Sunday

July 24, 2016
Total # Posts: 35,337

**math**

smaller number --- x larger number ---- x+5 "the sum of two numbers is 25" translate into an equation and solve.
*July 23, 2016*

**Maths**

Use your definitions: a + ar^2 = 7/3 a( 1 + r^2) = 7/3 ** ar + ar^3 = 7/4 a(r + r^3) = 7/4 *** divide *** by ** (r + r^3)/(1 + r^2) = (7/4) / (7/3) = 3/4 4r + 4r^3 = 3 + 3r^2 4r^3 - 3r^2 + 4r - 3 = 0 r^2(4r - 3) + 1(4r-3) = 0 (4r-3)(r^2 + 1) = 0 4r = 3 or r^2 = -1 , the last ...
*July 23, 2016*

**Math - Trig**

All you have to do is follow the same steps I used to get the answer of 4.51 http://www.jiskha.com/display.cgi?id=1469238292
*July 22, 2016*

**Math**

Stacey/ba, please don't switch names 7.8 + sin3.5 (pi/6(t-3)) = 10.29 sin3.5 (pi/6(t-3)) = 2.49 not possible, sin(?) cannot be > 1 when you first posted this, you had 3.5sin (pi/6(t-3)) I will change it to 7.8 + 3.5sin (pi/6(t-3)) = 10.29 3.5sin (pi/6(t-3)) = 2.49 sin (...
*July 22, 2016*

**correction - Math**

forget the first part of my solution, I read it as 3x^3−x^2+bx−24 we know : f(x) = ax^3−x^2+bx−24 since x-2 is a factor, f(2) = 0 f(2) = 8a - 4 + 2b - 24 = 0 8a + 2b = 28 4a + b = 14 ** f(-4) = 0 -64a - 16 - 4b - 24 = 0 -64a - 4b = 40 16a+ b = -10 *** ...
*July 22, 2016*

**Math**

ax^3−x^2+bx−24 = (x-2)(x+4)(ax + c) the ax^3 can only come from the multiplication of the first terms of each of the binomials, (x)(x)(ax) = 3x^3 ----> a = 3 the -24 can only come from the multiplication of the last terms of each of the binomials, (-2)(4)(c) = -...
*July 22, 2016*

**Futher maths**

tanØ + 2secØ = 2cotØ + 3cscØ sinØ/cosØ + 2/cosØ = 2cosØ/sinØ + 3/sinØ multiply each term by sinØcosØ sin^2 Ø + 2sinØ = 2cos^2 Ø + 3cosØ sinØ(sinØ + 2...
*July 22, 2016*

**math**

John's rate = 1/4 Michael's rate = 1/x combined rate = 1/4 + 1/x = (x+4)/(4x) given: 1/( (x+4)/(4x) ) = 3 4x/(x+4) = 3 4x = 3x + 12 x = 12 Michael alone would take 12 hours check: combined rate = 1/4 + 1/12 = 1/3 time at combined rate = 1/(1/3) = 3
*July 21, 2016*

**math**

Think about the method and the pattern if you had 80% ----> 80/100 = 4/5 if you had 8% -----> 8/100 = 2/25 if you had .8% ----> .8/100 = 8/1000 = 1/125 your .8/100 * 10/10 = 8/1000 , not 8/100
*July 21, 2016*

**Math**

"Which statement best describes the sum 7/8? " - first of all 7/8 is not the "sum" - secondly, there is no mathematical reason for Jack to come up with 7/8 - thirdly , this is a silly question.
*July 21, 2016*

**Math**

" ...all the possible values for angle Ø, given that Ø =-3/8and 0<theta<3pi " this makes no sense, did you skip the trig function in front of Ø, such as sinØ = -3/8 ??
*July 21, 2016*

**Math**

one question at a time. period of your cosine is 4 s so 2π/k = 4 4k = 2π k = π/2 so let's start with A = cos (πt/2) the min is .08, and the max is .82, thus a = (.82-.08)/2 = .37 so far: A = .37 cos (πt/2) the min of that is .37, but we want the ...
*July 21, 2016*

**Math**

Are you assuming the relation follows a trig function, either a sine or cosine ?
*July 21, 2016*

**Math**

area to be covered = 4(90) or 360 square feet, assuming your room is square. number of gallons = 360/120 = 3 gallons
*July 21, 2016*

**Arithmetic/Geometric Sequence**

A quick check shows it is neither arithmetic nor geometric, so mess around with it a bit how about (1/18)( 12, 6, 4, 3, ....) , 18 is the LCD notice : 12/1 = 12 12/2 = 6 12/3 = 4 12/4 = 3 so it looks like term(n) = (1/18)(12/n) = 2/(3n)
*July 21, 2016*

**Math**

Chandra ---- x years Ben's age ---- x+6 yrs Ali's age ---- x+6 + 3 = x+9 yrs (x + x+6 + x+9)/3 = 10 solve for x, then back-sustitute.
*July 21, 2016*

**Calc**

P = 5cos (pie/2 (t)) +5 the period of this function is 2π/(π/2) = 4 for the lowest productivity, we need the minimum of the function. we know that cos (pie/2 (t)) has a minimum of -1 then 5cos (pie/2 (t))has a minimum of -5 and 5cos (pie/2 (t)) +5 has a minimum of 0 ...
*July 20, 2016*

**math**

cotx = 6/5 ---> tanx = 5/6 secy = 3/2 ---> cosy = 2/3 sketch your triangles in quad I using Pythagoras, if tanx = 5/6 r^2 = 25 + 36 = 61 r = √61 if cosy = 2/3 by Pythagoras: 2^2 + Y^2 = 3^2 Y = √5 tany = √5/3 tan(x+y) = (tanx + tany)/(1 - tanxtany) = (5...
*July 20, 2016*

**Math - Trig**

the period of your function is 2π/(π/6) or 12. So it represents 1 year of temperature change. first look at the graph: http://www.wolframalpha.com/input/?i=plot+y++%3D+12.5+%2B+15.8sin+(%CF%80%2F6+x+%E2%88%922%CF%80%2F3)+,+y+%3D+12.5+from+0+to+12 notice the sine ...
*July 20, 2016*

**Math - Trig**

period = 2π/k in our case k = 2π/3 period = 2π/(2π/3) = 3 so one rotation takes 3 seconds, thus 4 rotations would take 12 seconds The radius of the wheel would be the amplitude of your cosine curve which is 17.5 cm Here is a graph of your courve: http://www...
*July 20, 2016*

**Math**

So the zero can only come from the numerator, thus r^2 + 5r + 6 = 0 (r+2)(r+3) = 0 r = -2 or r = -3 BUT, as noted in your other replies, r cannot be -2 so r = -3 which is C
*July 20, 2016*

**Math**

let's graph the original function http://www.wolframalpha.com/input/?i=plot+y++%3D+%E2%88%92+sin+(3x+%2B+%CF%80%2F3+)+%E2%88%92+2 Notice that the curve does not cross or touch the x-axis, that is , it can never be zero. Therefore the reciprocal can never be undefined and ...
*July 20, 2016*

**Math**

We all know that 4 quarters make up 1 dollar. so how many quarters do we need to make up $50.50 ?
*July 20, 2016*

**math**

let the three numbers be x-1, x, and x+1 , where x is the middle number x-1 + x + x+1 = 18 3x=18 x=6 so the middle number is 6, and the three numbers are 5,6, and 7 btw, You could define the numbers any way you want. I could say, let the first number be (5x+7), then the next ...
*July 20, 2016*

**Math**

1/4 -1/x+6= 1/x ? I have this feeling you meant 1/4 - 1/(x+6) = 1/x multiply by 4x(x+6) , the LCD x(x+6) - 4x = 4(x+6) x^2 + 6x - 4x = 4x + 24 x^2 - 2x - 24 = 0 (x-6)(x+4) = 0 x = 6 or x = -4
*July 20, 2016*

**maths**

total trip = 2(27) + (11/2)(20) km = 164 km total time = 2+11/2 or 7.5 hours average speed = 164/7.5 or appr 21.87 km/h
*July 20, 2016*

**trigonometry**

2sin(t)cos(t)-cos(t)+2sin(t)-1=0 cost(2sint - 1) + (2sint - 1) = 0 (2sint - 1)(cost + 1) = 0 sint = 1/2 or cost = -1 if sint = 1/2 t = π/6 or t = 5π/6 if cost = -1, look at your cosine curve, t = π
*July 19, 2016*

**Math**

make a sketch of the first few bounces and you will see: 1 bounce --- 56 m 2nd bounce = 2(28) = 56 3rd bounce = 2(14) = 28 4th bounc = 2(7) = 14 5th bounce = 2(3.5) = 7 6th bounce = 2(1.75) = 3.5 add them up to get ..... 164.5 or: from the 2nd on , we have a geometric sequence...
*July 19, 2016*

**mathes**

The room is 800 cm by 600 cm, and the tile is 8 cm by 10 cm, so the tiles will fit exactly along either side. (ignoring any grouting gaps) area of floor = 480,000 cm^2 area of one tile = 80 cm^2 number of tiles = 480,000/80 or 6000 tiles or tiles along the length = 800/8 = 100...
*July 19, 2016*

**math**

cosine law: x^2 = 2.4^2 + 2.4^2 - 2(2.4)(2.4)cos 30° ....
*July 19, 2016*

**Math**

This one is a bit different. In the first one, the "16" was the value of one of the terms of the ratio. In this one, the "240" is the sum of the terms of the ratio. Let Anton's number of stamps be 4x let Maria's number be 2x 4x + 2x = 240 x = 40 ...
*July 19, 2016*

**Find the probability**

following your "steps" prob(both red) = C(4,2)/C(9,2) = 6/36 = 1/6 or , straightforward way .... prob = (4/9)(3/8) = 1/6
*July 19, 2016*

**Calculus**

let y = 1/sinx = (sinx)^-1 dy/dx = -1(sinx)^-2 (cosx) = cosx (1/sin^2 x) = cosx/sinx * 1/sinx = cotx cscx
*July 18, 2016*

**Calculus the derivative**

Did you not look at my solution to the same question ? http://www.jiskha.com/display.cgi?id=1468890453 All I can see wrong with it, I labeled part D as B for B all you have to do it sub t = 1 and t = 3 into your velocity equation: v = -32t.
*July 18, 2016*

**Calculus the derivative**

A . correct B. for the average velocity no Calculus is needed P(1) = -16(1) + 1454 = 1438 P(3) = -16(9) + 1454 = 1310 average velocity = (1310 - 1438)/(3-1) = -64 ft/s C. now you want to set -32t = -64 t = 2 E. correct F. I disagree. you want P(t) = 0 -16t^2 + 1454 = 0 t^2 = ...
*July 18, 2016*

**Math**

i = .0275/12 = .002291666... what is 5700(1.00229166..)^144 ?
*July 18, 2016*

**MATH**

just use your definitions: the terms would be a, ar, and ar^2 so a(ar)(ar^2) = 343 a^3 r^3 = 343 (ar)^3 = 343 ar = 7 or a = 7/r a + ar + ar^2 = 49/2 a(1 + r + r^2) = 49/2 (7/r)(1 + r + r^2) = 49/2 7/r + 7 + 7r = 49/2 times 2r 14 + 14r + 14r^2 = 49r 14r^2 - 35r + 14 = 0 2r^2 - ...
*July 18, 2016*

**MAth**

Let's consider how I got the values of x we started with sinx = -1/2 We know from our basic trig functions or by the CAST rule, that x must be in quadrants III or IV (you must know that!) We then find the angle in standard position, that is the corresponding angle if it ...
*July 18, 2016*

**MAth**

normally our domain is 0 ≤ x ≤ 2π perhaps if you think in degrees it might be easier to see. -π/6 radians is -30° now where is -30° ? doesn't it coincide with 330°, and isn't 330° = 11π/6 radians ?
*July 18, 2016*

**MAth**

It factors (2sin x + 1)(3sin x + 1) = 0 sinx = -1/2 or sinx = -1/3 If sinx = -1/2, I know x must be in III or IV x = 210° or 330° x = 7π/6 or 11π/6 if sinx = -1/3, x must be in III or IV angle in standard position is appr 19.47° x = 199.47° or 340.53&...
*July 18, 2016*

**Math - Trig**

To "solve" we need an equation. I will assume you meant: 4cos^2 x - 3 = 0 cos^2 x = 3/4 cosx = ± √3/2 , ----> all 4 quadrants you should recognize that cos π/6 = √3/2 x = π/6 or x = π - π/6 = 5π/6 or x = π + π/...
*July 18, 2016*

**oops - Calculus rate of change**

thanks Steve
*July 18, 2016*

**Calculus rate of change**

Since the height is twice the diameter, the height is equal to the radius of the circular base. Let the radius be r V = (1/3)π r^2 h, but h = r V = (1/3) π r^3 dV/dt = π r^2 dr/dt dr/dt = 20/(πr^2) ** when t = 5 min, V = 5(20) = 100 m^3 100 = (1/3)πr^3...
*July 18, 2016*

**Math**

re-writing your equation: (1/x)/((1/3)x^(-2/3)) = 3/x^(1/3) (3/x) x^(2/3) = 3/ x^(1/3) divide by 3 (1/x) x^(2/3) = 1/x^(1/3) multiply both sides by x^(1/3) (1/x)(x)^1 = 1 1 = 1 so the equation is true for all x, except of course x = 0, or else we would be dividing by zero
*July 18, 2016*

**Maths**

length : breadth : perimeter = 100 : 80 : 360 = .... reduce to lowest term ratio
*July 18, 2016*

**math**

prob(star) = 1/8
*July 18, 2016*

**math**

percentage = (12 + 10)/(25 + 10) = 22/35 = .6285.. or appr 62.9 %
*July 18, 2016*

**math**

smaller ----- x larger ------ x+6 Just translate the English into Math: 2(6+x) + 10 = 3x - 2 solve for x
*July 17, 2016*

**Maths**

look at the second question below in Related Questions answered by Mathmate in 2011 http://www.jiskha.com/display.cgi?id=1304625732
*July 17, 2016*

**Maths**

Are you taking Calculus? Hint: Newton's Law of Cooling
*July 17, 2016*

**math**

Isn't that just 7 choose 3 ??
*July 17, 2016*

**math**

So in 1 day, the earth rotates 24,000 miles (according to your data) after 4 hours it rotated 4000 miles 4000/24000 = 1/6 1/6 of a rotation after 4 hours do the others in the same way
*July 17, 2016*

**Math**

the sum of my numbers is .... ? incomplete
*July 17, 2016*

**@ Asfand**

For most of your replies you have just blurted out the answer. Supplying the answer is not what the purpose of this webpage is. A student has to understand how the question is done, the answer to me is just an afterthought. A reply should contain solutions, part of solutions, ...
*July 17, 2016*

**Math**

first equation: 4h + 6j = 71 second equation: ???????
*July 17, 2016*

**math**

Continue from where you left off when you were "dany" http://www.jiskha.com/display.cgi?id=1468749031
*July 17, 2016*

**math**

let the sales be s solve for s: .12s + 4000 = .02s + 10000
*July 17, 2016*

**math**

You are probably just as good as googling and counting as I am Goggle a list of primes. count how many primes you see from 23 to 97
*July 17, 2016*

**algebra**

mmmhhh, how many sides does a hexagon have?
*July 17, 2016*

**math**

distance at 20 mph = 5(20) = 100 miles distance at 25 mph = 2(25) = 50 miles percent of longer distance more than shorter distance = 100%
*July 17, 2016*

**math**

I assume you are trying to solve this system. 9x+3y-4z=35 ** x+y-z=4 *** 2x-5y-4z = -48 **** subtract **** from ** 7x + 8y = 83 ## 4 times *** ----> 4x + 4y - 4z = 16 subtract **** from the above 2x + 9y = 64 ### 7 times ### ---> 14x + 63y = 448 2 times ## ----> 14x...
*July 17, 2016*

**MATHS**

I assume you made a sketch On mine, I labeled the centre of the smaller circle P and the centre of the larger circle Q There is a common chord, I called that AB Adding the areas of the two circles would count the overlap twice, so we have to subtract the overlap. The overlap ...
*July 17, 2016*

**math**

let w represent the work done A's rate ---- w/24 B's rate ---- w/9 C' rate ----- w/12 B and C's combined rate = w/9 + w/12 = 7w/36 work done by B and C in 3 days = 21w/36 amount left to be done by A = w - 21w/36 = 15w/36 time for A to finish the job = (15w/36...
*July 17, 2016*

**algebra**

looks like you expect somebody to do an assignment or homework for you, and you have not shown any work or indication where your problems lie. What don' t you understand about these questions. They all seem to deal with "geometric mean" btw, you will have more ...
*July 16, 2016*

**pre cal**

1.05( u dot v)
*July 16, 2016*

**small oops - math**

just noticed the - sign in front of √3 so our z = -√3 + i no big deal: the magnitude stays the same, however, the angle would now be in quad II so Ø = 150° or 5π/6 making our √z = √2(cos 75° + i sin75°) OR √2( cos 5π/...
*July 16, 2016*

**math**

let z = √3 + i magnitude = √(√3^2 + 1) = 2 angle Ø: tanØ = 1/√3 Ø = π/6 or 30° so z = 2(cos30° + i sin30°) or 2cis 30° or 2 cis π/6 √z = z^(1/2) = √2( cos 15° + i sin15°) or √2(cos...
*July 16, 2016*

**math**

-12-12√3 i magnitude = √( 144 + 432) = √576 = 24 tan Ø = -12√3/-12) = √3 Ø = 60° or π/3 but from my sketch I see that we are in quadrant III so Ø = π/3 + π = 4π/3 -12-12√3 i = 24(cos 4π/3 + i...
*July 16, 2016*

**math**

just evaluate, even if you don't have a calculator, you should be able to find cos 11π/6 or cos 330° = cos30° = √3/2 sin 11π/6 = -1/2 9(cos 11pi/6 + i sin 11pi/6) = 9(√3/2 - 1/2) = 9√3/2 - 9/2 i
*July 16, 2016*

**Math**

I agree with Steve's answer, but I don't understand why he initially used a plus sign in his cosine equation. I did a similar question to yours about 5 years ago http://www.jiskha.com/display.cgi?id=1303931140 Back to yours, if the resultant of two forces is less than ...
*July 16, 2016*

**MATHS**

What's with all the + signs in the first post? smaller ---- x larger ----- 30-x 2x - 6 = 30-x 3x = 36 x=12 smaller is 12, larger is 30-x or 18 2nd: I will assume you meant to type: "The denominator of a fraction exceeds the numerator by 3" so the original ...
*July 15, 2016*

**Math**

Contains a typo How many own birds ? anyway .... suppose 4 own birds ratio of bird owners : cat owners = 4 : 9 Make the appropriate changes to my solution once you know how many bird owners.
*July 15, 2016*

**Math**

done, look back
*July 14, 2016*

**Math**

to cost $2.25 there must have been 5 ingredients on each of the tacos. number of ways to choose 5 from 10 = C(10,5) = 252
*July 14, 2016*

**Math**

see your previous post of this
*July 14, 2016*

**Math**

This is a very strange question. When I used to have a record player, the needle did not travel around, the record did, but I know what you mean to say. in one rotation the 40π cm of the groove will travel past the neddle or appr 125.66 cm so in 1 minute the distance ...
*July 14, 2016*

**MATH**

Your answer to a) is correct, but I find your order of arithmetic odd. I would have found the probability of disease first = 500/100000 = 1/200 then number of expected deaths = (1/200)(600,000) = 3000 b) ratio of observed : expected = 4500 : 3000 = 3 : 2 (it asked for the ...
*July 14, 2016*

**Math**

you are traveling at 200/2.92 ft/se or appr 68.5 ft/s
*July 14, 2016*

**maths**

I will assume 2:00 am to 11:00 am or 2:00 pm to 11:00 pm one rotations is 360° The minute hand does 360° in each hour. How many hours from 2:00 pm to 11:00 pm ?
*July 14, 2016*

**Math**

Here is a list of Pythagorean triples up to 2100 http://www.tsm-resources.com/alists/trip.html notice the only set that contains 7 is 7 24 25 since 7^2 + 24^2 = 25^2
*July 14, 2016*

**Geometry**

only if the circle touched both sides of the rectangle. Then the diameter of the circle would be the width of the rectangle. Take half the diameter to get the radius
*July 14, 2016*

**Geometry**

You did not describe the diagram. What region is shaded? how big is the circle, what is its radius ? anyway: subtract the area of the circle from the area of the rectangle.
*July 14, 2016*

**Math**

Use the "back door" approach. prob(all 4 boys) = (1/2)^4 = 1/16 We don't want that case so prob(at least 1 girl in 4 kids) = 1 - 1/16 = 15/16 or find prob(1 girl of 4) + prob(2 girls of 4) + prob(3 girls of 4) + prob(4 girls of 4)
*July 14, 2016*

**Vectors**

well let's just substitute ... 2(6+8t) - (-5+t) - 5(2+3t) = 0 12 + 16t + 5 -t - 10 - 15t = 0 7 = 0 This was false when I went to school , and I don't think it has changed since then. So, since we end up with a contradiction, (7=0), there is no solution, and the line ...
*July 14, 2016*

**Math**

what is 75% of 36 ?
*July 14, 2016*

**Math**

Why are you switching names ?
*July 14, 2016*

**Math**

your equation takes the form cost = nx + b, where x is the number of boys, n is the cost per boy and b is the constant given: (150,10000) and (120,8400) cost per boy = (10000 - 8400)/(150-120) = 160/3 (notice this is just like finding the "slope" ) so Cost = (160/3)x...
*July 14, 2016*

**Math (PLEASE HELP!)**

2π/k = period 2π/k = 24 k = 2π/24 = π/12 <---- that's the b of your equation. also we know a = 13 so we start with h(t) = 13 cos (π/12 t) the minimum of this graph is -13, we want the min to be +1, so we have to raise it 14 units h(t) = 13 cos...
*July 13, 2016*

**Math**

let the distance each way be x miles time for first trip = x/30 time for return trip = x/45 x/30 + x/45 = 2 multiply by 90 , the LCD 3x + 2x = 180 5x = 180 x = 36 So the roundtrip was 72 miles check: time at first leg of trip = 36/30 = 1.2 hrs time at 2nd leg of trip = 36/45...
*July 13, 2016*

**Math (PLEASE HELP!)**

sin2θ−cosθ=0 2sinØcosØ - cosØ = 0 cosØ(2sinØ - 1) cosØ = 0 or sinØ = 1/2 from cosØ = 0 , where does the cosine curve cut the x-axis in your domain? http://www.wolframalpha.com/input/?i=y+%3D+cosx where is ...
*July 13, 2016*

**math**

let the sides be 2x, 3x, and 4x perimeter = 9x given: 2x = 6 so, x = 3 perimeter = 9x = 9(3) = 27
*July 13, 2016*

**math**

I think we are to assume that San Francisco is just about north of LA airspeed of plane ---- x mph speed from SF to LA --- x + 20 speed from LA to SF ---- x - 20 distance one way = 4(x-20) distance the other way = 3(x+20) same distance, so 4x - 80 = 3x + 60 x = 140 speed of ...
*July 13, 2016*

**maths**

area = 5x(6x) = 280 30x^2 = 280 x^2 = 28/3 or 84/9 x = √84/3 width = 6x = 6√84/3 = 2√84 = appr 18.3 ft or 18 ft to the nearest foot
*July 13, 2016*

**Math**

rise/run = slope rise/10 = .1 rise = 10(.1) = 1
*July 13, 2016*

**Maths**

take a look at the graphs http://www.wolframalpha.com/input/?i=y%5E2%3D12x+and+x%5E2%3D12y clearly they intersect at (0,0) and (12,12) height of region = 2√3 x^(1/2) - (1/12)x^2 area from 0 to 3 = ∫ (2√3 x^(1/2) - (1/12)x^2) dx from 0 to 3 = [ 4√3/3 x^(...
*July 13, 2016*

**maths**

look how I just did this one. Yours is very similar http://www.jiskha.com/display.cgi?id=1468408379
*July 13, 2016*

**Math**

after dress she has 4/5 of her money left after book would have left (3/5)(4/5) or 12/25 of her money left so (12/25)x = 72 x = 150 I will leave it up to your to check my answer
*July 13, 2016*

**Pre Calculus**

[8(cos10° + i sin10°)] [5(cos 200° + i sin 200°)] = 40(cos10° + i sin10°)(cos 200° + i sin 200°) = 40 ( cos10cos200 + i(cos10sin200) + i(sin10cos200) + i^2 sin10sin200) = 40( cos10cos200-sin10sin200 + i(sin10cos200 + cos10sin200) , recall i^2...
*July 13, 2016*

**Studying for Pre Cal exam**

let z = ( -1/2 + √3/2 i) = (cos 120° + sin 120 i) z^(1/4) = cos (120/4) + sin(120/4) i = cos 30 + sin30 i ------> my primary solution. there will be 4 roots, and 360/4 = 90° by adding multiples of 90 to 30° we can get the other 3 z^(1/3) = cos 30 + sin 30 ...
*July 13, 2016*