Friday
July 29, 2016

Posts by Reiny

Total # Posts: 35,362

MATH
Neither arithmetic nor geometric, but there is a nice pattern. We can write it as a recursive formula. term(n) = term(n-1) + n, n>1, term(1) = 2
March 15, 2016

Algebra 1
a^2 + 14a^5 + a^7 - 16 Why is this a problem? Looks like just a nice innocent expression to me.
March 15, 2016

Math
Liv, you are just shuffling the letters around. Surely you can't think that 3P=s, Ps=3 and P=3s are all the same. I gave you the answer
March 15, 2016

Math
just divide both sides by 3 s = P/3
March 15, 2016

Algebra I
not correct (sqrt(3) - sqrt(7))(sqrt(3)+sqrt(7)) = 3 - 7 = -4
March 15, 2016

Algebra I
When you multiply a binomial by its conjugate, you are duplicating the pattern of the difference of squares: a^2 - b^2 = (a+b)(a-b) so (sqrt(13) - 2)(sqrt(13) + 2) = 13 - 4 = 9 (2+3sqrt(5))(2-3sqrt(5)) = 4 - 45 = -41 try the last one, let me know what you get
March 15, 2016

Math
d = rt <----> r = d/t <----> t = d/r
March 15, 2016

math
will be here for a short time more
March 15, 2016

math
your choice is correct
March 15, 2016

Maths
prob(swim)=4/5 prob(not swim) = 1/5 prob(at least 4 swim) = prob(4of5 swim)+prob(5of5 swim) = C(5,4) (4/5)^4 (1/5) + (4/5)^5 = .... #2 how does "at most 3 are swimmers" relate to what we just found ?
March 15, 2016

math
No such triangle can exist Proof: let AB=x, then AC=3x by the cosine law, x^2 = 9x^2+36-2(6)(3x)cos75 8x^2 - 9.32x + 36 = 0 for which b^2-4ac= -165.14 Thus there are no real values possible for x
March 15, 2016

math
Is there a question ? I asssume you want the volume of water. Sketch a cross-section. let the width of the water level be x by ratios: x/3 = 5/8 8x=15 x=15/8 volume = (1/3)base x height = (1/3)(15/8)^2 (5) = appr 5.86 m^3 check my arithmetic
March 15, 2016

Math
I am sure you made a sketch Let M(x,y) be that point, so that PM:MQ = 2:1 complete the two right-angled triangles with PM and PQ as the hypotenuse. by ratios: (x-0)/(3-0) = 2/3 3x=6 x=2 (y+1)/(2+1)=2/3 3y+3=6 3y=3 y=1 your point is (2,1) check: PM = sqrt(2^2+2^2)= sqrt(8) = ...
March 15, 2016

maths
Assuming the two rectangles are similar, the areas of similar shapes are proportional to the square of their corresponding sides. So their lengths are in the ratio 5/3 b) where do the cones come from ???
March 15, 2016

math
use the properties of sum and product of roots sum of roots = h+k = 10/5 = 2 product of roots = hk = 2/5 we know: (h+k)^2 = h^2 + k^2 + 2hk 2^2 = h^2+k^2 + 2(2/5) h^2+k^2 = 4-4/5 = 16/5
March 15, 2016

algebra
x(3-x)=x-(x^2-2x+4) 3x - x^2 = x - x^2 + 2x - 4 0 = 4 which is a false statement, so , you are right, there is no solution
March 15, 2016

math
Assuming the card is returned after each draw, number = (4/52)(39) = 3 To get an 8: 2,6 3,5 4,4 5,3 6,2 prob of getting an 8 = 5/36 to get 11: 5,6 6,5 prob of 11 = 2/36 compare Second-last one makes no sense What is the prob of getting a head on the coin and either a white or ...
March 14, 2016

math
what is 5x4 ?
March 14, 2016

Algebra
Assuming the circle reaches the edge of the square .... area of square = 400 area of circle = 16pix^2 area not covered by circle = 400 - 16pix^2 = 16( - pix^2) none of the answers given match
March 14, 2016

Trigonometric Identities
My general approach is to change all ratios to sines and cosines. I will do the first one, and one other, you try the rest using the same approach. (sinA+tanA)/(1+secA) = sinA LS = (sinA + sinA/cosA)/(1 + 1/cosA) = ((sinAcosA + sinA)/cosA)/((cosA + 1)/cosA ) = sinA(cosA + 1)/...
March 14, 2016

Happy Pi Day, 2016
I think that is totally irrational
March 14, 2016

Algebra 2
N = k(A)(1/P) for the given: 1800 = k(34000)(1/25) solve for k, then you have the actual equation. Plug in A=42000, P = 25
March 14, 2016

oops - hit "post" too early - Math
not on my usual computer, and hit the wrong return key LS = 12 RS = 1(6-3-1)/2 = not = LS check your typing, I assume your general term is (3n-2)^2 which produces the sequence: 1 + 16 + 49 + ... which is not your series
March 14, 2016

Mat
12 + 42 + 72 + . . . + (3n - 2)2 = n(6n^2-3n-1)/2 by induction: 1. show it to be true for n = 1 LS = 12\
March 14, 2016

Calculus Related Rates
at a time of t sec after they started walking, their distances are 4t and 5t ft, and the angle between them is 48 degrees by the cosine law: x^2 = 16t^2 + 25t^2 - 2(4t)(5t)sqrt(2)/2 x^2 = 41t^2 - 20sqrt(2)t^2 2x dx/dt = 82t - 40sqrt(2)t when t= 30 x^2 = 41(900) - 20sqrt(2)(900...
March 14, 2016

Calculus Related Rates
At a time of t sec, let the height be h ft. let the angle of elevation be k let the distance between them be y 1. h^2 + 50^2 = y^2 2h dh/dt = 2y dy/dt dy/dt = (h dh/dt)/y when t = 5, h = 100 y^2 = 50^2 + 100^2 = 12500 y= 50sqrt(5) dy/dt = 100(20)/sqrt(5) = 50/sqrt(5) = appr 22...
March 14, 2016

math
an infinite number of combinations: e.g. 5x4 10x2 2.5x8 ....
March 14, 2016

incomplete - maths-equadratic eqn
no root given
March 14, 2016

Algebra HELP PLEASE
Volume = Pi r^2 h = Pi (4x+2)^2 (5x-4) = Pi (16x^2 +16x + 4)(5x^2 - 4) without completing the whole expansion, I know it has to start with 80Pi x^3 and end in -16Pi The only answer that matches that is C
March 14, 2016

Maths
13,000,000 = 1.3 x 10^7
March 14, 2016

Maths
N(T or F) = N(F) + N(T) - N(T and T) = 42+15-12 = 45 Number who liked neither football or tennis =50-45 = 15
March 14, 2016

Math
number of members --- x number who play tennis = .2x number who play rounder = .25(.2x) = .05x but .05x = 8 5x = 800 x = 160
March 14, 2016

Algebra
w = k(1/l)(wh^2) for the given: 14 = k(1/12)(6(2^2)) 14 = k(2) k = 7 so w = 7(wh^2/l) = (7/14)(4(9)) = 18 tons
March 11, 2016

maths
Ummhh, what am I missing? Didn't you just state that it takes 18 days to finish the work ?
March 11, 2016

Math
number of 13 cent stamps --- x numbr of 8 cent stamps -- y 13x + 8y = 100 both x and y have to be whole numbers clearly 0 < x < 7 y = (100-13x)/8 furthermore, for 100-13x to be divisible by 8, it must be even, so x must be even A quick check tells us that x = 4 is the ...
March 11, 2016

Algebra 2
current charge -- $180 membership ---- 1000 Let the number of $5 increases be m new charge = 180 + 5n membership = 1000 - 10n revenue = (180+5n)(1000-10n) = 180000 + 3200 - 50n^2 = -50(n^2 - 64n - 3600) this is a parabola and the vertex will yield our answer the n of the ...
March 11, 2016

Algebra 1
-x/3 > -3 times 3 -x > -9 divide by -1, must reverse inequality sign x < 9
March 10, 2016

geometry
1/4 of the original area
March 10, 2016

Math
no, slope = (6-4)/(2-3) = 2/-1 = -2
March 10, 2016

Geometry
let the diagonals be a and b respectively. given : ab = 144 but the area of a rhomus = (1/2) product of diagonals = 1/2 (144) = 72 and that was also given. So we have redundant information, but not enough to find the values of a and b a and b could be any values, so that ab = ...
March 10, 2016

math
final price = 35(.8)(1.06) = ...
March 10, 2016

math
total cost of the 25 tables before tax = 1706.25/1.05 = 1625 so cost of each table = 1625/25 = 65 refund of 5 without tax = 5(65) = $325
March 10, 2016

Math
for the first, you are adding 3/4 to a term to get the next one for the second , you are subtracting 7 from a term to get the next one.
March 10, 2016

Math
what about it ? If you are solving, let y = x^2 - 4 then you have y^2 - y - 30 = 0 (y-6)(y+5) = 0 y = 6 or y = -5 sub back in: case1: x^2 - 4 = 6 x^2 = 10 x = ± √10 case2: x^2 - 4 = -5 x^2 = -1 x = ± i , if you want complex number solutions.
March 10, 2016

Trigonometry
I will use x instead of beta for easier typing tanxsinx + cosx = secx I usually try to express everything in terms of sines and cosines, so LS = (sinx/cos)sinx + cosx = sin^2x/cosx + cos^2 x/cosx = (sin^2 x + cos^2 x)/cosx = 1/cosx = secx = RS Give the other two a try using ...
March 10, 2016

maths
one rotation is πd = 21π cm so the belt covers 21π(1600) cm/min = 105,557.51 cm/min = 1.05557 km/min = appr 63.33 km/h
March 10, 2016

maths
old radius -- x old height -- h old volume = (1/3)πr^2 h new radius = 1.1r new height = 1.1h new volume = (1/3)π (1.1r)^2 (1.1)h = 1.1^3 (1/3)πr^2 h ratio of increase = 1.1^3 (1/3)πr^2 h/((1/3)πr^2 h) = 1.1^3 = 1.331 there is a 33.1% increase
March 10, 2016

math
7/x + 8 = 6/2 x 7/x + 8 = 3x times x 7 + 8x = 3x^2 3x^2 - 8x - 7 = 0 x = (8 ± √148)/6 = (8 ± 2√37)/6 = (4 ± √37)/3
March 9, 2016

MATH OPEN RESPONSE
height = 3x + 7 , where x is the number of years when is 3x+7 = 28 ? 3x = 21 x = 7 It will take 7 years to grow to 28 ft check: now -- 7 after 1 year -- 10 2years -- 13 3 years --16 4 years -- 19 5 years -- 22 6 years -- 25 7 years -- 28
March 9, 2016

Trig - Ambiguous Cases
I got the same result, so I am with you. No solution. I verified the "no solution" by using the cosine law to find HA let HA = x then : 7.2^2 = x^2 + 8.5^2 - 2x(8.5)cos124° x^2 + 9.506x + 20.41 = 0 x = -3.276 or x = -6.23 but x can't be negative, confirming ...
March 9, 2016

Math
What is (1/6)(1/6) ?
March 9, 2016

Data Management (need help)
Not possible to show tree diagram here, but I would start a tree for each school with two branches whose endpoints would be W and L (for win and lose) From the W end, I need two more branches, again labeled W and L Do the same for the L end, etc until a series of branches has ...
March 9, 2016

Math
an ellipse, a hyperbola, or a parabola Google conic "sections" or take a styrofoam cone and do it.
March 9, 2016

Algebra
follow the same method I just showed you in your previous post of a very similar problem.
March 9, 2016

Algebra
original speed --- x mph new speed ---- x+12 km/h time at original speed = 60/x time at new speed = 60/(x+12) but the difference in those times is 10 minutes or 1/6 hr 60/x - 60/(x+12) = 1/6 times 6x(x+12) , the LCD 360(x+12) - 360x = x(x+12) 360x + 4320 - 360x = x^2 + 12x x^2...
March 9, 2016

Math
There are 2^24 subsets here. That would include all your choices of 1 at a time, 2 at a time, 3 at a time, etc It also includes not taking any, which we probably want to exclude. so 2^24 - 1 = 16777215
March 9, 2016

math
height = -16t^2 + 600 when does it reach a height of 300? 300 = -16t^2 + 600 16t^2 = 300 t^2 = 300/16 t = √300/4 = 10√3/4 = appr 4.33 seconds It will be above or equal to a height of 300 ft for the first 4.33 seconds
March 9, 2016

math
log3 9 = 2 ---> log form 3^2 = 9 ----> equivalent exponential form
March 9, 2016

Math
Just did this, see below
March 9, 2016

problems on age
son's present age ..... x father's present age = 64-x age at which father was the same as son = 64-x - x = 64-2x (e.g. suppose the father is now 44 and the son is now 20 the number of years ago, when the father was the same as the son's present age = 44-20 = 22 64-...
March 9, 2016

Maths
a) prob(4 women) = C(6,4)/C(10,4) = 15/210 = 1/14 b) prob(2 women, 2 men) = C(6,2)C(4,2)/C(10,4) = 15(6)/210 = 3/7 c) with 3 sisters in, we need just one more of the remaining7 (could be man or woman) prob(of event as stated) = 1x C(7,1)/210 = 7/210 = 1/30 d) prob(choosing any...
March 9, 2016

Maths
number of ways to choose 6 from 10 = C(10,6) = 1056 b) number with 2 men and 4 women = C(5,2) x C(5,4) = 10(4) = 40 prob(choosing 2men and 4 women) = 40/1056 = 5/132 c) at least 4 women --> 4 women or 5 women = C(5,4)C(5,2) + C(5,5)C(5,1) = 5(40) + 1(5) = 205 prob(at least ...
March 9, 2016

maths
Let Google be your friend
March 9, 2016

Pre calc quadratic stuff
area = (x+2)(20-2x) = 20x - 2x^2 + 40 -4x = -2x^2 + 16x + 40 which is a quadratic function because of the -2x^2 term
March 9, 2016

math
#1 2x-8 ≥ 0 2x≥ 8 x ≥ 4 #2 x-2 ≥ 0 x ≥ 2
March 9, 2016

math
πr^2 < 100 cm^2 r^2 < 100/π r < 10/√π
March 8, 2016

Math
#14, V = (4/3)π(4^3) = appr 268 m^3 , not m^2 the answer you gave would be the surface area. Is it a typo? the others are correct
March 8, 2016

trig
recall cos 2x = 2cos^2 x - 1 2cos^2 x = cos 2x + 1 cos^2 x = (cos 2x + 1)/2 cos^2 (112.5°) = (cos 225° + 1)/2 now cos 225 = cos(180 + 45) = cos180cos45 - sin180sin45 = -1(√2/2) - 0 = -√2/2 cos^2 112.5 = (-√2/2 + 1)/2= (2-√2)/4 cos(112.5) = &...
March 8, 2016

Algebra
Yes, you have the | key, look to the right of } key |2y + 4| < 10 2y+4 ≤ 10 AND -2y-4 ≤ 10 2y < 6 AND -2y < 14 y < 3 AND y > -7 -7 < y < 3
March 8, 2016

algebra
speed of faster plane --- x km/h speed of slower plane ---- x - 100 km/h time for faster plane = 1800/x time for slower plane = 180/(x-100) 1800/(x-100) - 1800/x = 36/60 = 3/5 multiply each term by 5x(x-100) , the LCD 9000x - 9000(x-100) = 3x(x-100) 9000x - 9000x + 900000 = 3x...
March 8, 2016

math
original: y = 9 - 4/x^2 inverse: x = 9 - 4/y^2 solving that for y: xy^2 = 9y^2 - 4 xy^2 - 9y^2 = -4 y^2(x -9) = -4 y^2 = -4/(x-9) y^2 = 4/(9-x) y = ± √(9-x) the new equation is NOT a function
March 8, 2016

Math
let the total be x blues = (5/8)x greens = (5/9)x but 5/8 + 5/9 = 85/72 which is > 1 not possible, so far we would have 85/72 of x check the wording Did it say: 5/9 of the remaining are green ?
March 8, 2016

Algebra
then V = k/p for the given: 5 = k/158 k = 790 or V = 790/p for p = 395 V = 790/395 = 2
March 8, 2016

German Language
I speak German, so I could possible help.
March 8, 2016

Math
(3/2)x^2 + 2x | from 1 to t = (3/2)t^2 + 2t - (3/2 + 2) = 13/2 (3/2)t^2 + 2t - 10 = 0 3t^2 + 4t - 20 = 0 (t - 2)(3t + 10) = 0 t = 2 or t = -10/3 depending on what interpretation is given to the integral, we might reject the t = -10/3
March 8, 2016

math
Let the number be x Now just translate the English to Math 5x + 13 ≤ 2x - 20 3x ≤ -33 x ≤ -11
March 8, 2016

math [pls help. it is urgent]
total number of beads --- x yellows ----- (2/5)x = 2x/5 remaining: 3x/5 green ---- (7/13)(3x/5) = 21x/65 rest are black. black = x - 21x/65 - 2x/5 = 65x/65 - 21x/65 - 26x/65 = 18x/65 yellow = blacks + 32 2x/5 = 18x/65 + 32 times 65 , the LCD 26x = 18x + 2080 8x = 2080 x = 260 ...
March 8, 2016

Math
done, see above to your other post
March 8, 2016

algebra
simply sub t = 2 into your equation and do the math. at ground level, h = 0 0 = -16t^2 + 48t 16t^2 - 48t = 0 t^2 - 3t = 0 t(t-3) = 0 t = 0 ---> at the start it is at ground level or t = 3 state your conclusion
March 8, 2016

maths
amount of solid in the original sphere = (4/3)π(4^3) - (4/3)π(2^3) = (4/3)π(64-8) = 224π/3 This must become the volume of a cone (1/3)π(4^2)h = 224π/3 time 3/π 16h = 224 h = 14 cm
March 8, 2016

trig
you should know the expansions for cos(A+B) and for cos(A-B) cos(x-π/6) = cosxcos π/6 + sinxsin π/6 = (√3/2)x + (1/2)sinx cos(x+ π/6) = (√3/2)cosx - (1/2)sinx so .... cos(x - π/6) = 1 + cos(x + π/6) (√3/2)x + (1/2)sinx = 1 + (&#...
March 8, 2016

Trig please
you would want: 3.75sin(733t) + 7.5 = 3.75sin[733(t+ 4π/3)] + 7.5 divide each term by 3.75, (how convenient ?) sin(733t) + 2 = sin[733(t+ 4π/3)] + 2 sin(733t) = sin[733(t+ 4π/3)] this can only be true if 733t = 733(t + 4π/3) OR 733(t+4π/3) = π - ...
March 8, 2016

Finite
what is 50( (1+.05/52)^208 - 1)/(.05/52) ?
March 7, 2016

Trigonometry
from 3cos^2 Ø -4sinØ =sin^2 Ø , why not replace the cos^2 Ø 3(1 - sin^2 Ø) - 4sinØ - sin^2 Ø = 0 .. 4sin^2 Ø + 4sinØ - 3 = 0 (2sinØ - 1)(2sinØ + 3) = 0 sinØ = 1/2 or sinØ = -3/2 which is...
March 7, 2016

algebra 1
let her monthly payment be P P( 1 - (1+.046/12)^-60)/(.046/12) = 8500 P = 158.85 total paid = 60(158.85) = $9531.15
March 7, 2016

correction - Maths
surface area of earth which is land = (1/4)4πr^2 = π(6370)^2 = 127,476,091 km^2 =
March 7, 2016

John is wrong - precalc
John, you misread the question 2^(3x + 1) = 3^(x − 2) is not the same as 2 log(3x+1) = 3 log(x-2) then, log(3x +1) /log (x-2) ≠ log (3x + 1 -x +2) e.g. is log100/log10 = log(100-10) ??? LS = 2/1 = 2 RS = log 90
March 7, 2016

precalc
take logs of both sides and use log rules (3x+1)log2 = (x-2)log3 3log2 x + log2 = log3 x - 2log3 x(3log2 - log3) = -2log3 - lo2 x = (2log3 + log2)/(log3 - 3log2)
March 7, 2016

precalc
using our rules of logs , which you should have at your fingertips, log2 ( (x+17)/(x-2) ) = 1 so (x+17)/(x-2) = 2^1 solve for x , remember x> 2 for the log to be defined.
March 7, 2016

Math
They both would have run the same time. Let that time be t hrs. distance covered by zebra = 40t miles distance covered by lion = 50t miles The difference in their distances is 1000 ft or 1000/5280 miles 50t - 40t = 1000/5280 10t = 1000/5280 t = 100/5280 = .0189.. hrs = 1.13636...
March 7, 2016

Math
unit digit --- x tens digit --- x-1 hundred digit --- 6 , to be between 600 and 700 Just translate the English into Math using my definitions: the sum of the digits = x + x-1 + 6 the 3-digit number = 600+10(x-1) + x 600 + 10(x-1) + x = 30(x + x-1 + 6) - 1 solve for x and all ...
March 7, 2016

math
amount = 600(1.05)^2 = ... how can you not be sure ?
March 7, 2016

math
with 3 girls: = C(10,3) x C(15,1) = .. with 4 girls = C(10,4) x C(15,0) = add them up
March 7, 2016

math
The two numbers: x and x+1 (x+1)^2 = x(x+1) solve for x
March 7, 2016

geometric progression
given: ar^4 = 48 ar^6 = (1/8)ar^3 8ar^6 = ar^3 8r^3 = 1 r = 1/2 back into ar^4 = 48 a(1/16) = 48 a = 768 series is 768 + 384 + 192 + 96 + 48 + 24 + 12 + .... Check: is the 5th term 48 ? YES is the 7th term 1/8 of the 4th ? is 12 =(1/8)(96) ?, YES My answer is correct
March 7, 2016

trig
sin 4x = sin 2x 2sin 2x cos 2x - sin 2x = 0 sin 2x(2 cos 2x - 1) = sin2x = 0 so 2x = 0, π, 2π, 3π, .. x = 0, π/2, π , 3π/2, 2π for 0≤x≤2π or cos2x = 1/2 2x = π/3, 2π-π/3, ..., the primaries x = π/6, 5π...
March 7, 2016

Math
Are you using tables, charts, or software?
March 6, 2016

trig plz help
You obviously have a diagram. Mark in all the given information. let the horizontal (adjacent to 46°21') be x ft What trig ratio involves opposite and adjacent?
March 6, 2016

trig
cot Ø = 4 then tan Ø = 1/4, and Ø is acute, thus in quadrant I Did you make a sketch of the triangle? recall that tanØ = y/x so y = 1, and x = 4 can you find r ? How is sinØ defined in terms of x, y, and r ? Did you know that cos 2Ø = ...
March 6, 2016

Probability
What is the definition of probability? So in your experiment in how many of the 500 cases did you get the required event ?
March 6, 2016

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