Wednesday

August 20, 2014

August 20, 2014

Total # Posts: 26,966

**math (trade and cash discount)**

let the list price be x .85(.92)x = 239.29 x = 239.29/(.85(.95)) = ....
*April 26, 2014*

**math**

One step calculation price = 1780(.7)(.9)(.95) = 1065.33 Discount = 1780-1065.33 = $714.67 or first discount = .3(1780) = 534 leaving 1246 2nd discount = .1(1246) = 124.60 leaving 1121.4 3rd discount = .05(1121.4 = 56.07 leaving 1065.33 Discount = 1780 - 1065.33 = 714.67 as ...
*April 26, 2014*

**MATH**

tried: ±1, ±2, ±3 success at x = -3 by synthetic division 21x^3+67x^2-36=(x+3)(21x^2+ 4x - 12) = (x+3)(3x-2)(7x+6) so what do you think?
*April 26, 2014*

**good catch- maths**

Good catch Steve, the smallest 3-digit number divisible by 7 is 105 So count one more, 128 of them
*April 26, 2014*

**maths**

smallest 3 digit number divisible by 7 is 112 largest 3 digit number divisible by 7 is 994 look at the arithmetic sequence 112, 119, .... 987 , 994 how many terms are there? a=112, d = 7 term(n ) = a+(n-1)d 994= 112 + (n-1)(7) 882 = 7n - 7 889 = 7n n = 127 2. really!? (I will ...
*April 26, 2014*

**maths**

I will assume you meant, "How many red marbles should be added" let the reds to be added be x so we have 10+x reds total = 40+x (10+x)/(40+x) = (3/5) 50 + 5x = 120 +3x 2x = 70 x = 35 #5 reds should be added check: reds = 45 total = 75 percentage of reds = 45/75 = .6 ...
*April 26, 2014*

**Maths**

a) flipping 2 counters, Cam's outcomes: 11 , 12 , 21, and 22 , two ways to get a 3 ---> prob(3) = 2/4 = 1/2 flipping a die, outcomes 1,2,3,4,5,6 , one way to get a 3 --> prob(3) = 1/6 prob(both get a 3) = (1/2)(1/6) = 1/12 CA DE ---- Cam's loss ---> Dean's...
*April 26, 2014*

**math**

amount left of 1 unit after the series of 3 discounts = (.8)(.9)(.96) = .6912 amount left of 1 after a single discount of 32% = .68 which is the better discount?
*April 25, 2014*

**Math**

Just like 3(2x+5) = 6x + 15 just like 3(7+2) = 21 + 6 so is √5(2+√5) = 2√5 + √25 = 2√5 + 5 you could also check by evaluating it with your calculator.
*April 25, 2014*

**Math**

√5/(2-√5) ?? what about it? If you are rationalizing it, then = √5/(2-√5) * (2+√5)/(2+√5) = (2√5 + 5)/(4-5) = -2√5 - 5
*April 25, 2014*

**Calculus**

" 50 m away from you" -measured along the string, or measured along the ground? There is not enough information , there are 3 rates involved, but you only give one. Are we ignoring the fact that the string cannot form a straight line ? Is the kite always 40 m high?
*April 25, 2014*

**Algebra 1**

sure, if it exists For a "vertical " parabola there will always be a y-intercept For a sideways parabola, there may not be one.
*April 25, 2014*

**math (9)**

picture: http://www.wolframalpha.com/input/?i=plot+y%3D+-x%5E2%2B2x%2B4+%2C+y+%3D-x%2B4 looks like they intersect at (0,4) and((3,1) (the points satisfy both equations) area = ∫( -x^2 + 2x + 4 - (-x+4)) dx from 0 to 3 = ∫( -x^2 + 3x ) dx from 0 to 3 = [ -x^3/3 + 3x...
*April 25, 2014*

**math (2)**

we see no shaded region.
*April 25, 2014*

**Math (6)**

Since x ≥ 0 for y = √x the graph shows that we cannot have a closed region. see ... http://www.wolframalpha.com/input/?i=plot+y%3D+√%28x%29+%2C+y%3D+x-2
*April 25, 2014*

**math**

must exclude no heads and 1 head prob(no heads) = (1/2)^6 = 1/64 prob(1 head) = C(6,1) (1/2)^1 (1/2)^5 = 6/64 prob (more than 1 head) = 1 - 1/64 - 6/64 = 57/64
*April 25, 2014*

**Calculus Please Help4**

You appear to have found their intersection correct as (3,3) and (19,-5) USING VERTICAL SLICES: y^2 = x+6 so y = ± √(x+6) = ± (x+6)^(1/2) so for the part from -6 to 3 height = (x+6)^ - ( -(x+6)^(1/2) = 2(x+6)^(1/2) integral of that is (4/3)(x+6)^(3/2) area ...
*April 25, 2014*

**Calculus Please Help3**

intersection points: y = 5 with 2y = 3√x ---> (100/9 , 5) y = 5 with 2x+2y = 5 ---> (-2.5, 5) 2y = 3√x with 2x + 2y = 5 ---> 1 , 3/2) So I see it as area = ∫(5 - (5-2x)/2) dx from -2.5 to 1 + ∫((5-(3/2)(x^.5) )dx from 1 to 100/9 = 6.125 + 14....
*April 25, 2014*

**Algebra**

Suppose the question had said: when a number is divided by 4 the quotient is 6 with a remainder of 1 we would write: number = 6(4) + 1 = 25 so f(x) = (x^3 + x^2 - 4)(x+3) + 8 = x^4 + 3x^3 + x^3 + 3x^2 - 4x - 12 + 8 = x^4 + 4x^3 + 3x^2 - 4x - 4
*April 24, 2014*

**Calculus Help Please Urgent!!!**

height = -1.6t^2 + 32t + 3 b) need the vertex of that parabola t of vertex = -b/(2a) = -32/-32 = 1 second height = -16(1) + 32(1) + 3 = 19 m c) hits the moon ground when h = 0 -16t^2 + 32t + 3 = 0 t = (-32 ± √1216)/-32 = -.089 or 2.09 seconds so , "in the air...
*April 24, 2014*

**Math**

prob(H win) = 1/3 , prob(A win) = 2/3 prob(H loss) = 2/3 , prob(A loss) = 1/3 a) not good on trees in this forum, hard to show b) Prob (HH) = (1/3)(1/3) = 1/9 Prob(AA) = (2/3)(2/3) = 4/9 c) to go 3 games, could be AHA or HAH prob of that = (2/3)(1/3)(2/3) + (1/3)(2/3)(1/3) = 4...
*April 24, 2014*

**mathematics**

1. What is 1 - 1/13 ? 2. ....... 3. to get a 2 ---> 11 to get a 5 ---> 14, 41, 23, 32 or 4 ways so to get a 2 or 5 ----> 5 possible outcomes prob(2 or 5) = 5/36 so in 1000 tosses we expect (5/36)(1000) or appr 139 times
*April 24, 2014*

**typo correction -Math**

my first equation should have been cosØ = 49/50 = .98
*April 24, 2014*

**Math**

Make a situation diagram where you have a triangle with the vertical angle as Ø, the hypotenuse 50 cm (the pendulum) and a vertical leg of 49 cm so we would get cosØ - 49/50 = .98 then Ø = .20033.. (I stored that in my calculator to keep accuracy) so we ...
*April 24, 2014*

**finances**

P(1.04^35 - 1)/.04 = 1000000 P = $ 13,577.32
*April 24, 2014*

**Algebra**

I did a synthetic division (or you can do a long algebraic division) to get a remainder of (c+1188) So for the division to be exact, x+1188 = 0 c = - 1188 http://www.wolframalpha.com/input/?i=%28x%5E4+-+3x%5E2+-1188%29%2F%28+x%2B6%29 look at "quotient and remainder" ...
*April 24, 2014*

**Math**

a) the only even prime is the number 2 so prob = 1/6 b) primes less than 5 are : 2 and 3 so prob = 2/6 = 1/3 c) if not a 6, then it must be: 1, 2, 3, 4, or 5 how many of those are prime? d) which of 1 or 2 is prime ? e) how many even's < 4 are prime? etc.
*April 24, 2014*

**Algebra**

(√5a^-2)/(√10a^-1) = (√5 a)/(√10 a^2) = 1/(√2 a)
*April 24, 2014*

**Math**

volume of whole apple = (4/3)π(6^3) = 288π cm^3 volume of inner part of apple with radius 5 cm = (4/3)π(5^3) = 500π/3 cm^3 part of apple within 1 cm of outside = 288π - 500π/3 = 364π/3 prob(being in outer part of apple) = (364π/3) / (288...
*April 24, 2014*

**Math**

expected income = .2(0) + .3(-1000) .25(-10000) + .25(20000) = 2200
*April 24, 2014*

**Math**

Let the line joining (1,-4) and (6,-4) be the base of your triangle. This is a horizontal line, and it should be easy to see that its length is 5 let the height be h (1/2)(5)h = 20 5h = 40 h = 4 so any point on the x-axis (or 4 units above your base) would be such a third ...
*April 24, 2014*

**math**

So they must enter in the order G B B B G number of ways = 2 * 3*2*1 * 1 = 12
*April 24, 2014*

**Math**

could be 1. YY --->(5/29)(4/28) = 20/812 2. GG ---> (7/29)(6/28) = 42/812 ... 5. BB ---> 4/29)(3/28) = 12/812) Add them up (20 + 42 + .. + 12)812 = ....
*April 24, 2014*

**Math**

so prob that 5 of the 10 smoke = C(10,5)(.4^5)(.6^5) = appr .2 40% of college students smoke ??? Are those stats from the 50's ?
*April 24, 2014*

**Math**

number of slices per pizza = 360/40 =9 so for 2 pizzas we have 18 pieces and at 1 slice per person, we would have 18 people. (cutting a pizza into 9 pieces ??? Good luck Are you going to lay a protractor on the pizza and measure 40° ?)
*April 24, 2014*

**Math - Answer Check**

What is (2/3) of (2 1/10) ? = (2/3)(21/10) = 7/5 units of distance or 1.4 units or 1 2/5 units
*April 24, 2014*

**Math**

First one is easy. The cow can cover 3/4 of a circle with radius 40 (the missing quarter is the barn) area = (3/4)(π(40^2) = 1200π yds^2 2nd one: let's tie the cow up at the top left corner. with a rope of 75 yds, the cow can cover (3/4)(π(75^2) or 4218.75&#...
*April 24, 2014*

**math**

Since cost usually varies with the area and the area is proportional to the square of the corresponding sides, the area would be 4 times as large, thus the cost would be 4($1.5) or $6.00 ( ratio of sides = 2:1 so ratio of areas = 2^2 : 1^2 = 4 : 1 ratio of costs = 4 : 1 )
*April 24, 2014*

**Math**

√(3f^3) = √3 * √(f^2) * √f = √3*f*√f = f√3√f = f√(3f)
*April 24, 2014*

**Math**

Taking it just the way you typed it ... = √3/( (√f)^-3) = √( 3/f^-3) = √(3f^3) = f√(3f)
*April 24, 2014*

**math**

? ? ? What does that mean?
*April 24, 2014*

**math**

I would make time (t) my horizontal axis marking it up to 5 hours. Make your vertical axis the calorie axis , marking it as 100 , 200, ... up to 1000 calories. plot the ordered pairs (1,300) , (2, 600) , (3, 900) and (4,1200) you should get a straight line Notice (0,0) should ...
*April 24, 2014*

**Calculus**

mmmhh v = ∫(5t/4)(t^2 + 1)^2 dt = (5t/4)(((1/3)(1/(2t)) (t^2 + 1)^3 + c = (5/24)(t^2 + 1)^3 + c differentiate to get ((5/4)(t)(t^2 + 1)^2
*April 24, 2014*

**Calculus**

right now: price of rent = 900 number of units rented = 50 Let the number of $25 increases be n (e.g. If n= 2 , new rent is 900+2(25) = 950 if n = 5 , the new rent 900 + 5(25) = 1025 so the new rent = 900 + 25n number rented = 50-n maintenance cost = 75(50-n) Profit = P = (900...
*April 24, 2014*

**Calculus**

Make a sketch ... Place the first vehicle A at the origin P, showing the position of the first vehicle draw a short line east of P and label it A2 Place the second vehicle B at a distance of 5 above P showing the initial position of the second vehicle draw line downwards from ...
*April 24, 2014*

**math**

Steve did this for you http://www.jiskha.com/display.cgi?id=1398006054 All that was required of you want a bit of "counting" .
*April 24, 2014*

**Math Help**

You have been helped repeatedly by several tutors for these same type of questions. I think it is time that you try them yourself and show where your difficulties lie with these. e.g In every one, wasn't the first step to find the LCD ? We then multiplied each term by that...
*April 24, 2014*

**trig**

16cos(x)-3sec(x)=0 16cos(x) = 3sec(x) 16cosx = 3/cosx cos^2 x = 3/16 cosx = ± √3/4 x = 1.123 or x = π - 1.123 = 2.0186 or x = P + 1.123 = 4.266 or x = 2π - 1.123 = 5.160
*April 23, 2014*

**algebra**

you LCD is 12 so .... 6x/12 + 4y/12 - 3z/12 = (6x + 4y - 3z)/12
*April 23, 2014*

**math**

given function: y = x+1 Two step process inverse function: (interchange x and y variables) 1. x = y+1 2. solve new equation for y y = x-1 so f^-1 (x) = x-1 Use the above two step method for finding any inverse if it exists.
*April 23, 2014*

**Math Help? Check my answers.**

#1 Aren't the terms decreasing by 8 ? So after 6 , you would have -2, -10, -18 #2 aren't the terms increasing by 3 each time ??? So how can you possibly get 14 as the next number after 12 ??? #3 I am puzzled by your choices you started with -1, 9, 19, 29, adding 10 ...
*April 23, 2014*

**math**

Draw a "side view" of the cut sphere. draw a line from centre of the circular cut to the centre of the sphere. You will have a right-angled triangle with base 10 (half the diameter of the circle) and a hypotenuse of 15. let the third side be h h^2 + 10^2 = 15^2 h...
*April 23, 2014*

**Math**

Your given example illustrates a case where there is a definite number of ways for things to happen, thus it is a theoretical probability situation, you had that one. But you said: You draw five cards from a standard deck of 52 cards. P(heart) = 4/5 (fraction) Did you mean ...
*April 23, 2014*

**ALGEBRA**

For any centre (a,b) and radius r, the equation of the circle is (x-a)^2 + (y-b)^2 = r^2 look at your second equation, (x+6)^2 + (y-4)^2 = 16 or 4^2 doesn't it fit that pattern perfectly ? for a centre of (-6,4) and radius of 4 Now you can sketch it. Do the same for the ...
*April 23, 2014*

**math**

think of money $.700 = 70 cents $.007 = .7 cents which would you rather have ? or .700 contains 7 tenths .007 contains zero tenths, none, nada, nichts, nil. ...
*April 23, 2014*

**math**

No, the area of similar shapes is proportional to the square of the corresponding sides So 2:1 ----> 2^2 : 1^2 = 4 : 1 The area would be 4 times as large, or quadrupled. Proof: area of original = 5*3 = 15 new sides are 10 and 6 new area = 10*6 = 60 and 60 = 4 times 15
*April 23, 2014*

**triangle measurements**

Are you sure that there was no angle given, or perhaps the area was given? With only 2 pieces of information, we can't go further.
*April 22, 2014*

**triangle measurements**

Trying very hard to visualize a triangle that has a "top length" and a "lower length". You appear to give the length of 2 sides, which is not enough information to find anything else.
*April 22, 2014*

**angle measurements HELP ME PLZ QUICKLY!!!**

Yes, it is right-angled triangle. I thought you had answered A) and used "a" as your answer. Since you don't use any capitals in your sentence, and use "no" instead of "know" etc, it was easy to mis-interpret your answer. Your statement : I ...
*April 22, 2014*

**angle measurements HELP ME PLZ QUICKLY!!!**

yes, you are wrong I don't know how much more of a hint I could have given you. 1. I ruled out your choice with a reason for doing so 2. I gave you a very blatant hint !
*April 22, 2014*

**angle measurements HELP ME PLZ QUICKLY!!!**

An acute angle is an angle less than 90° your triangle has a 90° angle, often called a "right angle" Do you wish to rethink your choice? Aghast at : I no what this triangle would look like thought u should no!
*April 22, 2014*

**Math**

monthly rate = .0575/12 = .004791666.. n = 12(12) = 180 P ( 1 - 1.00479166..^-180)/.00479166.. = 250000 I get P = $ 2076.03
*April 22, 2014*

**math**

using the formula x = (-2 ± √(4 - 4(3)(2) )/6 = (-2 ± √ -20)/6 = (-2 ± 2√5 i )/6 = (-1 ± √5 i )/3
*April 22, 2014*

**bearings**

for intersection , use substitution in the 2nd equation 2x + 3y - 21 = 0 2x + 3(4x-7) = 21 2x + 12x - 21 = 21 14x = 42 x = 3 y = 4(3) -7 = 5 so we have the line going through (3,5) and (-2,8) slope of line = (8-5)/(-2-3) = -3/5 using (3,5) y-5 = (-3/5)(x-3) times 5 5y - 25 = -...
*April 22, 2014*

**Pre-Cal**

what about it? here is a picture of it http://www.wolframalpha.com/input/?i=y%3D%281%2F2%29cos%284%28t-6%29%29%2B6
*April 22, 2014*

**math**

Wow, 17% interest from a savings account ? anyway .... P( 1 - 1.17^-20)/.17 = 250000 .. P = $57, 309.99 this might seem unreasonably high, but remember the interest rate is unreasonable, As a matter of fact his fund will earn .17(250,000) or $42,500 in interest the first year...
*April 22, 2014*

**Math**

This time you want future amount i = .065/52 = .00125 P( 1.00125^312 - 1)/.00125 = 15000 ... P = 39.34 weekly payment is $39.34
*April 22, 2014*

**Math**

see same question in first of "Related Questions" below
*April 22, 2014*

**Math**

Car payments are usually calculated using compound interest. monthly rate = .07/12 = .005833333.. let the payment be P P( 1 - 1.0058333^-60)/.0058333 = 14000 P = 14000/50.50199.. = $277.22
*April 22, 2014*

**Math**

P(1.02)^20 = 5500 P = 5500/1.02^20 = 3701.34
*April 22, 2014*

**math**

if he knows the side to be x f(x) = x^2
*April 22, 2014*

**Math**

d(t) = 250 - 100t when t = 0 , d(0) = 250 ---> (0 , 250) when d(t) = 0 250 - 100t = 0 -100t = -250 t = 2.5 ----------------> (2.5 , 0) the d(t) intercept is 250 (just like the y-intercept of y = mx + b) the t intercept is 2.5 meaning: at the beginning the plane was 250 ...
*April 22, 2014*

**Algebra 2**

looks like y = (1/3)x , so you might call 1/3 as the constant of variation.
*April 22, 2014*

**Calculus**

After t hours, ship A has traveled 20 t km ship B has traveled 25t I sketched a right-angled triangle with legs 120-25t and 20t let D be the distance between them , making D the hypotenuse D^2 = ((120- 25t)^2 + (20t)^2 at 8:30 , t = .5 D^2 = 11656.25 D = 107.964.. 2D dD/dt = 2...
*April 22, 2014*

**Algebra1**

given: a = 3 term(33) = a+32d = -253 32d = -256 d = -8 sum(33) = (33/2)(first + last) = (33/2)(3 -253) = -4125
*April 22, 2014*

**maths**

still can't read what you are typing.
*April 22, 2014*

**calculus**

x ' (t) = 9t^2 - 81t + 162 so objects are "speeding up" when x ' (t) > 0 and slowing down when x ' (t) < 0 Consider the zeros of the expression 9t^2 - 81t + 162 = 0 t^2 - 9t + 18 = 0 (t-3)(t-6) = 0 t = 3 or t = 6 so the t of the vertex would be half...
*April 22, 2014*

**maths**

check your typing, I can't make out what you are saying.
*April 22, 2014*

**Math**

Did you want Maximum profit ? find the vertex of your parabola the x of the vertex is -b/(2a) = -1.4/(2(-.02)) = 35 days p(35) = 1.4(35) - .02(35)^2 - 20 = 4.5 whatever units
*April 22, 2014*

**math (SIMPLE INTEREST)**

repeat steps I showed you in your previous post (5 and 1/4 years = 5.25 years , or use 21/4 years )
*April 22, 2014*

**math (SIMPLE INTEREST)**

I = PRT = 20000(.11)(4.5) = 9900 so amount = 20000+9900 = .... (4 years, and 6 months = 4.6 years)
*April 22, 2014*

**algebra**

let's take the first 3 points and find the equation of the plane containing them direction vector #1: (-3,2,2) direction vector #2: (1,2,1) normal to these , take the cross-product = (-2, 5, -8) or (2, -5, 8) in the opposite direction equation of plane is 2x - 5y + 8z = c ...
*April 22, 2014*

**math**

Their normals are (1,4,-1) and (5,-3,-7) respectively clearly they are not parallel, or one of the normals would be a multiple of the other nor are they coincident let's look at their dot product: (1,4,-1) . (5,-3,-7) = 5 - 12 + 7 = 0 So they are perpendicular or orthogonal.
*April 22, 2014*

**Physics waves- check answer please**

in air , v = 331.4m/s + 0.606m/s/degree celsius times T = 331.4 + .606(30) = 349.58 m/s time to travel 1.2 km = 1200/349058 = 3.4327 seconds in water: time = 1200/1498 = .801 seconds time difference = 3.4327 - .801 or 2.63 seconds for yours, ok, so far, but you have not yet ...
*April 22, 2014*

**math**

Something is sightly off mathematically 7/10 + 1/5 + 1/6 > 1 some must have arrived by more than one method. (insufficient data or bogus question)
*April 22, 2014*

**math**

more by car than foot = 7/10 - 1/6 = "How many fewer came by foot? " = 1 - 7/10 - 1/5 = assuming they came by one of those 3 ways.
*April 22, 2014*

**probability**

at most 5 dots --> 2 , 3, 4, 5 dots 11, 12, 21, 22, 23, 32 ---> 6 ways showing odd number of dots: 3, 5, 7 , 9 , 11 {12, 21, 23, 32, 43, 34 , 54, 45 , 65 , 56} so we want {at most 5 dots} AND {showing odd sum} = {12, 21, 23, 32} or 4 ways prob(stated event) = 4/36 = 1/9
*April 21, 2014*

**math**

solve: 5000(1.07)^n = 10000 1.07^n = 2 log both sides log 1.07^n = log 2 n log1.07 = log2 n = log2/log1.07 = appr 10.24 It will take appr 10 years
*April 21, 2014*

**Math (Number Theory)**

... = (1+n)+(1+n)+(1+n)+... for a total of n/2 such binomials = (n/2)(n+1 or n(n+1)/2 or (1/2)(n)(n+1) or (n^2 + n)/2
*April 21, 2014*

**Math**

That's better. multiply each term by 12 , the LCD 6x - 4 = 3x 3x = 4 x = 4/3 you are correct.
*April 21, 2014*

**math**

Proof of my answer: now ----- 3250 end of 1st year: 3250(1.06) = 3445 end of 2nd year: 3445(1.06) = 3651.70 end of 3rd year: 3641.70(1.06) = 3870.80 >> as I had before suppose they did 3250(1.06)3.5 = 3985.23 which is one of the choices, BUT contradicts the concept of &...
*April 21, 2014*

**math**

Trick question? Since the compounding is annually, the amount at 3.5 years is the same as it was after 3 years amount = 3250(1.06)^3 = 3870.80
*April 21, 2014*

**Math**

you have a geometric series, where a = 6 , r = -4 I suspect you have a typo. S(1) to me means the sum of 1 term that would simply be 6
*April 21, 2014*

**calc**

y^3 = 16x^2 when x = 4 y^3 = 16(256) y = 16 3y^2 dy/dt = 32x dx/dt sub in our values 3(256) (-1) = 32(4) dx/dt dx/dt = -768/128 = -6
*April 21, 2014*

**Math**

You have no right side of an equation. There was no equation to solve. Retype your question please
*April 21, 2014*

**Math**

Write fractions this way: x/2 - 1/3 - x/4 LCD = 12 6x/12 - 4/12 - 3x/12 = (3x - 4)/12 Your answer makes no sense. (It doesn't even have an x term)
*April 21, 2014*

**Math**

2 = 1( 1.0275)^n log 2 = n log 1.0275 n = log2/log1.0275 = ....
*April 21, 2014*

**Math question**

Did you notice that each term is half of the previous one? Which type of sequence matches that property?
*April 21, 2014*

**Inverse Trig**

for both cases, since for any -π/2 < y < 0 the sine will be negative, we only have to concern ourself with angles in the first quadrant. so if y = arcsin (√3/2) then y = π/3 ( I know sin 60° = sin π/3 = √3/2 ) and for the second one y = &#...
*April 21, 2014*

**Inverse Trig**

look at the sine curve, it is zero, or crosses the horizontal axis at 0 , ±π , ±2π .. or in general kπ , where k is an integer.
*April 21, 2014*

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