Sunday

May 1, 2016
Total # Posts: 34,402

**statistics**

If I recall correctly, sd = √5569 = appr 74.626 so we want between 4088+41 and 4088-41 that is , between 4129 and 4047 Using my favourite webpage for this stuff, http://davidmlane.com/hyperstat/z_table.html and entering the above data, I got a probability of .4173 So for...
*March 17, 2016*

**Precal/Math**

LS = (cos^2 B / sin^2 B)/cos^2 B - cos^2 B/sin^2 B = cos^2 B/(sin^2 B cos^2 B) - cos^4 B/(sin^2 B cos^2 B) = cos^2 B(1 - cos^2 B)/(sin^2 B cos^2 B) = cos^2 B sin^2 B/(sin^2 B cos^2 B) = 1 = RS
*March 17, 2016*

**Math**

let the tens digit of the original be x so original number was 10x+4 number reversed = 40+x 10x+4 = 40+x + 45 9x = 81 x = 9 the old was 94, the new one is 49 Their sum = 143
*March 17, 2016*

**math**

Then the sides of the similar triangles must be 3x, 5x, and 7x 3x+5x+7x=75 15x=75 x=5 the shortest side is 15 or perimeter of original = 15 perimeter of new one = 75 so the sides have been increased by a factor of 5 new triangle is 15, 25, and 35
*March 17, 2016*

**math**

110 km/13.5 L = 110(0.621371) miles/(13.5(0.264172)) = appr 19.2 mpg btw, in the metric world, gas consumption is not expressed as km/L, but rather as L/100 km So the above would be 12.27 L/100 km (which is quite poor, I use 8.9 L/100 km on my car)
*March 17, 2016*

**Calculus Related Rates**

let that distance be x angle be Ø by the cosine law: x^2 = 25+64-2(5)(8)cosØ x^2 = 89 - 80cosØ 2x dx/dt = 80sinØ dØ/dt dx/dt = 40sinØ dØ/dt / x *** when Ø = π/4 or 45° x^2 = 89-80sin π/4 = 32.431... x = 5....
*March 17, 2016*

**Calculus Related Rates**

did you make your sketch ? let the height be h ft let the angle be Ø tanØ = h/70 h = 70tanØ dh/dt = 70sec^2 Ø dØ/dt *** when t = 5 sec, h = 75 ft tanØ = 75/70 = 15/14 sketching a right-angled triangle with that data, shows a hypotenuse...
*March 17, 2016*

**Calculus Related Rates**

V = (4/3)πr^3 dV/dt = 4πr^2 dr/dt given: dV/dt = 6, r=3 6 = 4π (9) dr/dt dr/dt = 6/(36π) inches/min = 1/(6π) in/min
*March 17, 2016*

**Algebra**

width --- x length ---9x x(9x) = 81 x^2 = 9 x = 3 the pool is 3 ft by 27 ft. (I bet whoever swims in that pool is fantastic at flip-turns )
*March 17, 2016*

**Advance Math**

If I recall correctly: cosh(x) = cos(ix) or in your case cos(je) so cos^2 (ej) = (cosh(e))^2 (Haven't done this in over 60 years)
*March 17, 2016*

**math**

So perimeter of stamp is 2x + 2y and the perimeter of the envelope is 4x + 4y given: 2x+2y + 8x+8y = 50 10x+10y=50 x+y=5 Hence the perimeter of the stamp = 2x+2y = 2(x+y) =2(5) = 10 cm
*March 17, 2016*

**Math**

in 1 hour it gains s seconds in 1 day it gains 24s seconds in d days it gains 24sd seconds in d days it gains 24sd/60 minutes in d days it gains 2sd/5 minutes
*March 17, 2016*

**Math**

your answer contains the factor x^16, but it was supposed to be x^8 so you would need (x^2)^4 to be in your expression. term(5) = C(12,4) (x^2)^4 (3)^8 = 495 x^8 (6561) = 3247695 x^8 verification: look for the term containing x^8 in http://www.wolframalpha.com/input/?i=expand...
*March 17, 2016*

**Precal/Math**

LS = (1/cos^2 A)(sin^2 A) = tan^2 A RS = (tan^2 A + 1 - 1) = tan^2 A = LS
*March 16, 2016*

**Math/Precal**

remember that tan^2 x + 1 = sec^2 x also that cos 2x = 2cos^2 x - 1 RS = (2 - (1 + tan^2 x) )/sec^2 x = (2 - sec^2 x)/sec^2 x = 2/sec^2x - 1 = 2cos^2 x - 1 = cos 2x = LS
*March 16, 2016*

**Geometry**

midpoint for (-4,1) and (-2,-3) = (-3,-1) slope through the two given points = -4/2 = -2 so slope of perpendicular = 1/2 equation of right-bisector: y+1 = (1/2)(x+3) 2y + 2= x+3 x- 2y = -1 ** midpoint of (-4,1) and (5,-2) is (1/2 , -1/2) slope of chord = -3/9 = -1/3 so slope ...
*March 16, 2016*

**maths**

cos(60° + 45°) = cos60cos45 - sin60sin45 = (1/2)(√2/2) - (√3/2)(√2/2) = ( √2 - √6)/4
*March 16, 2016*

**Math**

what is 1.5(8) ? what is 1.5(14) ? What is an em ?
*March 16, 2016*

**maths**

Ohh my !!!
*March 16, 2016*

**maths**

the statement is false log(1+2+3) ≠ log 1 + log 2 + log 3 we know log(1x2x3)=log 1 + log 2 + log 3 but not the way you wrote it if it were true, then 1x2x3 = 1+2+3 , good luck on that one!
*March 16, 2016*

**algebra**

y+9=3/5(x+7) y = (3/5)x + 21/5 - 9 y = (3/5)x - 24/5
*March 16, 2016*

**function:maths**

Assuming you mean f(x)=2/(x-1) and g(x)=(2x-2)/(3x+3) then g(x) = 2(x-1)/(3(x+1)) f+g = 2/(x-1) + (2/3)(x-1)/(x+1) = ( 6(x+1) + 2(x-1)(x-1))/(3(x^2 - 1)) = (6x + 6 + 2x^2 - 4x + 2)/(3(x^2 - 1) = (2/3)(x^2 + x + 4)/(x^2 - 1) you do fg, which means you just multiply them domain ...
*March 16, 2016*

**GEOMETRY/ALGEBRA**

rate of filling = 40 cm^3/4 min = 10 cm^3/min
*March 16, 2016*

**Maths**

Strange wording, since all squares and rectangles are "equiangular". Did you mean , find the side of the square which has the same area as the rectangle? then s^2 = 20(5) = 100 s = 10 cm
*March 16, 2016*

**Data Management**

number of ways to choose: 6W,9B 5W,10B Number of ways to arrange 6W,9B = (15!/6!9!) = 5005 number of ways to arrange 5W,10B = 15!/(5!10!) = 3003 total number of ways = 5005+3003 = 8008
*March 16, 2016*

**Math**

L's equation is correct 2x=13 x = 6.5 twice the number is 13 What is 9 less than that ?
*March 16, 2016*

**Maths**

Tom's amount --- x Bob's amount --- y case 1: tom gives 20 to bob Tom now has x+20 Bob has y-20 x+20 = y-20 x - y = -40 case2: Bob gives tom 22 Bob has y-22 Tom has x + 22 x+22 = 2(y-22) x+22 = 2y - 44 x - 2y = -66 subtract these equations: y = 26 sub back in x - 26...
*March 16, 2016*

**mathematics-simultaneous eqn**

from x+y+z=2 (x+y+z)^2= 4 x^2 + y^2 + z^2 + 2xy + 2xz + 2yz = 4 using #2: 14 + 2(xy+xz+yz) = 4 xy+xz+yz= -5 (x+y+z)^3 = 8 x^3 + y^3 + z^3 + 3x^2y + 3x^2z + 3y^2x + 3y^2z + 3z^2x + 3z^2y + 6xyz = 8 20 + 3x^2(y + z) + 3y^2(x + z) + 3z^2(x + y) + 6xyz = 8 starting to get messy ...
*March 16, 2016*

**maths**

25x^2+4y^2-50x-16y-59=0 25(x^2 - 50x + ...) + 4(y^2 - 4y + ..) = 59 25(x^2 - 2x + 1) + 4(y^2 - 4y + 4) = 59 + 25 + 16 25(x-1)^2 + 4(y-2)^2 = 100 (x-1)^2 /4 + (y-2)^2 /25 = 1 Now just use all the little formulas you must have to state the properties of this nice ellipse
*March 16, 2016*

**maths help!!!**

(1-x)^n = 1 + n(-x) + n(n-1)/2! (-x)^2 + n(n-1)(n-2)/3! (-x)^3 + ... = 1-6x+ax^2+bx^3 so -nx = -6x n = 6 n(n-1)/2! (-x)^2 = ax^2 6(5)/2=a a = 15 n(n-1)(n-2)/3! (-x)^3 = bx^3 6(5)(4)/6 = -b b = -20
*March 16, 2016*

**Math**

Shorter version: side costing $20/m --- x side costing $5/m -----y 20(2x) + 5(2y) = 1000 4x+y=100 y=100-4x area = xy = x(100-4x) = 100x - 4x^2 This can be represented by a parabola, whose vertex will yield your answer. the x of the vertex is -100/-8 = 12.5 then y = 100 - 4(12....
*March 16, 2016*

**sequence help!!!!! plz steve,reiny,damon,bob...anyone!!!!**

I looked at that yesterday, but I could not find an obvious pattern Found this: 5 = 2^2 + 1^2 13 = 3^2 + 2^2 but then it broke apart on the next one Took differences and got: 5 13 -- 8 32 -- 19 -- 11 69 -- 37 -- 18 -- 7 129 - 60 -- 23 -- 5 -- 2 221 - 92 -- 32 -- 9 -- 4 not ...
*March 16, 2016*

**Math**

smaller number --- x larger number ---- (x+10) sum of their squares = (x+10) + x^2 = x^2 + 20x + 100 + x^2 = 2x^2 + 20x + 100 this is a parabola opening upwards so it has a minimum. That minimum happens at the vertex. The x of the vertex is -20/4 = -5 so one number is -5, the ...
*March 16, 2016*

**Geometry Honors**

The new perpendicualar must be parallel to CD Let MN be that perpendicular with M on AC and N on AC I agree that AD = 28, so we can set up a ratio: MN/AM = 96/28 = 24/7 MN = 24AM/7 Area of triangle AMN = (1/2)(2304) = 1152 = (1/2)(AM)(MN) (1/2)(AM)(24AM/7) = 1152 AM^2 = 672 am...
*March 15, 2016*

**Algebra**

smaller --- x larger ---- x+9 4(x+9) = 10x solve for x
*March 15, 2016*

**Math/Precal**

I have no idea what "the coordinates of p(a+b)" is supposed to be. We could find such values as sin(a+b) or tan(a+b). something like sinb = 3/5 has an infinite number of points associated with its end-points. They could be P(4,3) or Q(8,6) or R(40,30) etc Please ...
*March 15, 2016*

**Math/Precal**

recall that sin(A+B) = sinAcosB + cosAsinB you have the same angle pair showing up in the two terms in that pattern, so (sin pi/8)(cos pi/24) + (cos pi/8)(sin pi/24) = sin(pi/8 + pi/24) = sin(pi/6) = 1/2 ----> you should know pi/6 =30 degrees and sin(30) = 1/2
*March 15, 2016*

**Maths**

Julie --- j her father --- 4j mother ---- 4j+7 more information is needed to find their actual ages
*March 15, 2016*

**Precal**

To prove an identity to be true you have to simplify the LS and the RS independently until you have LS = RS The first thing I usually try is to take any angle and sub it into the equation to see if it is valid. Here I took A=20, B=30 LS= cot(50) = .839... RS = cot20cot30-1/(...
*March 15, 2016*

**Geometry**

#4 how can you have 2 different scale factors yielding the same figure ?? 9(2/3)--->6 9(2/3)--->6 12(2/3)-->8 So .....? #5 x/(x+4) = 3/5 5x = 3x+12 2x=12 x = 6
*March 15, 2016*

**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*