Wednesday
July 30, 2014

Posts by Reiny


Total # Posts: 26,911

MATH
two identities you should have in your bag of ID's is csc^2 Ø -1 = cot^2 Ø , and sec^2 Ø - 1 = tan^2 Ø LS = left side = csc^2 Ø - 1 + sec^2 Ø - 1 = csc^2Ø + sec^2 Ø - 2 = 1/sin^2 Ø + 1/cos^2 Ø - 2 = (cos...

Maths
For this one the 30-60-90° and the 45-45-90° right-angled triangles are your friend. from those you should know cos30°= √3/2 sin30° = 1/2 cos60° = 1/2 sin60° = √3/2 sin45° = √2/2 cos45°=√2/2 cos15 = cos(45-30)° = cos4...

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...

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

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

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.

trigonometry
sinØ = 28/32 = .875 Ø = appr 61°

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.

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

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

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 = ...

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.

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 ...

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

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

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

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

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 3...

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

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

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

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

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

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...

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

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 p...

Math
(2/5) x = 4 times 5 2x = 20 x = 10

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

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

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 --->...

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

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 -2...

math
6(a-b) - 5(2a + 4b) = 6a - 6b - 10a - 20b = -4a - 26b

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

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)

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

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 ...

pre algebra
no, it is not linear, it is a quadratic

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

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

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

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]

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 t...

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...

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)

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 ?

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

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.

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 lef...

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

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...

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

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

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

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, ...

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...

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

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 lo...

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

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

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

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...

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

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

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....

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...

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.

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%

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.

maths
done, look back at your previous post

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...

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

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

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) ?

MATH(markup and markdown )
so you want 1.4x = 30 x = ....

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

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

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

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!

Math 2
what is .4(.20) ?

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(3...

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

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

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...

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 i...

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

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...

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.

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 = .7...

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&#...

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

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

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) )

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

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

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

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

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

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 -...

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

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