Thursday
August 28, 2014

Posts by Reiny


Total # Posts: 26,986

Geometry
Yup, I was so totally distracted by the second part of his post, that I completely missed and ignored the actual question. Another senior moment!!! but... wasn't that a great explanation?? reminds me of my teaching years, when during an exam a student replied to a certain ...
August 6, 2014

Geometry
both are variations of the relation cos 2A = cos^2 A - sin^2 A or cos 2A = 2 cos^2 A - 1 or cos 2A = 1 - 2sin^2 A We use this to either find trig ratios of double an angle or 1/2 an angle e.g. if we know sin 50° , I could now find ratios for 25° or 100° e.g. you ...
August 6, 2014

math
x^2 + 12x + 4 = 0 does not factor, so I will complete the square, easiest way for this one. x^2 + 12x + 36 = -4+36 (x+6)^2 = 32 x+6 = ±√32 = ±4√2 x = -6 ± 4√2
August 6, 2014

math
Must be mathemagics
August 6, 2014

math
Your post makes no sense to me How is this related to the binomial theorem? 32 ÷ 7 = 4 with a remainder of 4
August 6, 2014

college algebra
number of gallons of the 30% stuff --- x .3x + .14(60) = .2(60+x) 30x + 14(60) = 20(60+x) 30x + 840 = 1200 +20x 10x = 360 x = 36
August 5, 2014

geometry
I interpreted " two of its interior angles are 127 degrees and 135 degrees, and the remaining interior angles are 173 degrees each. " the wrong then. so I should have had 130 + 130 + 130 + 127 + 135 + 173(n-5) = 180(n-2) which gives 652 + 173n - 865 = 180n - 360 n = ...
August 5, 2014

geometry
But Damon's answer contradicts the sum of the inside angles property if n = 21 the sum of the interior angles = 127+135 + 19(173) =3949 which must be a multiple of 180
August 5, 2014

geometry
sum of interior angles of an n-gon = 180(n-2) 127 + 135 + 173(n-2) = 180(n-2) 262 + 173n - 346 = 180n - 360 276 = 7n n = 39.4.. , but n must be a whole number so the question is bogus. Check your wording and typing
August 5, 2014

Math
done
August 5, 2014

algebra
huh? I see no x in a^2 + b^2 = 2014
August 5, 2014

Math
If you want that sum to be less than 7000 x + x+2 + x+4 + x+6 + x+8 = 7000 5x = 6980 x = 1396 so 1396 + 1398 + 1400 + 1402 + 1404 = 7000 but you want the sum to be < 7000 so 1394 + ... 1402 = 6990 if you want the numbers to be less than 7000 6998 + 6996 + 6994 + 6992 + 6990...
August 5, 2014

Math
You have to give more information. It is not arithmetic , nor is it geometric I can make it a quadratic .... term(n) = 3n^2 - 10n + 10 and the three terms you gave me will match. so term(15) = 3(225) - 10(15) + 10 = 535 or a cubic or ....
August 5, 2014

advance algebra
ditto what Steve said in your previous post on this.
August 5, 2014

math test review
I do not understand your m<C=2m<b,m<A=6m<B. In our general usage of angles and sides, a capital letter usually stands for an angle, a small letter stands for the length of the opposite side to that angle, there also seems to be a missing equal sign. If you are ...
August 4, 2014

math
what is 2 more than p ? isn't it p+2 ? area = p(p+2) p^2 + 2p = 8 p^2 + 2p - 8 = 0 which factors to (p+4)(p-2) = 0 p = -4, which is not admissable or p = 2 so the table is 2 m by 4 m check: what is 2 x 4 ?
August 4, 2014

math
done! patience!, you posted the same question only about 8 minutes before this one.
August 4, 2014

math
I assume you meant: If b is a positive integer < 200 a/b = 2/9 9a = 2b a = 2b/9 So b must be a multiple of 9 to have a as an integer the smallest value of b is 9 and the largest value of b is 198 so we have: 9 18 27 .... 180 189 198 to find out how many terms are in this ...
August 4, 2014

MA 1310
rewrite it in the more general form as y = (1/4) cos 3(x + 7/3) compared to y = a cos k(Ø + p) the amplitude is 1/4 the period is 2π/3 the phase shift is 7/3 to the left for your equation in the original form a common mistake would be to state that the sphase shift...
August 4, 2014

geometry
should be 19 cm^3 x/19 = 3^3/2^3 x/19 = 27/8 8x = 513 x = 64.125 cm^3
August 4, 2014

math 4
Value of loan = $300 let the monthly rate be i then 34*(1- (1+i)^-10)/i = 300 hard to solve this type of equation but I have some methods and it gave me i = appr .02343 so the annual rate compounded monthly is 28.1 % check: 34(1 - 1.02343^-10)/.02343 = = 299.9988 , not bad I ...
August 4, 2014

Ha ha - algebra
got me, ( I think 15/60 = 1/3 in non-metric) anyway... Thank you Steve
August 4, 2014

algebra
15/60 or 1/3 chose an hour lunch with no breaks for in 500 people we would expect 1/3 of 500 or 167 to choose the above option
August 4, 2014

math
let Jim's distance be x miles then John's distance is 3-x miles Jim's time = x/4 John's time = (3-x)/5 when they meet, they will both have paddled the same time so ... x/4 = (3-x)/5 5x = 12 - 4x 9x = 12 x = 12/9 miles so Jim's time = (12/9) /4 = 1/3 hour or...
August 4, 2014

geometry
radius of base = 3√3 height^2 + (3√3)^2 = (6√3)^2 find the height, now you have everything needed in the formula for the volume of a cone
August 4, 2014

math
follow the same steps I just showed you in your previous post. Let me know what you got
August 4, 2014

math
let f(x) = 4x^2 - 3x - 8 and use the Remainder Theorem, f(a) = 4a^2 - 3a - 8 = 2 4a^2 - 3a - 10 = 0 (a-2)(4a + 5) = 0 a = 2 or a = -5/4 the 2nd is done the same way: f(3) = 81 + 9m + 3n + 5 = 128 9m + 3n = 42 3m + n = 14 f(-1) = -3 - m - n + 5 = 4 -m-n = 2 add them: 2m = 16 m...
August 4, 2014

Math
balance owing = 22000-5500 = 16500 We don't know the rate, but if the monthly rate is i , then 16500 = 406.69(1 - (1+i)^-48)/i Did some alternate numerical calculations and found n = .007083333.. which makes it an annual rate of 8.5% compounded monthly So balance owing ...
August 3, 2014

algebra
Number(Ipad or Car) = number(Ipad) + number(carss) - number(Ipads and cars) = 65 + 45 - 15 = 95 which leaves 5 unaccounted for from the 100 so .... a) 95 owned either Ipad or car b) 5 owned neither or you could get the same result by constructing a Venn diagram
August 3, 2014

math
In your text or in your notes you should find the following relationship between (r,Ø) and (x,y) x = rcosØ -->cosØ = x/r y = rsinØ --> sinØ = y/r r^2 = x^2 + y^2 and tanØ = y/x so in r = 1/(sinØ + cosØ) r(sinØ...
August 3, 2014

Proof: math
amount at end of t = 2 = 500(1.015)^8 = 563.25 add additional payment of 273.14 = 836.39 amount of that after 3 more years = 836.39(1.015)^12 =999.9986.. not bad, eh?
August 2, 2014

oops - math
I miscounted on my "time line" should have been: 500(1.015)^20 + x(1.015)^12 = 1000 ... x = $273.14
August 2, 2014

math
500(1.015)^20 + x(1.015)^16 = 1000 1.268985... = 326.572.. x = $257.35
August 2, 2014

maths
height/100 = tan 60° height = ..... ?
August 2, 2014

math
for Tia: distance = 29-75(t-1) for Kathie: distance = ..... (what do you think)
August 2, 2014

Math
log (10A)/(7B^2) = log(10A) - log(7B^2) = lof 10 + logA - (log7 + 2logB) = 1 + logA - log7 - 2logB
August 2, 2014

college math
From a Physics point of view, this question is really flawed. First of all, it should be -16t^ (gravity works downwards, not upwards) Secondly, at the moment of jettison of the tanks, the tank still has an upwards velocity, so there should be term in t after the -16t^2 anyway...
August 2, 2014

College math
-In45=3.80666249 this statement is false should say: In45=3.80666249 then e^3.80666249 = 45 again, I will assume you meant: Log sub.B T^5=W , I read that as: logB T^5 = W by definition: T^5 = B^W
August 2, 2014

College math
yes it is 1: y = x^3 - 27 ----> x = y^3 - 27 2: x = y^3 - 27 y^3 = -x - 27 y = (-x - 27)^(1/3)
August 2, 2014

College math
follow same steps as I showed you
August 2, 2014

College math
Inverse: step 1. switch the x and y variables y = 5/(x+3) -----> x = 5/(y+3) step 2: solve this new equation for y xy + 3x = 5 xy = 5-3x y = (5-3x)/x I was able to find the inverse, but both the original and the inverse have restrictions, so it is not a one-to-one function ...
August 2, 2014

Greg/kat - calculus
Please stick to one name done in previous post
August 2, 2014

Precalculus
All you want is the linear equation passing through the two points (0,20000) and (5,10000) slope = (10000-20000)/(5-0) = -2000 So if we let t be the time V = -2000t + 20000 the rate of depreciation is $2000/year
August 2, 2014

Math
well! , just set 164t - 16t^2 = 400 -16t^2 + 164t - 400 = 0 4t^2 - 41t + 100 = 0 (t-16)(4t - 10) = 0 t = 10 or t = 10/4 or 2.5 seconds So it will reach that height first at 2.5 seconds, (and again after 10 seconds on its way back down)
August 2, 2014

Math
As you can see from the many similar questions, this poorly worded question comes up again and again with just a change of numbers We must assume that the width is the same for the kitchen and the dining room let the dining room be x by x area of dining room = x^2 area of ...
August 2, 2014

math
let the mileage be m 65 + .7m < 114 + 0m .7m < 49 m < 70 so for m> 70 miles, company A is cheaper check: if m = 50 company A charges $114 company B charges 65 + .7(50) = 100 if m = 71 company A charges $114 company B charges 65+.7(71) = $114.70 . which is more btw...
August 2, 2014

math
assuming neither of the two given sides is the hypotenuse, make a sketch to see that tan B = 960/490 angle B = appr 63°
August 2, 2014

math
if GP , then (2x-4)/4 = (21x+2)/64 128x-256 = 84x + 8 44x = 264 x = 6 check: 4, 8, ... , 64, 128 YUP, common ratio of 2
July 30, 2014

typo - Math
In all that lengthy typing, I just noticed an error. When I stated De Moivre's Theorem, it should of course have been: then z^n = r^n( cos (nØ) + i sin (nØ) ) I did use it correctly in my work.
July 30, 2014

Math
How did I get 171.9 ? from tanØ = -1/7 I know that the tangent is negative in II and IV by the CAST rule but <-7,1> ends up in quadrant II so I took tan-inverse of 1/7 to get 8.13° , had it been in quad I in quad II we have 180-8.13 = appr 171.9
July 30, 2014

Math
Jane, you will have to be able to change a complex number from standard form to trig form in general a + bi = (√(a^2 + b^2) [cosØ + isinØ] where Ø is such that tanØ = b/a e.g. change 3 + 4i to trig form = √(3^2+4^2) (cosØ + isin&...
July 30, 2014

Math
2nd: let z = 0 + 8i = 8( 0 + i) we need 0+i in the form cosØ + isinØ we need Ø, so that cosØ = 0 and sinØ = 1 mmmmhhh, Ø = 90 comes to mind so z = 8(cos90° + isin90°) so the cube root, and using De Moivre's z^(1/3) = 8^(1/3...
July 30, 2014

Math
For the 2nd: are you familiar with D' Moivres Theorem? let me know, and I will go through with this one 3rd: make a sketch and use the cosine law 35.1^2 = 32.7^2 + 20.2^2 - 2(20.2)(32.7)cosØ ( see if you get Ø = 100.7° )
July 30, 2014

Math
I assume <2,1> and <-1,1) are vectors then -2A + 3B = <-4,-2) + <-3,3) = <-7,1> magnitude = √(49+1) = √50 or 5√2 direction: let the angle be Ø tanØ = -1/7 Ø = appr 171.9° with the x-axis
July 30, 2014

Alegbra1
You will have to use brackets to show where the square root ends I suspect it is f(x) = √(-x+2) - 1 , or else why not combine the +2-1 ? then the number under the square root must not be negative, that is ... -x + 2 ≥ 0 -x ≥ -2 x ≤ 2
July 30, 2014

math
job/rate = time --> rate = job/time let the fathers rate = job/x let the son's rate be job/2x combined rate =job/x + job/2x = 3job/(2x) combined time = job ÷(3job/2x) = job (2x/3job) = 2x/3 but 2x/3 = 6 2x = 18 x = 9 It would take 9 hrs for the father to work ...
July 30, 2014

math
Making the first 3 as small as possible, they would have to be 1, 2, and 3 let the 4th be x and the 5th be y then 1+2+3+x+y = 90 x+y = 84 remember, y has to be the largest we want x to be as large as possible but still be less than y x y .. .. .. .. 40 44 41 43 42 42 --->...
July 30, 2014

maths
2(x^2 - 4x + ... ) + 2(y^2 + (5/2)y + ... ) = -10 2(x^2 - 4x + 4 ) + 2(y^2 + (5/2)y + 25/16 ) = -10+ 8 + 25/8 2(x-2)^2 + 2(y+ 5/4)^2 = 9/8 (x-2)^2 + (y+5/4)^2 =9/4
July 30, 2014

Algebra
let's work on the bottom 6^(2n+1) = 3^(2n+1)* 2^(2n+1) = 3^n * 3^(n+1) * 2^n * 2^(n+1) = 3^n * 2^n * 6^(n+1) now the 3^n would cancel the 3^n on top, leaving you with 1/(2^n * 6^(n+1) )
July 30, 2014

Math; Alegbra
If r = 3 Volume of sphere = (4/3)π r^3 = 36π volume of a cone = (1/3)π r^2 h =3π h 3π h = 36π 3h = 36 h = 12
July 30, 2014

mathematics
H = (1/28)L L = 28H L + H = 116 28H + H = 116 29H = 116 H = 4 then L = 112 one number is 16 let the other number be 4x then : 16 = 4*4 4x = 4*x 16x = 112 x = 7 and 4x= 28 The other number is 28 check: 16 = 2*2*2*2 28=2*2*7 LCF = 2*2 = 4 HCM = 2*2*2*2*7 = 112 is 4 equal to 1/28...
July 30, 2014

early morning oops - Math
But .... if the second derivative is linear, the original function must be a cubic. y'' = 6x y' = 3x^2 + a at x = 1 we have y = 5 - 3x is a tangent, so y' = -3 when x=1 -3 = 3(1) + a a = -6 y' = 3x^2 - 6 then y = x^3 - 6x + b at (1,2) 2 = (1)^3 - 6(1) + b b...
July 29, 2014

Math
ARrgghhh, really? Matrices for such a simple system? ok .... we need the inverse of 4 -2 7 1 I will assume you know how to find the inverse of a 2by2 I get 1/18 2/18 -7/18 4/18 now if we multiply that by 4 -2 7 1 we get 1 0 0 1 on left and the column matrix 33/18 3/18 on the ...
July 29, 2014

Algebra
from 3x = 4y ---> x = 4y/3 from 12y = 5z --> z = 12y/5 so z/x = (12y/5) / (4y/3) = (12y/5)(3/4y) = 9/5
July 29, 2014

Calculus
direction of the given line is (1,1) so if Ø is the angle it makes with the x-axis, then tanØ = 1/1 Ø = 45° so a line which makes an angle of 60° with the given line would have an angle of (45°+60°) or 105° or -15° now tan 105°...
July 29, 2014

Calculus
A normal to r is (0,1,1) cross (-1,0 3) or (3, -1, 1) , (I assume you know how to find a cross-product) So the plane must look like, 3x - y + z = c , where c is a constant from the line (x-3)/2 = (y+1)/-3 , z=1 the point (3,-1 ,1) must lie on the line, so it must also lie in ...
July 29, 2014

Math
Ok, starting to make sense now So I will assume you are given: sin(alpha+beta)=(sin alpha)(cos beta)+(cos alpha)(sin beta) and cos(alpha+beta)=(sis alpha)(cos beta)+(sin alpha)(sin beta) I will use A and B for easier typing You must also know that 1. sin(-A) = -sinA 2. cos(-A...
July 29, 2014

Math
That's not what you said originally, look at your post. So which identity are we deriving ?
July 29, 2014

Math
so you want us to use the identity: sin(A - B) = sinAcosB - cosAsinB to prove sin(A - B) = sinAcosB - cosAsinB ? mmmhhh? did you mean sin(A+B) ??
July 29, 2014

Math
let the time taken since 10:00 am till they meet be t hrs at 10:00 am , train will have already gone 130 miles when they meet, they both will have traveled the same distance, so ... 90t = 130 + 65t 25t = 130 t = 5.2 hrs or 5 hrs and 12 minutes that would put the time at 10:00...
July 29, 2014

Math
1 ---> 4 = 2^2 2 ---> 8 = 2^3 3 ---> 16 = 2^4 4 ---> 32 = 2^5 mmmhhh, look at the exponent of 2 and compare it to your input value. isn't it always one greater ? so .....
July 29, 2014

error - Algebra
Whoahh there Sheenybeany if the inequality is y/6 > 10 then y > 60 Why did you reverse the inequality sign? It is reversed only if you multiply or divide by a negative. Since we simply multiplied by 6, it stays the same. Since y > 60 is not one of the choices, we ...
July 29, 2014

geometry
mmmh, I guess that explains why he is still a bachelor
July 29, 2014

arggg! ... Geometry
How did I possible see 4 of equal sides ? but... my algebra worked out sooo nice! Reminds me of the classic StarTrek episode where Cpt Picard is tortured by the Kardashians and sees 4 lights. https://www.youtube.com/watch?v=moX3z2RJAV8
July 29, 2014

Geometry
let the sides be a, b, and c We know: 4a +4b + 4c = 24 ----> a+b+c = 6 and 4ab + 4ac + 4bc = 22 2ab + 2ac + 2bc = 11 The length of the diagonal is √(a^2 + b^2 + c^2) by algebra, we know (a+b+c)^2 = a^2 + b^2 + c^2 + 2ab + 2ac + 2bc subbing in 6^2 = a^2 + b^2 + c^2 +11...
July 29, 2014

math
The way it is written, I must agree with Steve
July 29, 2014

Math
start at (-3,-4) and mark it since slope = rise/run = 2/3 the rise is 2 and the run is 3 so from the point (-3,-4) go to the right 3 (run of 3), then go up 2 (rise of 2) mark this new point, join with a line and you are done Easy, eh ??
July 28, 2014

Math
you replaced the y with -8 , but not the x with -3 Why not? -8 = -2(-3) + b -8 = 6 + b -14 = b so y = -2x - 14
July 28, 2014

Math
done below
July 28, 2014

math
1. can you think of two numbers which when multiplies yields -36 and when added is 16 how about 18 and -2 ???? (x+18)(x-2) 2. can you think of two numbers which when multiplies yields 9 and when added is -10 how about -1 and -9 (x^2 - 1)(x^2 - 9) now we have the difference of ...
July 28, 2014

Math
Natalie, use the method I showed you in your previous post slope of lines parallel to 8x + 4y = 7 = -8/7 slope of perpendicular lines = + 7/8
July 28, 2014

math
profit = 12.50 - 8.00 = 4.5 percentage profit = 4.5/8 = .5625 or 56.25%
July 28, 2014

math
I will assume from your poorly worded question that the sale price is $10.00 so if the original is $x .8x = 10 x = 10/8 = 12.50 Now, do you need the profit percentage before or after the sale? You decide
July 28, 2014

Math
use a two step process 1. take all terms except the y term to the right side 4x + 5y = 3 ----> 5y = -4x + 3 2. divide each term by the coefficient of the y term 5y = -4x + 3 y = (-4/5)x + 3/5 now you have it in the form y = mx + b, where m is the slope, so the slope is -4/5
July 28, 2014

Calculus
if F' (x) = -7x then F(x) = -(7/2)x^2 + c but F(0) = 1 1 = 0(-7/2) + c c = 1 F(x) = (-7/2)x^2 + 1
July 28, 2014

math
Johnny, looks like "homework dumping to me" How about showing us what steps you have taken in these problems or indicate where your difficulties lie.
July 28, 2014

math
I suppose we could do this .... 12V = 3W V = 3W/12 = W/4 then 2W - 8V = 2W - 8(W/4) = 2W - 2W = 0
July 28, 2014

Geometry
I agree with Bob My understanding of a trifoil has been this: http://www.google.com/imgres?imgurl=http://upload.wikimedia.org/wikipedia/commons/9/9d/Trefoil-Architectural.png&imgrefurl=http://commons.wikimedia.org/wiki/File:Trefoil-Architectural.png&h=218&w=231&tbnid=...
July 28, 2014

general math
This is how I would have expected my students to write up the solution to this equation 5x − 2 = 2x + 7 5x - 2x = 7 + 2 3x = 9 x = 3
July 28, 2014

Maths (differentiation)
the way you typed it, Wolfram read it as http://www.wolframalpha.com/input/?i=+Y+%3D+1%2FSinX%5E2 and y = (sinx)^-2 dy/dx = -2(sinx)^-3 (cosx) = -2cotx /sin^2 x or = -2cotx csc^2 x if you meant: y = 1/ sin(x^2) then y = sin(x^2)^-1 dy/dx = -1sin(x^2)^-2 cos(x^2) (2x) = -2x cot...
July 28, 2014

Math
number of tests before the last one ---> x total marks at that point = 84x then (84x + 100)/(x+1) = 86 86x + 86 = 84x + 100 2x = 14 x = 7 So there were 8 tests, including his perfect test at the end.
July 27, 2014

Maths
Kelvin --- x Ken ----- x+6 average of Kelvin and Ken = (2x+6)/2 = x+3 David = (x+3) + 6 = x+9 (x + x+6 + x+9)/3 = 42 3x + 15 = 126 3x = 111 x = 111/3 = 37 David is 37+9 = =46 check: Kelvin --> 37 Ken----> 43 David ---> 46 average of Kelvin and Ken = (37+43)/2 = 40 Is ...
July 27, 2014

math
number of girls = 3x number of boys = 4x (check: total is 7x) total weight of all children = 7x(36) = 252x total weight of all the girls = 3x(32) = 96x so the weight of all the boys = 252x-96x = 156x average weight of boys = 156x/(4x) = 39 kg
July 27, 2014

Maths
Did you make a sketch? If so, you can see that cosØ = 2/6 = 1/3 Ø = cos^-1 (1/3) = appr 70.5°
July 27, 2014

math
Let the salaries of A, B, and C be 2x, 3x, and 5x respectively. then 3x + 5x = 8000 8x=8000 x = 1000 A's is 2000 C's is 5000 we don't really have to find their actual salaries amount that C has more than A is 5x-2x = 3x Percentage of that of A = 3x/2x = 3/2 = 1.5 ...
July 27, 2014

math
breadth --- x length ---- 1.2x 2(x+1.2x) = 88 x+1.2x = 44 2.2x = 44 x = 20 area = x(1.2)x = 1.2(20^2) = 480 m^2
July 27, 2014

correction - calculus 2
∆x = (6-1)/3 = 5/3 , so ∆x/3 = 5/9 should be ∆x = (6-1)/10 = 5/3 , so ∆x/3 = 5/30 = 1/6 and the 5/3 in front of the big brackets should be 5/30 or 1/6
July 26, 2014

calculus 2
I assume that you know the formula .... in case you don't, here is the method http://www.mathwords.com/s/simpsons_rule.htm ∆x = (6-1)/3 = 5/3 , so ∆x/3 = 5/9 interval = (6-1)/10 = 1/2 then we have (5/9)[ f(1) + 4f(1.5) + 2f(2) + 4f(2.5) + 2f(3) + 4f(3.5) + 2f(4...
July 26, 2014

calculus 2
fix your equation first
July 26, 2014

math
since the function is linear, the slope must be constant for any pair so (12-a)/(1-0) = (b-12)/(2-1) 12-a = b-12 24 = a+b
July 26, 2014

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