Wednesday
December 7, 2016

Posts by Reiny

Total # Posts: 36,897

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

pre calculus
??
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

Maths
not enough information. If the spinner is labeled, A B C D E F prob(4) = 0/6 = 0 If the spinner is labeled 1 2 3 4 5 6 prob(4) = 1/6 If the spinner is labeled 1 1 4 4 4 6 then Prob(4) = 3/6 = 1/2 do you see my point ?
July 13, 2016

Maths
from the first: 10-p = q-10 q = 20-p from the second: pq = 36 by substitution, p(20-p) = 36 20p - p^2 = 36 p^2 - 20p + 36 = 0 ----> thus shown (p - 18)(p - 2) = 0 p = 18 or p = 2 then q = 36/18 = 2 or p = 36/2 = 18 for p = 18, q = 2 the AS is 18, 10 and 2 the GS is 18, 6, 2...
July 13, 2016

math
to form a GS, the square of the middle term must equal to product of the outer terms (k+1)^2 = (k-3)(4k-2) k^2 + 2k + 1 = 4k^2 - 14k + 6 3k^2 - 16k + 5 = 0 (k - 5)(3k - 1) = 0 k = 5 or k = 1/3
July 13, 2016

Pre-Cal
Amber, this is a public site, please do not post your phone number, I will ask one of the monitors to delete your above reply. As to your question, they really are not that difficult. I suggest you sketch a right-angled triangle in the appropriate quadrant and recall that sin&...
July 12, 2016

Math
For quadrilaterals, the largest area and the least perimeter is obtained when the quadrilateral is a square.
July 12, 2016

MAth
24m^9 - 27m^7 - 24m^5 = 3m^5(8m^4 - 9m^2 - 8) so the GCF is 3m^5
July 12, 2016

Maths
your equations are jumbled and garbled did you mean: -7x + 7y = -21 and -9x + 9y = -27 ?? dividing the first one by -7 and the second by -9 produces the same equation, x - y = 3 So they are both one and the same equation. Look up how each of your classifications is defined in ...
July 12, 2016

pre algebra
prob(red) = 1/3 prob(not red) = 2/3 odds in favour of red = (1/3) : (2/3) = 1 : 2
July 12, 2016

math
Assuming a total loss, what is 80% of 288,000
July 12, 2016

Math
There are 69 shells, you said so.
July 12, 2016

Algebra
I agree with PsyDAG Your question makes about as much sense as this one: Sara can drive to Chicago in 5 hours, Jasmin can do the same trip in 7 hours. How long will it take the two of them driving together?
July 12, 2016

pre cal
x^4>4x^2 x^4 - 4x^2 > 0 x^2(x^2 - 4) > 0 x^2(x+2)(x-2) > 0 critical values are -2, 0, +2 for x < -2 , --->(+)(-)(-) >0 , so true for x = 0 , no good for -2 < x <0 , say x = -1 ---> (+)(+)(-) < 0 , false for 0 < x < 2 , ---> (+)(+)(-) &...
July 12, 2016

Calculate y' and y'' at the point (1,1)
Gee, you posted this same question only 3 minutes ago. I know we are fast but .... btw, it has been answered.
July 12, 2016

Math
first derivative: 5x y^2 + 9y - 14 = 0 5x(2y)dy/dx + 5y^2 + 9dy/dx = 0 dy/dx(10xy + 9) = -5y^2 dy/dx = -5y^2/(10xy+9) at (1,1) dy/dx = y' = -5/19 , you had that from 5x(2y)dy/dx + 5y^2 + 9dy/dx = 0 10xy y' + 5y^2 + 9 y' = 0 recall the rule for derivatives of triple...
July 12, 2016

pre cal
Just noticed that Steve answered your question yesterday. http://www.jiskha.com/display.cgi?id=1468295145 Why are you repeating it? (this time with a typo)
July 12, 2016

pre cal
First of all, your equation contains a typo, it should say: h(t)= (−g/2) t^2+v0t+h0 secondly, what units are you using? thirdly, did you drop the rock or did you give it a downwards velocity? let me know before I can answer your question.
July 12, 2016

Math - Studying for Pre Calc exam!
6 sin 2x − 8 cos x + 9 sin x = 6 12sinxcosx - 8cosx + 9sinx - 6 = 0 4cosx(3sinx - 2) + 3(3sinx - 2) = 0 (3sinx - 2)(4cosx + 3) = 0 sinx = 2/3 OR cosx = -3/4, the last one is not possible sinx = 2/3 x = .7297.. which matches b) Make sure your calculator is set to radians ...
July 12, 2016

math
Haven't done this kind of question in over 55 years, had to look it up try this: http://math.stackexchange.com/questions/315317/orthogonal-trajectories-for-a-given-family-of-curves
July 12, 2016

Math
don't like fractions, so how about Ø = x/2 or x = 2Ø then your equation becomes cosØ - sin 2Ø = 0 cosØ - 2sinØcosØ = 0 cosØ(1 - 2sinØ) = 0 cosØ = 0 or sinØ = 1/2 Ø = π/2, 3π/2...
July 12, 2016

Pre-Cal
tan^(2)xsecx+secx = secx( tan^2 x + 1) , common factor = secx(sec^2 x), by identity = sec^3 x (csct-sint)/(csct) = (1/sint - sint)/(1/sint) multiply top and bottom by sint = (1 - sin^2 t)/1 = cos^2 t
July 11, 2016

Pre-Cal:(Cont.)
2 cos 2θ − 1 = 0 cos 2Ø = 1/2 I know cos π/3 = 1/2 , and the cosine is positive in I and IV so 2Ø = π/3 , in I OR 2Ø = 2π - π/3 = 5π/3 , in IV Ø = π/6 or Ø = 5π/6 (Ø = 30° or Ø...
July 11, 2016

Math
I am sure you meant: f(x) = (ax + b)/(cx + d) "the horizontal asymptote is y=2" ----> ax/(cx) = 2 , as x ---> infinity a/c = 2 a = 2c so we have f(x) = (2cx + b)/(cx + d) "the vertical asymptote is x =5" ---> (x-5) <---> cx + d c = 1, d = -5 ...
July 11, 2016

Even or Odd Funciton
let's take your answer a bit further ... 1/((-x)^3-5(-x)) = 1/( -(x)^3 + 5x) = -1/(x^3 - 5x) = - f(x) so the function is odd by definition: odd ---> f(-x) = -f(x) even ---> f(-x) = f(x)
July 11, 2016

calculus
You are correct!
July 11, 2016

calculus
I assume you used: tan(A - B) = (tanA - tanB)/( 1 + tanAtanB) then (tan17pi/12 - tan pi/4) / (1+tan 17pi/12 tan pi/4) = tan(17π/12 - π/4) = tan( 7π/6) or tan 210° ---> quad III = 1/√3
July 11, 2016

math
I am sure you meant: (tan 7x − tan x)/( 1 + tan 7x tan x) compare to : tan(A-B) = (tanA - tanB)/(1 + tanAtanB)
July 11, 2016

math
you should recognize this as the use of cos(A+B) cos 60° cos 65° − sin 60° sin 65° = cos(60°+65°) = cos 125°
July 11, 2016

calculus
poor choices for answers, they should have rationalized the answer. That's where my hint about a calculator comes in. Both our answers were (1/4)(√2 - √6) if you work that out on your calculator you get appr -.2588 working out c) you get appr -.2588 so c) is ...
July 11, 2016

calculus
correct Why not just check your result with a calculator?
July 11, 2016

calculus
60.1 − 43.9 cos πt/ 6 ≥ 77 − 43.9 cos πt/ 6 ≥ 16.9 cos πt/6 ≤ - .38496... consider cos πt/6 = - .38496... I know cos 1.1756.. = +.38496 so πt/6 = π - 1.1756 = appr 1.966 t = 3.755 or πt/6 = π + 1.1756.. = 4....
July 11, 2016

amth
I know cos 30° or cos π/6 = +√3/2 so x/2 = 180-30 or x/2 = 180+30 x = 300° or x = 420° or x = 5π/3 or 7π/3 To do these type of questions, you MUST know the ratio of sides of the 30-60-90° as well as the 45-45-90° triangles, and you MUST...
July 11, 2016

math
incomplete question. Are you not getting any interest on your money?? in that case amount = 450 + 58.5w
July 11, 2016

math
Along the 12 ft length, the 6 inch tiles will fit exactly and you will need 24 along that side. Along the 14 ft side, you will need 28 tiles. total = 24(28) or 672 tiles or area = 168 square feet, but with 6 inch tiles, you will need 4 tiles per square inch total = 4(168) = ...
July 11, 2016

Math
and here is why ... pq - q = p+12 q(p - 1) = (p+12) q = (p+12)/(p-1) = 1 + 13/(p-1) clearly p > 1 , to have positive values for q to be an integer, 13/(p-1) has to be an integer, that is, p has to be either 2 or 14 so (2,14) or (14,2) e.g. if p = 2, q = 14 , Steve's ...
July 11, 2016

pre cal
I think you have a typo. Being familiar with these type of questions, it probably said: (x/x-1)^2 - (x/x+1) -2=0 if so, let y = x/(x-1) and carry on like I showed you in your previous post
July 11, 2016

pre cal
hint: let y = x^2, then your equation becomes 2y^2 - 5y + 2 = 0 carry on
July 11, 2016

mathematics
total = 36 students prob(boy) = 15/36 = 5/12
July 11, 2016

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