Wednesday
October 1, 2014

Posts by Reiny


Total # Posts: 27,219

Trig
One of the ID's you should know is cot^ Ø + 1= csc^ Ø then: csc^2x -(√3+1)cotx+(√3-1)=0 cot^2 x + 1 - (√3+1)cotx + (√3-1)=0 cot^2 x - (√3+1) cotx + √3 = 0 cot^2 x - cotx - √3cotx + √3=0 cotx(cotx - 1) - √3...
May 9, 2014

Math (Calculus)
y-intercept is 6 y = 6-3x 3x = -y + 6 x = -y/3 + 2 x^2= y^2/9 - 4y/3 + 4 vol = π[integral] y^2/9 - 4y/3 + 4 dy from 0 to 6 = π[ y^3/27 - 2y^2/3 + 4y] from 0 to 6 = π( 8 - 24 + 24 - (0) ) = 8π better check my arithmetic
May 8, 2014

math
costA= 3.00 + .5(x-1) costB = 2.00 + .7(x-1) 2 + .7(x-1) - 3 - .5(x-1) = 15 .7x - .5x - .7 + .5 -1 = 15 .2x = 16.2 x = 81 check: if x = 81 costA = 3+.5(80) = 43 costB = 2 + .7(80) = 58 , which is $15 more
May 8, 2014

Math
right side = (2x-6)/(x+6) + 1 = (2x-6)/(x+6) + (x+6)/(x+6) now we have a common denominator = (2x-6 + x+6)/(x-6 = 3x/(x+6) as you required.
May 8, 2014

trigonometry
sinØ = 28/32 = .875 Ø = appr 61°
May 8, 2014

math
area of picture = 16(24) = 384 in^2 area of picture and frame = 18(26) = 468 area of frame = 468-384 = 84 picture/frame = 384/84 = appr 4.57 I guess they rounded that off to 5 times.
May 8, 2014

math
Abbe's rate = 1/15 lawns/min Ben's rate = 1/20 lawns/min Carls' rate = 1/30 min combined rate = 1/15 + 1/20 + 1/ 30 = 3/20 lawn/min but they mowed for 5 minutes so time x rate = 5(3/20) = 15/20 or 3/4 They mowed 3/4 of the lawn
May 8, 2014

trig
(tanx - 1)(tanx - 2) = 0 tanx = 1 or tanx = 2 for tanx = 1, x = π/4 or π+π/4 = 5π/4 for tanx = 2 x = appr 1.107 or π+1.107 = 4.249
May 8, 2014

Math Help!
term 4 = C(6,3)(2x)^3 (3y)^3 = 20(8x^3)(27y^3 = 4320x^3 y^3 2. hard to show synthetic division here and make the numbers line up properly, in effect you are dividing by x+1 I got -8 3. I noticed that 4096 is a perfect square x^6 + 128x^3 + 4096 = 0 (x^3 + 64)^2 = 0 x^3 + 64 = ...
May 8, 2014

Algebra
2W+2(2W+40) = 470 2W + 4W + 80 = 470 6W = 390 W= 65 Then L = 2(65) + 40 = 170 Your equation made no sense. How did you plan to work in the 470 ? Where did it say that the perimeter was 80, which is what your equation claimed.
May 7, 2014

Math
number of nickels ---- x number of quarters --- 36-x value of nickels = 5x value of quarters = 25(36-x) "The value of his nickels is 1/15 of the value of his quarters" ---> 5x = (1/15)(25)(36-x) times 5 25x = 25(36-x) 75x = 900 - 25x 100x = 900 x = 9 so 9 nickels ...
May 7, 2014

Math
Case 1: AB = AC--> angle B=70° Case 2: AC = BC --> angle B = 40° Case 3: BC = AB --> angle B = 100°
May 7, 2014

Math 12
yes C(n,r) = nCr its an easier notation to type
May 7, 2014

Math 12
a) prob = C(13,3) * C(13,2)/C(52,5) = 286*78/2598960 = 286/33320 = 11/99960 b) prob = C(4,2) * C(4,2)* C(44,1)/C(52,5) = 6*6*44/2598960 = 3*11/54145 = 33/54145
May 7, 2014

Math 12
Prob(Andy, Briana, Cam) = (1/100)(1/99)(1/98) = 1/970200 prob (those 3 win) = 1/C(100,3) = 1/161700
May 7, 2014

geometry
I will assume that we paint only the lateral surface of each cone SA = πrs, where s is the slant height http://math.about.com/od/formulas/ss/surfaceareavol_2.htm so s^2 = 7^2 + 24^2 s = √625 = 25 So each cone has a lateral SA of π(7)(25) or 175π inches^2 ...
May 7, 2014

Algebra
Your definition of L is opposite of what it should be L = 2W - 3 now use your definition of perimeter to solve Perimeter of a rectange = 2W + 2L 2W + 2(2W-3) = 24 2W + 4W - 6 = 24 6W = 30 W = 5 then L = 2(5)-3 = 7 Your rectangle is 5 by 7 check: P = 2(5)( + 2(7) = 10+14 = 24
May 7, 2014

Maths
are we solving? if so, from the first ----> y = 5-x plug into the 2nd: 2x^2 - x - 13 =5-x 2x^2 = 18 x^2 = 9 x = ± 3 then if x = 3, y = 2 if x = -3 , y = 8
May 7, 2014

calculus
check out this video https://www.youtube.com/watch?v=01LzAU__J-0
May 7, 2014

precalculus sem 1
wherever you see an x, replace it with 1, and evaluate
May 7, 2014

math
done here http://www.jiskha.com/display.cgi?id=1399500377
May 7, 2014

Help w/ Math PLS
let the 3 terms be defined in the usual way of a a GS a, ar, and ar^2 so we have to show that (a^2 + a^2 r^2 + a^2 r^4) / (a + ar + ar^2) divides evenly that is, our denominator should cancel (a^2 + a^2 r^2 + a^2 r^4) / (a + ar + ar^2) = a^2(1 + r^2 + r^4)/( a(1+r + r^2) ) = a...
May 7, 2014

Math
stated rule: add 4, then subtract 1 effective rule: add 3 5, 8, 11, 14, 17, .... what do you think ?
May 7, 2014

Math
let N = a e^(kt) when t=1, N = 10 10 = a e^k also 17 = a e^2k divide them 17/10 = a e^2k/(a e^k) 1.7 = e^k k = ln 1.7 so N = a e((ln1.7)t) when t=1 , N=10 10 = a e^(ln1.7) 10 = 1.7 a a = 10/1.7 N = (10/1.7) e^(ln1.7(t)) which does not produce the third point So I plotted the ...
May 7, 2014

Math
(2/5) x = 4 times 5 2x = 20 x = 10
May 7, 2014

math
Use your definitions and evaluate e.g. 11C5 (not your question) = 11! / (5!6!) = 462
May 7, 2014

math
difference in days = 365.2425 - 365.24220 = .0003 How many times does .0003 divide into 8 ?
May 7, 2014

math
let the number of bags needed be n so 2n ÷ (5/6) must be a whole number = 2n(6/5) = 12n/5 The smallest value of n is 5 So he should buy 5 of the 2 lbs bags Check: if n=5 , he will have 10 lbs. number of smaller bags he can fill = 10 ÷ (5/6) = 10(6/5) = 12 --->...
May 7, 2014

math
I think Ms Sue took the sum of the two temperatures instead of their difference 41 - (-70) = 41 + 70 = 111 degrees
May 7, 2014

Algebra
Just like in one of your previous posts let the shorter piece be x m then the longer piece is 53-x "The short piece is 19 meters shorter then the long piece" or the difference between the longer and the shorter is 19 ---> (53-x) - x = 19 53-x-x = 19 -2x = 19-53 -...
May 7, 2014

math
6(a-b) - 5(2a + 4b) = 6a - 6b - 10a - 20b = -4a - 26b
May 7, 2014

Algebra
no, 2x is not correct think in terms of actual numbers ... suppose you had a 3 foot board and cut off 1 foot left over = 3-1 = 2 suppose you had a 3 foot board and cut off x ft. left over = 3-x
May 7, 2014

Algebra
close, but "difference" implies subtraction so "eight times the difference of a number and 3 --- 8(x-3) so ... 8(x-3) = 6(x+1)
May 7, 2014

Algebra
one seventh of a number ---> (1/7)x now add 4 ----- (1/7)x + 4 or 4 + 1/7x you are correct
May 7, 2014

Math
since the sine is negative in III or IV and the cotangent is negative in II or IV, and we are told that neither is in IV a must be in III and b must be in II sin a = -7/25, a in III cos a = -24/25 cot b = -8/15 , b in II tan b = -15/8 sinb = 15/17 cosb = -8/17 cos(a+b) = cosa ...
May 6, 2014

pre algebra
no, it is not linear, it is a quadratic
May 6, 2014

algebra
They ran for the same length of time let the time be t seconds then distance covered by faster runner = 8t distance covered by slower runner = 2t so 8t - 2t = 99 6t = 99 t = 99/6 or 16.5 seconds
May 6, 2014

Trigonometry
1. sinØcotØ = sinØ(cosØ/sinØ) = cosØ 2. ( 1 - sin^2Ø)/cosØ = cos^2 Ø/cosØ = cosØ
May 6, 2014

Math
mmmh, with no restriction? that would be just 10!
May 6, 2014

FInite Math
transition matrix: .8 .2 .7 .3 so [.5 .5 ] x .8 .2 .7 .3 = [.75 .25) next day after 2 days: [.75 .25] x .8 .2 .7 .3 = [.775 .225]
May 6, 2014

algebra
I bet you meant: (2b - 2)/(2b^2 - 8) = 2(b-1)/(2(b^2- 4)) = (b-1)/((b+2)(b-2)) domain, any real value of b, b ≠ ± 2 range: any real value see: graph of y = (x-1)/(x^2 - 4) http://www.wolframalpha.com/input/?i=y+%3D+%28x-1%29%2F%28x%5E2+-+4%29+from+-5+to+5 notice ...
May 6, 2014

Math
probability - wise, the easiest pair to pick would be the yellow pair. best case scenario: you have picked 1 yellow, 9 reds and 6 blue. So you definitely have a pair of blues , a pair of reds but no pair of yellows. you have picked 16 balls. So the 17st pick would have to be a...
May 4, 2014

Math
a) is correct b) you want to round off 11.6725 to the nearest 10 watts, so that would be 10 watts. (11.6725 is closer to 10 than to 20) c) no it would be 1.16725 x 10^1 (you moved the decimal only 1 place)
May 4, 2014

MATH ✿╣Check╠✿
no, if you want to arrange all the letters of the word EQUATION, that would be 8! or 8P8 Your answer would be from: How many 4 letter arrangements can you form from the word EQUATION ?
May 4, 2014

MATH ✿╣Check╠✿
correct if you are picking one cookie from the bag.
May 4, 2014

math
the x's increase by 2 and for each of those increases of 2 , the y's increase by 4 Yup, you are right.
May 3, 2014

Pre Calculus
You typed an equation, not an inequality If you meant 2^x > x^2 , follow my method in your previous post, or let's look at 2^x = x^2 obviously one trivial solution is x = 2 what about x = 4 ? LS = 2^4 = 16 RS = 4^2 = 16 , yup! the graph shows another solution to the ...
May 3, 2014

oops - Pre Calculus
mis-stated the result of the graph notice that the sin(x) is always below y = √x so there is no solution to sin(x) > √x
May 3, 2014

Pre Calculus
sin x > √x we can say immediately that x≥0 , since we can't take the square root of a negative. so I would graph y = sinx and y = √x and look at the region where the sinx is above the √x http://www.wolframalpha.com/input/?i=y+%3D+sin%28x%29+%2C+y...
May 3, 2014

Math word problem
(x-4)(104/x+6) = 126 104 + 6x - 416/x -24 - 126 = 0 6x - 46 - 416/x = 0 times x 6x^2 - 23x - 416 = 0 3x^2 - 11x - 208 = 0 (x - 13)(3x + 16) = 0 x = 13 or x = -16/3, but x can't be negative, so x = 13
May 3, 2014

math
Did you notice for each increase of 2 in the x's , there is a decrease of 3 in the y's so quick way: slope = -3/2
May 3, 2014

Math
yes, that is what I had stated in my reply.
May 3, 2014

Math
a) the vertical asymptote equation is x = -1 , you had just -1 , but it asked for the equation. your horizontal asymptote is correct g(x) = x-6 is a straight line, with no asymptotes. b), yes , find the roots ... 3/(x+1) = x-6 x^2 -5x - 6 = 3 x^2 - 5x - 9 = 0 does not factor, ...
May 3, 2014

Math
Really no work needed here. Notice for both pairs, the y values are the same. So in both cases we would have a horizontal line, and the y-intercept would simply be the y value of the 2 points So for the first pair, the y-intercept is 4 for the second pair, the y-intercept is 6...
May 3, 2014

MATH(markup and markdown )
last line should say: Show me what you did for the above problem and I will look at your solution.
May 2, 2014

MATH(markup and markdown )
Ok FIZZ, enough is enough! I count over 20 questions of a similar type in the last few days, which have been answered for you. Not once have you shown any of your steps , or indicated where your difficulties lie. Show me what you did for the above problem and I will let you ...
May 2, 2014

math
3. x( 1 - 1.005^-360)/.005 = 543408.48 x = 3258.01 per month
May 2, 2014

math
1. At a rate of inflation of 2%, the value of today's 300,00 in 30 years is 300,000(1.02)^30 = $ 543,408.48 2. (3000(1.08^5 - 1)/.08) (1.08)^25 + x(1.08^25 - 1)/.08 = 543408.48 I will leave all that button-pushing up to you to solve for x
May 2, 2014

algebra
easy way to tell, just sub it in Left Side= 21E-7 = 21(.33) - 7 = .07 ≠ 0 so , no, you are wrong 21E - 7 = 0 21E = 7 E = 7/21 = 1/3 as the accurate answer. 1/3 = .3333.... , not .33
May 2, 2014

Calc 2
tried integration by parts on the 2nd, but it got messy, probably made an error Gave up and used Wolfram with results of log(2(√(x^2-4) + x)) - x/√(x^2-4) + C http://integrals.wolfram.com/index.jsp?expr=%28x%5E2%29%2F%28%28x%5E2+-+4%29%5E%283%2F2%29%29&random=false...
May 2, 2014

Calc 2
a) (sin^2)(3x) using cos 2A = 1 - 2sin^2 A cos 6x = 1 - 2sin^2 (3x) sin^2 3x = 1/2 - (1/2) cos 6x so integral sin^2 3x = (1/2)x - (1/12)sin(6x) Take it from there, I will let you do the substitution and evaluation
May 2, 2014

math
width --- w length --- w+3 w(w+3) = 88 which of your choices matches this after simplifying ?
May 2, 2014

Alg
from the hyperbola: x^2 = y^2 + 4 sub into the ellipse 2(y^2+4) + 3y^2 = 48 5y^2 = 40 y^2 = 8 y = ±√8 or ± 2√2 the x^2 = y^2 + 4 = 8+4 = 12 x = ±√12 or ± 2√3 ---> your 4 points enter as instructed. http://www.wolframalpha....
May 2, 2014

Calculus
It looks like your profit function is correct as p(x) = (-1/2) e^(-x^2) + c 15000 = (-1/2)(e^-1) + c 15000 = -1/(2e) + c c = 15000.184 so p(x) = (-1/2) e^(-x^2) + 15000.184 strange result. Since the exponential term always has a negative value and approaches zero the profit is...
May 2, 2014

link to Wolfram - math
http://www.wolframalpha.com/input/?i=solve+9500+%3D+227.5%28+1+-+%281%2Bx%29%5E-60%29%2Fx look at second line output, the negative rates are to be ignored.
May 2, 2014

math
9500 = 227.5( 1 - (1+r)^-60)/r where r is the monthly rate a very tough equation to solve .... Wolfram says r = .01275 as the monthly rate so annual rate compounded monthly = .153 or 15.3 % equivalent annual rate: 1+i = 1.01275^12 = 1.164 or 16.4%
May 2, 2014

math
3000 r^6 = 1250 r^6 = .416666... r = .416666...^(1/6) r = .864 so the annual rate of depreciation was 1 - .864 = .136 or 13.6% you did not list your choices.
May 2, 2014

maths
done, look back at your previous post
May 2, 2014

MATH(markup and markdown )
I will assume cost price is 40 less 10%,5% so actual cost price = 40(.9)(.95) = 34.20 let list price be x .4x = 34.20(1.25) x = 34.20(1.25)/.4 = 106.875 I interpreted "25% of the cost" as the actual cost, not the stated RM40 less 10%, 5% " check: 60% discount on...
May 2, 2014

maths
6 red 9 blue total is 15 prob(red) = 6/15 = 2/5 prob(blue) = 9/15 = 3/5 I assume that is a typo and should say "red or blue" prob(red or blue) = 1
May 2, 2014

Math
Side C --- x side A --- 2x side B ----1.5x side D ---- x+4 x + 2x + 1.5x + x+4 = 81 5.5x = 77 x = 14 plug in 14 into each of my definitions to find the lengths
May 2, 2014

MATH(markup and markdown )
no, if 1.4x = 30 then 1.4x/1.4 = 30/1.4 x = 30/1.4 = RM 21.43 check: take 40 % of 21.43 and add it to 21.43 or what is 1.4(21.43) ?
May 2, 2014

MATH(markup and markdown )
so you want 1.4x = 30 x = ....
May 2, 2014

math
markdown = .2(40) = 8.00 new price = 40-8 = 32.00 or what is .8(40) ?
May 2, 2014

MATH(markup and markdown )
I respectfully disagree, the answers are not the same If I take a take a 20% markdown on your $300 I get $60, which would leave a new price of $240, not $250
May 2, 2014

MATH(markup and markdown )
old price --- x .8x = 250 x = 250/.8 = 312.50 check: markdown on 312.50 = .2(312.50) = 62.50 new price = 312.50 - 62.50 = 250
May 2, 2014

algebra
number of pages ---- n n/4 + 2n/3 + 5 = n times 12 3n + 8n + 60 = 12n n = 60 check 1/4 of 60 = 15 2/3 of 60 = 40 15 + 60 + 5 = 60 , check!
May 2, 2014

Math 2
what is .4(.20) ?
May 2, 2014

Function Maths 11
for Ø if Ø is in I , that is your related angle if Ø is in II, related angle = 180-Ø if Ø is in III, related angle = Ø - 180 if Ø is in IV, related angle = 360-Ø so tan 110 = - tan(180-110) = -tan 70° sin 350 = -sin(...
May 1, 2014

math
4πr^2 = 2058 r^2 = 2058/(4π) r = √ ... = appr 12.8 cm
May 1, 2014

Algebra
rate of new = 72/2 copies/min rate of old = 72/x copies/min combined rate = 72/2 + 72/x = (72x + 144)/(2x) copies per min 72/(72x+144)/(2x)) = 1.5 72(2x)/(72x+144) = 1.5 144x = 108x + 216 36x = 216 x = 6 rate of old machine = 72/6 or 12 copies/minute
May 1, 2014

last question - math
if m , m+3, m^2 + 3 are in geometric progression, then (m+3)/m = (m^2 + 3)/(m+3) m^3 + 3m = m^2 + 6m + 9 m^3 - m^2 - 3m - 9 = 0 normally cubics are hard to solve, but I tried factors of 9 and found m = 3 to work so the numbers are 3, 6, 12 so each number is double its previous...
May 1, 2014

math
For a quadratic function , the turning point would be the vertex of the parabola. since your equation is written in vertex form f(x) = (x+3)^2 - 16 the vertex is (-3,-16) , which would be your turning point. If your quadratic is written in the form f(x) = ax^2 + bx + c there ...
May 1, 2014

math
difference of squares = (1 + 4(1-y) )(1- 4(1-y)) = (1 + 4 - 4y)(1-4 + 4y) = (5-4y)(4y - 3)
May 1, 2014

Alg
are we looking at two inequalities: y^2/4 - x^2.25 ≤ 1 y ≥ 2x/3 + 4 ?? What about them? are we graphing their intersection? if so, ... x^2/4 - y^2/25 = 1 is a hyperbola so x^2/4 - y^2/25 ≤ 1 would be the region "inside" the hyperbola see: http://www...
May 1, 2014

math
dimes --- x nickels ---2x value equation: 10x + 5(2x) = 70 20x=70 x = 3.5 NO WAY!! , can't have 3.5 dimes this question is bogus, no solution. Check your typing, or the problem is silly.
April 30, 2014

College Algebra and Trigonometry
looking back at your earlier attempts at typing this question I am going to guess you meant x(t)= 2 cos (5πt+π/3) you want this to be 1.5 2cos (5πt + π/3) = 1.5 cos (5πt + π/3) = 1.5/2 = 3/4 I know cos( .722734..) = 3/4 so 5πt + π/3 = ....
April 30, 2014

math
(-1 , √3) ----> (-1 , -√3) after reflection in the x-axis new point is in III, tanØ = -√3/-1 = 240° in III magnitude = √(1^2 + √3^2) = √4 = 2 point in polar coordinates: (2cos240°, 2sin240°) or (2cos 4π/3, 2sin 4&#...
April 30, 2014

math
number with 1 Lavender = 1 x C(13,4) = 715 number with 1 yellow = C(5,1) x C(9,4) = 630 exclude yellow and lavender = C(8,5) = 56 number as described = 715+630-56 = 1289
April 30, 2014

Calculus
I answered the same type of question back in 2009 http://www.jiskha.com/display.cgi?id=1245646756 Just change the numbers.
April 30, 2014

Math
a) prob winning = 1/C(49,6) = 1/13,983,816 b) 10,000/13,983,816 c) x/13,983,816 = 1/2 , solve for x d) prob not winning = 13,983,815/13,983,816 odds against winning = 13,983,815 : 13,983,816 e) expected value = 1,000,000(prob of a) )
April 30, 2014

math
100% + 5% salestax = 1 + .05 = 1.05 to increase something by 5% , just multiply it by 1.05
April 30, 2014

math
.85(1.05)x = 30 x=30/(.85(1.05)) = $33.61
April 30, 2014

Algebra
same type of question here http://www.jiskha.com/display.cgi?id=1397438547 just change the numbers.
April 30, 2014

Algebra 1/2
prob(3 or 5) = 2/8 = 1/4 prob(2) = 1/8 prob(3or5 then 2) = (1/4)(1/8) = 1/32
April 30, 2014

Algebra 1/2
not enough information, what kind of spinner? how many positions are possible ?
April 30, 2014

math
let the time taken by the eastbound plane until they meet be t hrs let the time taken by the westbound plane until they meet be t-1/2 hrs distance covered by the easbound plane = 700t distance covered by the westbound plane = 750(t - 1/2) 700t + 750(t-1/2) = 3420 700t + 750t...
April 30, 2014

math
What about it ? Are we integrating ? if so ... ∫sin(πx+1)dx = (-1/π)cos(πx+1) + C
April 30, 2014

Algebra 2
I answered this as part of the reply to your log question http://www.jiskha.com/display.cgi?id=1398883636 about the third line down ....
April 30, 2014

Probability
doubles --- 6 of them sumof 8 --- 26,35,44,53 62 total = 10 (we have to count 44 only once) prob = 10/36 = 5/18
April 30, 2014

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