Thursday
June 30, 2016

Posts by Reiny

Total # Posts: 35,111

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

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

  1. Pages:
  2. <<Prev
  3. 8
  4. 9
  5. 10
  6. 11
  7. 12
  8. 13
  9. 14
  10. 15
  11. 16
  12. 17
  13. 18
  14. 19
  15. 20
  16. 21
  17. 22
  18. Next>>