in .05 sin[(2pi/.75)(x+.375t)]

**Math**

(x-1)(3x-2)(x-4i) but (x-4i)is not allowed alone, we also need its complex conjugate (x-1)(3x-2)(x-4i)(x+4i) I get 3x^4-5x^3+50x^2-80x+32

**Math**

8x + x = 9 x = 63 x = 7 so 8x = 7*8 which is about 56 as I remember.

**physics**

v = g t = 9.81 * 10 = 98.1 if no air drag but with friction terminal speed is 21 so 21 m/s

**Math**

x = -2 is a vertical line through the point (-2,0). Y can be anything.

**Math (optimization) really confused**

three fences of length x two fences of length y A = xy = 225 so x = 225/y p = total length = 2y + 3 x we want to minimize p p = 2 y +3(225/y) dp/dy = 0 at max or min dp/dy = 0 = 2 -675/y^2 2 y^2 = 675 y^2 = 337 y = 18.4 x = 225/18.4 so what is 2y+3x?

**History Please Help**

They were people, humans.

**Physics**

F * 0.24m = 31Nm so F = 31 Nm/0.24m

**Physics**

try throwing something up and see if time stops and moved backwards while the object falls back down.

**what do you think ?**

The force on this object is F = - m g so a = -g What are your answers?

**Physics**

v = Vi +a t 30 = 10 + 2 t t = 10 seconds but your answers are about distance d = Vi t + (1/2) a t^2 d = 10(10) + 10^2 = 200 m

**Physics**

You are welcome. Remember that figure skater spinning slowly with arms extended, then suddenly speeding up when she pulls her arms in :)

**Physics**

Ip = I of platform =(1/2)(95)(2.4^2) Angular momentum = Ip(2.3) IT STAYS THAT FOREVER New In = Ip +30*(2.4^2) In omega = Ip (2.3) omega = (Ip/In)(2.3) (Part a) b) Her I = mr^2 is zero BACK to original I and 2.3 rad/s c) (1/2) In omega^2 - (1/2)Ip(2.3^2)

**physics**

You are welcome.

**physics**

200 food calories for a half cup so 400 for a whole cup 400 cal (4184 J/cal) = 1,673,600 J watts = 1,673,600 J/600 s = 2789 Watts which is 3.74 hp

**Physics**

height above bottom call it h h = 33(1-cos 31) initial energy = m g h speed at bottom = sqrt(2gh) because (1/2)mv^2 = m g h for part b initial energy = m g h +(1/2)m(25) so at bottom (1/2) m v^2 = that initial energy

**Physics**

LOL, you answered your own question Potential energy = m g h Kinetic energy = (1/2) m v^2 so (1/2) m v^2 = m g h = 73.8*9.81*23.9 Joules (your first answer) so v = sqrt (2 g h) (by the way, remember that. You need it frequently)

**Math**

4 1/3 = 13/3 cans/64 oz = 13 cans/192 oz so 96 oz (13 cans/192 oz) = 6.5 cans

**Math**

Sketch a number line mark them on it like from left to right -13 -7 0 +1 +7

**Algebra 1**

3 y = - 2 x + 12 so y = (-2/3) x + 4 m = -2/3 and b = 4

**History**

You are welcome.

**History**

Oh my ! First check Constitution Amendment 10. Powers not delegated to the US gov. by the Constitution are reserved to the states or to the people (look up exact wording). Local governments do not exist in the Constitution but States reserve powers for them. We are a UNION of ...

**Math**

You are welcome and good luck ! I hope your grandmother comes through all right.

**Math**

To check #1 You say B which is y=3x+6 if x = 6 y = 3(6) + 6 = 18+6 = 24 NO! See, you can check without asking me. y = 18+b y = 8 8 = 18+b b = -10 so the RIGHT answer is y = 3x -10 which is A now slope of first = -3 second is 6y = 2x + 3 , slope = +1/3 second slope = -1/first ...

**Math**

9-t

**Math**

6*37+43 if she always works 37 hours per week income = 6 * 37 + tip otherwise income = 6 * hours + tip

**Physics**

second problem same Newton One stuff.

**Physics**

x momentum = 61.2 * 2.25 FOREVER y momentum = 66.2 * 1.30 FOREVER so final mass = 61.2+66.2 = 127.4 final x momentum : 127.4 * Vx = 61.2*2.25 Remember? final y momentum 127.4 * Vy = 66.2* 1.30 final speed = sqrt(Vx^2+Vy^2) tan theta = Vy/Vx where theta is angle above +x axis

**Algebra 2 Honors**

You are welcome.

**oh my**

My work - 2 = 1/4 ?(100 - h) I multiplied both sides by 4 from - 8 = ?(100 - h) ------------- OK SO FAR BUT square both sides 64 = 100 - h h = 100-64 h = 36 domain from 100-h must be + 0<h<100 for range if h = 0, t = 10/4 hits ground if h = 100, t = 0 drop it then so 0&...

**Thank you Philip**

Thanks :)

**Physics**

3.4 WHAT?? I assume radians/second but hard to say. I will use that but if RPS or something, convert I disk = (1/2)m r^2 so Id = .5*.4*.36^2 and It = .5 * 1.7 * .36^2 initial angular momentum = It*3.4 final angular momentum (the same of course) = It omega +Id omega = omega(It+...

**Math**

13 people ( 2 pounds/5 people) = 26/5 = 5.2 pounds

**Chem**

http://www.google.com/search?q=positron+decay&ie=utf-8&oe=utf-8

**math**

You already have the answer minimum cost is at the vertex x = 20 cars and C = 700 dollars this is a parabola, its vertex is at the bottom,

**Math**

constant slope, straight line y = m x + b m is constant rate of change of y with x

**math algebra**

3.2 = .01 h^2 + .2 h + 1.2 .01 h^2 + .2 h - 2 = 0 h^2 + 20 h - 200 = 0 h = -10+/- 10sqrt3 h = 7.32 hr ===================== check h = about 7.3 .01 h^2 = .53 .2 h = .15 + 1.2 = 3.2 ok, it works

**Statistics**

Combinations p = .65 1-p = .35 P(7,10) = C(7,10) .65^7 * .35^3 C(7,10) = 10!/[7!*3!] =10*9*8/[3*2] = 5*3*8 = 120 so 120 * .65^7 * .35^3 = .252

**Physics**

there are 3600 seconds in an hour 2000 hr (3600 s/hr) = 7,200,000 seconds

**math**

You are welcome.

**math**

where is the vertex of that parabola? You do not say if you know calculus so I will assume we do it the hard way with algebra .009 x^2 -1.08 x = -h -.4 x^2 - 120 x = -111h - 44.4 x^2 -120 x + 3600 = -111h + 3556 (x-36)^2 = -111(h-32) vertex at x = 36 and h = 32 32 -26.5 = 5.5

**Physics**

friction force = 10*9.81*.42 = 41.2N net force = 200 - 41.2 = 158.8 N a = 158.8 / 10 = 15.9 m/s^2

**produces?**

if you put 150 in and get 40 out it is 100(4/15) = 27% but it has to get energy from somewhere. It can not "produce" 150 + 40 +110 without putting any energy in. I suspect a typo in the problem description. It does not produce 150 J, it absorbs 150 J

**physics**

sin 24 = h/3 v = sqrt (2 g h) Now this is virtually the same as your roller coaster problem. Study conservation of energy and potential energy in gravity field.(mgh) and kinetic energy (.5 m v^2)

**Chemistry**

perhaps this can help: http://physics.stackexchange.com/questions/7993/photon-hitting-an-atom-with-higher-energy-than-needed-to-ionize Also maybe Google: Einstein photoelectric effect

**Physics**

check, drops 15 meters to top of loop v^2 = 2 g (15) needs v^2/30 = g sure enough 2*15 g /30 = g

**Physics**

Note this does no depend on the mass (lucky or it would be different for skinny kids and fat adults), or even on g (independent of planet:)

**Physics**

g = v^2/r at top of loop g = v^2/30 solve for v^2 = 30 *g now the car drops A-2r to that point at the top of the loop (1/2) m v^2 = m g (A-60) v^2 = 2 g(A-60) 30 g = 2g (A-60 ) = 2 g A -120 g 150 g = 2gA A = 75 check my arithmetic !

**Trignometry**

He told you how to do it 1. add the south components of each to get the south component of the resultant , S 2. add the west components of each to get the west component of resultant, W get the magnitude sqrt(S^2+W^2) tan A =W/S where A is angle west of south

**wrong**

(4*4)/(4*6) = 4/6 = 2/3

**Math**

x _y____y(n)-y(n-1) ___ next diff 1__0______ 2__5______ 5 3__10_____ 5____________0 4__15_____ 5____________0 5__20_____ 5____________0 6__25______5____________0 THAT is constant diff now x _y____y(n)-y(n-1) ___ next diff 1__1______ 2__4______ 3 3__9_______5____________ 2 ...

**Physics**

1 what? coulombs/m^2? coulombs/cm^2 ? I will assume m^2 and call it x area = A = 4 pi r^2 A = 4 pi (r)^2 Q = 1* A potential= V = k Q/r = Q/(4 pi eo r) V = 1* 4 pi r^2/(4 pi eo r) V = r/eo

**Physics**

mass(specific heat * 40 + heat of fusion of water)

**Physics**

.25 * heat of vaporization of water

**no**

there is no temp change involved here, just the heat to melt at 0 Q = mass * heat of fusion = 3 * 3.3*10^5 = 9.9 * 10^5 Joules

**Maths**

(2/3)(600) = 2(200) = 400

**Algebra**

.7 x + .2 y = .4*500 x + y = 500

**Physics**

a = -9.81 =-g v = -9.8 t h =Hi - Vit - 4.9 t^2 = Hi -4.9 t^2 You do not say the original height, Hi Vi, initial speed, is 0 so t ____ a ___ v ___ h 0 ___ -g ___ 0 ___ Hi - 0 1 ___ -g ___-9.8__ Hi - 4.9 2____ -g____-19.6_ Hi - 19.6 3 ___ -g ___-29.4_ Hi - 44.1

**physics**

force in direction of motion * distance moved = 300*10 = 3,000 Joules

**science**

I am inclined to agree with you, thinking about India moving north.