Friday

July 29, 2016
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*