Thursday
July 28, 2016

Posts by Reiny

Total # Posts: 35,358

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

Pre Calculus
sum of sines: sinA + sinB = 2sin( (A+B)/2) cos( (A-B)/2) then: sin 150° + sin 30° = 2sin 90° cos 60° = 2(1)(1/2) = 1 Difference of sines: sinA - sinB = 2cos( (A+B)/2) sin( (A-B)/2) then: sin 4θ − sin 2θ = 2cos(3Ø)sin Ø
July 11, 2016

pre cal
let √x = y then: 2y^2 - 5y + 2 = 0 (2y -1)(y -2) = 0 y = 1/2 or y = 2 √x = 1/2 ----> x = 1/4 or √x = 2 ------> x = 4 or 2x+2 = 5√x square both sides: 4x^2 + 8x + 4 = 25x 4x^2 - 17x + 4 = 0 (x - 4)(4x - 1) =0 x = 4 or x = 1/4 btw, in both solutions...
July 11, 2016

Pre-Calculus 11
-3* cube root of 2 is a negative number, so your result has to stay negative. change it to - cuberoot(54)
July 10, 2016

math
just use for formulas for an AS term(n) = a + (n-1)d for yours a=22000 d=500 n=7 sum(n) = (n/2)(first + last) (you have the last term from above) or sum(n) = (n/2)(2a + (n-1)d )
July 10, 2016

Math
number of men --- m number of girls --- g m+g = 120 Tina danced with 7 men Reena danced with 8 men .... Raveena danced with 120-g men this is an arithmetic sequence with a=7, d=1 term(g) = m a + (g-1)d = m 7 + g-1 = m g - m = -6 also g+m = 120 add them 2g = 114 g = 57 m = 120-...
July 10, 2016

Math
construct your right-angled triangle. r^2 = x^2 + y^2 , (x is a side , not an angle) 2^2 = x^2 + 1^2 , since sinØ = opposite/hypoenuse or y/r x^2 = 3 x = √3 , we know the angle must be in Quad I sinx = 1/2 --- given cscx = 2 cosx = √3/2 secx = 2/√3 ...
July 10, 2016

Pre Calculus
5.4 radians coterminal with 5.4 - 2π = -.883.. radians, which is in the IV th or if you want to "think" in degrees 1 rad = 180/π ° 5.4 rad = 309.39.. ° ----> 4th
July 10, 2016

Pre Calculus
I did this yesterday http://www.jiskha.com/display.cgi?id=1468085862
July 10, 2016

mathematics
of the 40 oranges, 12 are unripe ----> 28 are ripe prob(ripe) = 28/40 = 7/10 so prob(unripe) = 1 - 7/10 = 3/10 you are correct
July 10, 2016

maths
nope , (x+y)^2=x^2+2xy+y^2
July 10, 2016

math
all the numbers that don't have a 5 in them: 8 x 9 = 72 , (they can start with 1,2,3,4,6,7,8,9 and they can end with 0,1,2,3,4,6,7,8,9 ) Those with a 5 are 100-72 = 28 prob(have a 5) = 28/100 = 7/25
July 10, 2016

math
smallest --- x middle one -- 2x largest ------ 3x x + 2x + 3x = 180 solve for x, sub back into my definitions
July 10, 2016

Pre-calculus
x = a(y-3)^2 + 0 but (4,9) lies on it, so 4 = a(9-3)^2 + 0 4 = 36a a = 1/9 x = (1/9)(y-3)^2 is your equation.
July 10, 2016

Pre-Calculus 11
is it (5/7)√(3/2) ? or 5/(7√(3/2) )?
July 9, 2016

math
3x-5y=16 -9x+15=48 notice that if you divide the 2nd by -3 , you get 3x - 5y = -16 clearly you will have two different parallel lines, thus no solution. or if we subtract: 3x-5y=16 3x-5y=-16 0 = 32 not very likely !!!! , so no solution
July 9, 2016

Mathematics
Memorize this relationship until you can state it in your sleep. π radians = 180° Use it to answer this, and your two previous questions.
July 9, 2016

Mathematics
repeatedly add 360° and note the results
July 9, 2016

Pre Calculus
You really really really MUST know that.
July 9, 2016

Mathematics
What is (2π - 11π/13) ? I get 15π/13 , which is not one of your choices. Do you have a typo?
July 9, 2016

Pre Calculus
same type of question as your last one
July 9, 2016

Pre Calculus
8π / 7= π + (1/7)π so just a bit more than π, so in quadrant III here is a "sneaky way" set your calculator to radians take sin 8π/7 to get a negative take cos 8π/7 to get a negative the only quadrant in which both sine and cosine are ...
July 9, 2016

Maths
Everybody studying trig should know the ratio of sides, and thus the trig ratios, of the 30-60-90° right angled triangles, as well as the 45 -45-90° triangle for the 30-60-90 the sides are 1 - √3 - 2 units respectively looking at your sketch of that triangle, ...
July 9, 2016

Spherical Trigonometry
h/100 = tan 38° solve for h
July 9, 2016

Calc.
I assume we are looking at vectors, then (6,2y) - (5x,10) = (6,-4) 6-5x = 6 , solve for x 2y - 10 = -4, solve for y
July 8, 2016

Calc.
⃗⃗u dot ⃗v =| ⃗⃗u| | ⃗v| cosØ, where Ø is the angle between them 2 + 20 + 2 = √21 √30 cosØ 24/(√630 =cosØ I get Ø = appr 17.02° check my arithmetic
July 8, 2016

Pre-Cal
I will do the 2nd one, which is the harder of the two. Follow my steps to do the first one. sinx = -5/13 ,and the angle x is in III recall that sinØ = y/r so y = -5, r = 13 sketch a right-angled triangle in III with hypotenuse 13 and y = -5 x^2 + y^2 = r^2 x^2 + 25 =169...
July 7, 2016

Raquel, check your answer - Algebra
Racquel, check your calculations. 2000(.08) + 8000(.09) = 880 , not 860 as needed.
July 7, 2016

Algebra
sue's rate = 1/60 (driveways/minute) Tom's rate = 1/35 (driveways/minute) combined rate = 1/60+1/35 = 19/420 (driveways/minute) time at combined rate = driveway/( (19/420) (driveways/minute) ) = 420/19 minutes = 22.1 minutes
July 7, 2016

pre cal
well, why don't you try expanding (x+s)^2 to see what comes out. btw, we use ^ to show exponents eg. x^2 is "x squared"
July 6, 2016

Math
Just translate the English using your definitions of a GS ar^3 = 30 ar^8 = 960 divide the 2nd by third, the a's will cancel r^5 = 32 r = 2 in ar^3 = 30 a(8) = 30 a = 15/4
July 6, 2016

pre cal
I will assume you meant: x^2/162 +x/18 + 1/9 = 0 the LCD is 162, so multiply each term by that x^2 + 9x + 18 = 0 (x+3)(x+6) = 0 x = -3 or x = -6
July 6, 2016

pre cal
number of twenties --- x number of tens ------- 3x 20x + 10(3x) = 1950 50x =1950 x = 39 so there are 39 twenties and 117 tens check: 39(20) + 117(10) = 1950
July 6, 2016

Pre Calculus
You really need help pushing buttons on your calculator???
July 6, 2016

Pre Calculus
form the half-life equation, amount = 69(1/2)^(t/12.4) , where t is in years plug in 75 for t show me your work and I will help you with the others.
July 6, 2016

lagdamat
What is "lagdamat" ?? width ----- x length ----- 2x+2 x(2x+2) = 24 2x^2 + 2x - 24 = - x^2 + x - 12 = 0 I will leave it up to you to solve this very simple quadratic. Hint1, it factors Hint2, reject the negative
July 6, 2016

math
What is (3/10)(2/7)(2905) ?
July 6, 2016

probability
I read that as a binomial distribution. so C(4,1) (1/2)^1 (1/2)^3 = 4(1/2)^4 = 1/4 or there are 2^4 or 16 cases your event could be HTTT THTT TTHT TTTH, or 4 possibilities prob(exactly one head) = 4/16 = 1/4
July 6, 2016

Analytic geometry
Name your points A(-8,8) and B(-2,2) So you want PA = 2PB Use you distance between points formula: √( (x+8)^2 + (y-8)^2 ) = 2√( (x+2)^2 + y-2)^2 ) square both sides (x+8)^2 + (y-8)^2 = 4( (x+2)^2 + y-2)^2 ) I will leave it up to you to expand and simplify the equation
July 6, 2016

math
Ahh, I see you fixed the problem from your earlier post. a) 20 men, 12 women, choose 5, with exactly 3 men = C(20,3) x C(12,2) = 2053(66) = 135498 b) at least 4 women ---> 4 women or 5 women = C(20,1) x C(12,4) + C(20,0) x C(12,5) = 20(495) + 1(792) = 10692 check my arithmetic
July 6, 2016

Math
Since the room is square, its side is √350 = 5√14 m your carpet is only 5√14 by 3√14 So clearly you will need an extra 2√14 m
July 6, 2016

math
your wording is gibberish. How can you have a committee of 5 people "if exactly three men must be on each committee and at least four women on each committee" Are there two different questions here?
July 5, 2016

Prealgebra
correct about the conversion to start. 3 m = 300 cm 2 m = 200 cm, (isn't the metric system great??) but 300/10.5 = 28.5 , so you will need 29 one way, and 200/10.5 = 19.04.. darn!, you will have to have 20 along the width So you will need 20x29 or 580 tiles. ( in reality ...
July 5, 2016

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