Friday

May 6, 2016
Total # Posts: 34,531

**Math**

ahhh, found this in the Related Questions below "In three more years,Miguel's grandfather will be six times as old as Miguel was last year.When Miguel's present age is added to his grandfather's present age, the total is 68.How old is each one now? " ...
*March 18, 2016*

**Math**

The wording of your question makes no sense. "In three more years, Miguel's grandfather will be six times as old as Miguel was." --- was when ?? " Last year, when Miguel's present age is added to his grandfather's present age the total is 68."...
*March 18, 2016*

**Math**

I did this back here http://www.jiskha.com/display.cgi?id=1458255127 all you had to do is multiply my .68 by 18,000
*March 17, 2016*

**Math**

I rotation = 70π cm 25(70π) cm per 10 sec 6(25)(70π) cm per minute 60(6)(25)(70π)/100 m per hour 6300π m/hr 6300π/1000 km/h = appr 19.8 km/h
*March 17, 2016*

**Pre-Calc**

carry on ... x^2(x-1) = 48 x^3 - x^2 - 48 = 0 some quick mental gymnastic will show that x = 4 works. (64-16 = 48) so it factors into (x-4)(x^2 +3x+12) = 0 some trivial calculations will show the remaining quadratic has no real roots, so x = 4 the original was 4 by 4 by 4
*March 17, 2016*

**Calculus**

Make a sketch. Let the points on the parabola be P(x,y) and Q(x,-y) Area = 2y(3-x) = 2y(3-(1/4)y^2) = 6y - (1/2)y^2 d(Area)/dy = 6 - y = 0 for a max of Area y = 6 the max area is 6(6) - (1/2)(36) = 18 square units check my arithmetic
*March 17, 2016*

**calc**

You are correct to the end, but keep it as 2x^3 + x - 3 = 0 try a few numbers, to get "nice" answers, (the thing would factor) , x has to be ±1,±3, ±3/2 sure enough x = 1 works so (x-1) is a factor. Either do long division or use something like ...
*March 17, 2016*

**math**

Make a sketch of a right-angled triangle the angle of elevation is 13°, the hypotenuse is 300, you want the horizontal (the adjacent) so clearly, the cosine comes to mind cos13° = x/300 x = 300cos13 = 292.311 , which is B
*March 17, 2016*

**math**

Why do you think that ? Wrong guess, btw
*March 17, 2016*

**math**

correct
*March 17, 2016*

**math**

Now Thomas! What do you think? This one is even easier than the other ones you posted. How about showing us your work?
*March 17, 2016*

**math**

and ..... ???
*March 17, 2016*

**math**

What part of my answer to your almost identical question about 2 hours ago did you no like ? Could you not make that minuscule adjustment? http://www.jiskha.com/display.cgi?id=1458258526
*March 17, 2016*

**math**

prob(yellow, then red) = (2/9)(4/8) = 1/9 follow the same kind of reasoning for your second part
*March 17, 2016*

**math**

is the first marble picked returned before the second is picked ? - very important.
*March 17, 2016*

**Trigonometry**

x= Arc cos 1/2 <-----> cosx = 1/2 then x = π/3 check: on your calculator, (set at degrees) 2ndF cos .5 = to get 60° which is π/3 radians
*March 17, 2016*

**Trigonometry**

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

**math**

prob(red) = 5/12 prob(blue) = 3/12 etc for the other colours. then multiply each prob by 60 you can check your answer by making sure all the prob's above add up to 1 and the sum in the colour distribution is 60
*March 17, 2016*

**math**

prob(red, then green) = (7/20)(5/20) = 35/400 = 7/80
*March 17, 2016*

**Math**

let the radius be r ft 2πr = 157 r = 157/(2π) = 24.987.. ft area = πr^2 = 1961.5 ft^2 time = 1961.5/400 = appr 4.9 hours
*March 17, 2016*

**Math**

You appear to have a typo You must have meant: $20.25 per hour for overtime. normal weekly wage = 40(3.50) = 140 leaving 661.50-140 or $521.50 for overtime. overtime hours = 521.5/20.25 = 25.75 So he worked 40 + 25.75 or 65.75 hours. strange question: very huge gap between ...
*March 17, 2016*

**Geometry**

None of them are if you meant it the way you typed your first equation. If you meant: (e+f)/(a-d) = b/a, then a(e+f) = b(a-d) would be the equivalent
*March 17, 2016*

**Math-Measure's & area**

#1 correct #2 if the 3 keeps repeating, then .12333... is a rational number equal to 37/300
*March 17, 2016*

**Math**

remaining value after 1 year = .8 or 80% remaining value after 2 years = .8(.85) = .68 or 68%
*March 17, 2016*

**Math**

Have you come across this identity and its variations? cos 2A = cos^2 A - sin^2 A = 1 - 2sin^2 A = 2cos^2 A - 1 so .... cos^2 4-sin^2 4 = 1 - sin^2 4 - sin^2 4 = 1 - 2sin^2 4 = cos 8 1 - 2sin^2 3 = cos 6
*March 17, 2016*

**mathematics**

Place the circle in such a way that the midpoint of CA becomes the origin, and B lies on the y-axis by Pythagoras BO = 12 cm so we have points A(5,0), B(0,12) and C(-5,0) let the centre be (0,k) and the radius r equation: x^2 + (y-k)^2 = r^2 using (5,0) --> 25 + k^2 = r^2 ...
*March 17, 2016*

**math**

number of T/F questions --- x number of multiple choice --- 20-x 3x + 11(20-x) = 100 3x + 220 - 11x = 100 -8x = -120 x = 15 15 T/F questions and 5 multiple choices
*March 17, 2016*

**mathematics**

draw lines from the centre to the midpoints of the two chords. You will have two right-angled triangles, one with sides x, 5, 13 the other with sides, y, 12, 13 Use Pythagoras to find x=12, and y=5 so the distance between them is 12+5 or 17 cm
*March 17, 2016*

**Precal/math**

(2sin pi/12)(cos pi/12) = 2tan (π/12) by definition
*March 17, 2016*

**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*