Thursday
November 27, 2014

Posts by Reiny


Total # Posts: 27,965

Math
I tried a slightly different approach I looked at the trapezoid, and drew two verticals upwards from the base, creating a rectangle of 25 by 50 cm and two right-angled triangles , each of height 50 and base 75/2 I drew a water line, of height h and width of r in each of the ...
May 12, 2014

Math
You don't have an equation, so "solving" is the wrong instruction. are you expanding 2a(a^2 + 4a) ? then... = 2a^3 + 8a^2
May 11, 2014

algebra
I don't know what h=−16t<E> 6<E>+s is supposed to say, but I know that h = -16t^2 is the relation between t seconds and the distance fallen in feet Since we just want to find the distance, let's use h = 16t^2 when t = 3 h = 16(9) = 144 feet If this is...
May 11, 2014

Math
slope for the first 2 points = (0-1)/(4-2) = -1/2 y = -1/2 x + b , but (2,1) lies on it 1 = -(1/2)(2) + b b = 2 y = -(1/2)x + 2 check if third point is on it LS = -1 RS = (-1/2)(6) + 2 = -1 yes, all is good y = (-1/2)x + 2
May 11, 2014

Math
nothing to "solve", you don't have an equation. did you mean: evaluate 5(3^n) for n = 1,2,3, ... then you would get 5(3) , 5(9), 5(27), 5(81) .. = 15, 45, 135, 405, looks like that is what you are doing, if so, you are correct.
May 11, 2014

Math
First of all you have not defined x and y Secondly, 2(x+y) does not look like an area, it looks like the perimeter of the original rectangle. I will attempt it anyway: I drew a rectangle of length x and width y I then drew two lines, one parallel to the length, the other ...
May 11, 2014

MATHHH
case1: no defence in 1st row - we can choose any 6 of the 8 players = C(8,6) = 28 case2: 1 defence - four ways to choose the defenseman, choose 5 from the remaining 8 = 4 x C( 8,5) = = 224 Case3 : 2 defense = C(4,2) x C(8,4) = 420 total = 28+224+420 = 672 for choosing the 6 ...
May 11, 2014

Math
first do this: 4√6/√30 = 4/√5 now multiply top and bottom by √5 4/√5 * √5/√5 = 4√5/5
May 11, 2014

alegbra
first of all your "equation" makes no sense. LS = 25 RS = 1/25 25 ≠ 1/25 secondly , equations tend you have a variable in there somewhere, else it simply becomes a mathematical statement which is either true or false e.g. 2+3 = 4 --- false 1+1 = 2 ---- true ...
May 11, 2014

alegbra
amount = initial (.5)^(t/5730) .75 = 1 (.5)^(t/5730) log .75 = (t/5730) log .5 t/5730 = log .75/log .5 = .415... t = 2378.16 age is about 2400 years to the nearest century
May 11, 2014

math
The way the question stands, the "bottom" of the kite could be any length along the missing part of the diagonal. The angle at the shorter diagonal's end wasn't a right-angle ?
May 11, 2014

math
I think we are missing information Was there an angle given?
May 11, 2014

ALGEBRA
13.29 = 14.7 e^(.21a) .90408.. = e^(.21a) by rules of logs .21a = ln .90408... .21a = -.0100835.. a = -.48016 miles or - 2535 ft below sealevel !!!!!!! Wow, since the lowest point in North America, Death Valley is only about 260 ft below sea level, you city is a mystery. ... ...
May 11, 2014

Math
The surface area is proportional to the square of their radii (1.5r)^2/r^2 = x/36π 2.25/1 = x/36π x = 2.2(36π) = 81π
May 11, 2014

Math
From 1 to 10, isn't 6 the only number divisible by both 3 and 2 ? so prob = 1/10
May 11, 2014

math 7Probability help
mmmmmhhhhh possible sums of 2 dice is 2 , 3, 4, .... 11, 12, there are 11 of those the evens are: 2 4 6 8 10 12 or 6 of them so prob(even sum) = 6/11
May 10, 2014

Finance
I will do the last one, you do the other two in the same way c) PV = 5000(1.09)^-4 = $3542.13
May 10, 2014

Math
suppose we just look at 1/3^x (1/3^x - 2) = 15 3^-x(3^-x - 2) = 15 let 3^-x = a for easier typing then we have a(a-2) = 15 a^2 - 2a - 15 = 0 (a-5)(a+3) = 0 a = 5 or a = -3 3^-x = 5 log 3^-x = log5 -x log3 = log5 -x = log5/log3 x = -log5/log3 the other part of 3^-x = -3 has no ...
May 10, 2014

MATHHH
success if you draw 2 granolas or 2 fruits or 2 cheese prob(success) = (12/30)(12/30) + (10/30)(10/30) + (8/30)(8/30 = 4/25 + 1/9 + 16/225 = 77/225
May 10, 2014

maths
I will use a for alpha and b for beta then from the properties of zeros of a quadratic a+b = -1 ab = 1 then 1/a + 1/b = (b+a)/(ab) = -1/1 = -1 a^2 + b^2 = (a+b)^2 - 2ab = (-1)^2 - 2(1) = 1 - 2 = -1
May 10, 2014

Math
You could do the tedious task of expanding and then collecting powers of y^3. I let Wolfram do this for me http://www.wolframalpha.com/input/?i=expand+%281%2By%2Bky%5E2%29%5E7 It might be easier to read the expansion in reverse order 1 + 7y + 21y^2 + ... Notice that y^3 ...
May 10, 2014

Calculus Please Help
What a mess! http://integrals.wolfram.com/index.jsp?expr=sqrt%28100x%5E2-400%29%2Fx&random=false add C to the result
May 9, 2014

Alegbra
I suspect that this is a log question and your IN is actually ln ( the natural logarithm) so let's try: t = -62.5 ln(1 - N/80) or is it t = -62.5 ln( (1-N)/80) look at the first of the Related Questions below. It is the same question and Steve had his doubts about the same...
May 9, 2014

Math
1^2-(2-x)^2=2^2-x^2 1 - (4 - 4x + x^2) = 4 - x^2 1 - 4 + 4x - x^2 = 4 - x^2 4x = 7 x = 7/4 I don't understand why a textbook would write a term as 1^2 and 2^2 in an equation. That is just silly.
May 9, 2014

Algebra (proportions)
let the number of bears be x 50/x = 2/100 2x = 5000 x = 2500
May 9, 2014

Calculus
y = u^3 + u^2 - 1 dy/du = 3u^2 + 2u u = 1/(1-x) = (1-x)^-1 du/dx = -1(1-x)^-2 (-1) = 1/(1-x)^2 when x = 2, u = 1/(1-2) = -1 du/dx = 1/(1-2)^2 = +1 dy/du = 3(-1)^2 + 2(-1) = 1 dy/dx = dy/du * du/dx = 1(1) = 1 check my arithmetic, I made several arithmetic errors tonight.
May 9, 2014

Math
It didn't, n = 0 became a solution. Are you not familiar that if you have a factored form = 0, such as (A)(B) = 0 , then A = 0 or B = 0 ???
May 9, 2014

Math
I took out a common factor of n expand n(1-2n) What do you get ?
May 9, 2014

Math
n(1 - 2n) = 0 n = 0 or 1 - 2n = 0 n = 0 or n = 1/2
May 9, 2014

Calculus
y= sqrt[(3x^2+2)^3] = (3x^2 + 2)^(3/2) dy/dx = (3/2)(3x^2 + 2)^(1/2) (6x) = 9x(3x^2+2)^(1/2) or = 9√(3x^2 + 2) , which is valid for all values of x since (3x^2 + 2) is always positive.
May 9, 2014

oops - Algebra
looks like I can't do a simple subtraction of course 50-32 = 18 as MathMate had
May 9, 2014

Algebra
let amount of stronger solution to be used be x L amount of weaker solution is 50-x L .8x + .3(50-x) = .62(50) .8x + 15 - .3x =31 .5x = 16 x = 16/.5 = 32 needs 32 L of the stronger and 36 of the weaker solution.
May 9, 2014

math
.48x = .35 x = .35/.48 = appr .73
May 9, 2014

Algebra
original width --- x original length --- y xy= 280 y = 280/x new width --- x+1 new length --- y-5 new area = (x+1)(y-5) = (x+1)(280/x - 5) = 280 - 5x + 280/x - 5 = 275 - 5x + 280/x = (275x - 5x^2 + 280)/x = -5( x^2 - 55x - 56)/x perfect squares in the neighbourhood of 280 are ...
May 9, 2014

Algebra
1/12 = 1/30 + 1/r The LCD is 60r , so multiply each term by 60 r 60r(1/12) = 60r(1/30) + 60r(1/r) 5r = 2r + 60 3r = 60 r = 20 or 1/12 - 1/30 = 1/r 5/60 - 2/60 = 1/r 3/60 = 1/r 1/20 = 1/r cross-multiply r = 20
May 9, 2014

Algebra
rate of passenger boat --- x mph rate of freighter --------- x-6 mph 2592/(x-6) - 2592/x = 72 , assuming they travel 24 hours per day multiply each term by x(x-6) 2592x - 2592(x-6) = 72x(x-6) 2592x - 2592x + 15552 = 72x^2 - 432x 72x^2 - 432x - 15552 = 0 9x^2 - 54x - 1944= 0 (x...
May 9, 2014

Calculus
#1 ??? #2. dy/dx = x cos x^2 y = (1/2) sin x^2 + C when x=0, y = -3 -3 = (1/2) sin 0 + c -3 = 0 + c c = -3 so y = (1/2)sin x^2 - 3 when x = π y = (1/2) sin (π^2) - 3 = -3.215... #3. let N = a e^(kt) when t = 2 ---> 100 = a e^(2k) when t = 4 ---> 300 = a e^(4k) ...
May 9, 2014

Algebra
From the choices of answers, I think you typed the equation incorrectly Looks like it should be y = 3√(6x+42) since we cannot take the square root of negatives, 6x + 42 ≥ 0 6x ≥ -42 x ≥ -7 , which is your last choice.
May 9, 2014

Calculus
at its vertex. the x of the vertex is -b/(2a) = -40/-10 = 4 it will change direction at t = 4 seconds
May 9, 2014

Math
There can't be a^2 in your answer just looking at the a's you had a^2/a^3 which is 1/a once more: 54 a^2 b^3 ___________ 81 a^3 b^2 = (3/2) (1/a) (b) = (3/2)b/a or 3b/(2a)
May 9, 2014

Math
You are right, I should have had (3/2)b/a or 3b/(2a)
May 9, 2014

Math
54 a^2 b^3 ___________ 81 a^3 b^2 = (54/81)(a^2/a^3)(b^3/b^2) = (2/3) b/a or 2b/(3a) I don't see that choice, but that is your answer.
May 9, 2014

calculus-answer check
1st two are corrrect #3. my derivative was f ' (x) = 15(x+1)(x-1)^9 (x+2)^4 = 0 for x = -1, 1, -2 verify at Wolfram http://www.wolframalpha.com/input/?i=plot+y+%3D+%28x-1%29%5E10%28x%2B2%29%5E5
May 9, 2014

Algebra
t=√(d/16) so you want √(d/16) > 1 square both sides d/16 > 1 d > 16
May 9, 2014

Mathematics
sketch triangles in quad 2 and quad 1 for the given info if sin a = 3/5 in II cos a = -4/5 if sin b = 5/13 in I cos b = 12/13 sin(a+b) = sina cosb + cosa sinb = (3/5)(12/13) + (-4/5)(5/13) = (36 - 20)/65 = 16/65
May 9, 2014

math
(3/5)(84+72+96)/3 + (2/5)x ≥ 80 times 5 84+72+96 + 2x ≥ 400 2x ≥ 148 x ≥ 74 check: average of first 3 tests = 84 going towards final mark = (3/5)(84) = 50.4 final mark = 74 (2/5) of that is 29.6 final mark = 50.4 + 29.6 = 80
May 9, 2014

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...
May 9, 2014

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)° = ...
May 9, 2014

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

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