Thursday
April 17, 2014

Posts by Reiny


Total # Posts: 25,996

Calculus
You are doing fine so far. For these kind of max/min questions, look for "something" which will be either maximized or minimized. What ever that "something" is , you will need an equation that says "something" = ...... In this case I see, " ....

Geometry
original dimensions: l, w, h volume = lwh new length --- 2l/3 new width ---- w/10 new height = h/4 new volume + (2l/3)(h/4)(w/10) = 2 lwh/120 = lwh/60 or (1/60)lwh so , yes, it is B

math
4 2/3-1 1/6 = 14/3 - 7/6 = 28/6 - 7/6 = 21/6 = 7/2 or 3 1/2 Your second has the correct answer, but is nonsense in between 10 1/2-6 2/5 = 21/2 - 32/5 , ( LCD = 10 ) = 105/10 - 64/10 = 41/10 or 4 1/10 PS, I always consider an "improper" fraction in lowest terms a bett...

Algebra
I will assume you mean u/(1-u) + 1 = 1.5 u/(1-u) = 1/2 2u = 1-u 3u = 1 u =1/3

Math
so let the width be x , we know the length is 30 30x = 600 x = 20 so he needs 20+20+30 = 70 ft

Math help
(2x^2)( y^4)( 2x^2 y) + 2xy - 3x^5 y^3 = 4x^4 y^5 + 2xy - 3x^5 y^3 now what? are we factoring ?

math fractions and decimals
ummhh, give me a whole number greater than 4 and less than 8. Am I missing something here?

Math - Check My Answers
remember , the method I used only works if the exponents are the same, that is, a^m * b^m = (ab)^m

Math - Check My Answers
#1. 2^(1/3)*4^(1/3) = 8^(1/3) = 2 #2,3 , ok #4 same reasoning as #1 3((1/3) * 9^(1/3) = 27(1/3) = 3 #5, 6, 7, 8, 9 are all ok

Gowith Steve - Geometry
messed up my typing don't know why my 1/3 suddenly became 2/3

Geometry
let the base of the pyramid and the cube be x by x let the height of the pyramid be h then the height of the cube is 2h volume of pyramid = (1/3)x^2 h = (2/3)h x^2 volume of cube = x^2 (2h) = 2h x^2 ratio of cube : pyramid = 2hx^2 : (2/3hx^2 = 2: 2/3 = 6:2 = 3:1 so it is 3 tim...

Math
I don't understand your notation ^-^4 I will assume you meant: (5.7 x 10^3)^-4 = 5.7^-4 x 10^-12 = .000947.. x 10^-12 = 9.47 x 10^-16

Geometry
Did you mean positive whole numbers ? let the base be y and each of the equal sides be x To be a triangle, x > 2y or y < x/2 2x + y = 99 y = 99-2x y-intercept is 99, x-intercept is 49.5 so the x, or the base, can only be a number from 1 to 49 but to even have a triangle,...

Foundations Math 12
option A: semiannual rate --- i 15000(1+i)^10 = 20000 (1+i)^10 = 4/3 1+i = 1.029186 semi-annual rate is 2.9186 % annual rate is 5.8372 % option B, monthly rate is .004864.. 15000(1 + .004864..)^60 = 20069.53 so option B Since the annual rate is the same, clearly the more frequ...

Math
I am going to assume you meant to type f(x) = 2/(x+3) (g ° f)(x) = g(f(x)) = g( 2/(x+3)) = 1/( 2/(x+3)) = 1(x+3)/2 = (x+3)/2 If you meant it the way you typed it, follow the same steps and make the appropriate changes.

algebra
width ---- x length --- 2x - 3 x(2x-3) = 44 2x^2 - 3x - 44 = 0 (x + 4)(2x - 11) = 0 x = -4, which would make no sense or x = 11/2 or 5.5 yds the width is 5.5 yrds and the length is 8 yards check: 8(5.5) = 44

Foundations Math 12
PV( 1.00075)^48 ) = 225.50 PV = $217.53

Math
3 ln 2 – ln 4 + 5 ln x = ln 3 + 2 ln 5 ln 2^3 - ln4 + ln x^5 = ln 3 + ln 5^2 ln ((8x^5)/4) = ln (75) none of those match this left in log form, I had ln (8x^5/4) = ln 75 none of your choices match this.

Math
So the midpoint is (5, -1) and the equation would be (x-5)^2 + *y+1)^2 = r^2 plug in one of the end points of the diameter to get r^2 check your answer by plugging in the other point, you should get the same r^2 value

Calculus
let the width of the rectangle be 2x let the height of the rectangle by y then sides of triangle are 2x each and its height is √3 x area = (1/2((2x)(√3x) + 2xy = √3 x^2 + 2xy 200 = √3 x^2 + 2xy u = (200 - √3x^2)/(2x) Perimeter = P = 6x + 2y = 6x +...

Math
what is 2000( 1.06^40 - 1)/.07 ?

Math
You want the ratio of fantasies : total books = 50 : 85 = 10 : 17 you had that. end of problem

Arithemetic progression
term(18) = a+ 17d but d = 3 and term(18) = 549 a + 17(3) = 549 a = 498 term(56) = a + 55d = ..... sum(32) = (32/2)(2(498) + 31(2) ) = ...

Math
We know that (√x)^2 = x , by the very definition of √x suppose we take x(1/2) and square it (x^(1/2)^2 by the exponents rules this would be x( (1/2)(2) ) = x so (√x)^2 = (x^(1/2) )^2 then √x = x^(1/2) so x^(1/2) behaves the same way as √x by the s...

Math (I'm really confused). Please help.
So the sides must be the same .... 9x - 14 = 7x 2x =14 x = 7 ( I am confused that this confused you)

Math PLZ help
sides of a 30-60-90 triangle are in the ratio of 1 : √3 : 2 so x : ? : 18 = 1 : √3 : 2 x/1 = 18/2 x = 9

ijhs
let original number be 10x + y then the number reversed is 10y + x difference= 10x+y - (10y+x) = 9x - 9y but 9x - 9y= 36 x - y = 4 since x and y must both be integers between 1 and 9 that little equation tells me that the difference between the digits is 4 possible (x,y) are (...

math
Huhh?

Math.G.P
arithmetic mean of 1st and 3d = (x-2 + x+6)/2 = (2x + 4)/2 = x+2 let the 2nd be y then y/(x-2) = (x+6)/y y^2 = (x-2)(x-6) y = ± √((x-2)(x+6)) mean:2nd = 5:3 (x+2)/√((x-2)(x+6)) = 5/3 square both sides and expand (x^2 + 4x + 4)/(x^2 + 4x - 12) = 25/9 25x^2 + ...

Math 2
number of feet = 8(2.5) = 20 number of yds = 20/3 or 6 yards and 8 inches

Math
-48x(7x^2 - 6) ...|336 288 4 |84 72 4 | 21 18 3 | 7 6 The GCF of 336 and 288 = 4x4x3 = 48

Maths
present value of remaining balance = 600( 1 - 1.00583333^-36)/.00583333 = $19,431.88 you are paying an extra $1000 leaving a present value balance of $18,431.88 so ... 600( 1 - 1.00583333^-n)/.005833333 = 18431.88 1 - 1.005833333^-n = .179198811 1.00583333^-n = .820801188 log ...

algebra
Looking at all the "Related Questions" below, you must have a typo. Most say "Alex spent twice as much as Terry" let Terry's amount be x let Nick's amount be y let Alex' amount be 865-x-y after the spending: Terry has (3/5)x = 3x/5 Nick has y-40...

Algebra
you will find that the question contained in http://www.jiskha.com/display.cgi?id=1305681090 has the same setup as yours, just change the numbers and follow my method.

math
number of paperclips ---- x reds ---- (1/6)x blue ---- (5/12)x sofar: x/6 + 5x/12 = (7/12)x remainders ---- x - 7x/12 = 5x/12 so (2/5)(5x/12) = 10 10x/60 = 10 x/6 = 10 x = 60 reds = 60/6 = 10 blues= 5(60)/12 = 25 So there are 15 more blues than reds check: reds and blues = 35 ...

Algebra
using y = mx + b -4 = (4/5)(7) + b -4 - 28/5 = b b = -48/5 y = (4/5)x - 48/5

German help - Reiny
correct

Maths
last term is a + (n-1)d = 37a 36a = 49(n-1) 36a = 49n - 49 n = (36a+49)/49 or (36/49)a + 1 but n must be an integer, so a must be a multiple of 49 if a=49 , n = 37 if a = 98 , n = 73 if a = 147 , n = 109 etc (n increases by 36) check my second example, a = 98 , n = 73 terms wo...

geometry
V = πr^2 h h = 335/(π r^2) SA = 2π r^2 + 2πrh = 2πr^2 + 2πr(335/(πr^2) = 2πr^2 + 670/r d(SA)/dr = 4πr - 670/r^2 = 0 for a min of SA 4πr = 670/r^2 4πr^3 = 670 r = (670/(4π))^(1/3) = 3.763757606.. subbing back into h h ...

maths
Did you mean: a grocery man bought 300 apples ... ? We need the cost price to establish the profit.

German Help please
Just noticed that your opening phrase in #5 is a mix of English and German. It should have been something like this: Die Schwester meines Vetters ist (if the cousin was male) or Die Schwester meiner Kusine ist (if the cousin was female)

German Help please
All correct except #3 I think you have a typo, since #3 is the same as #4 According to you choses answer of "meine Geschwister" , I will guess that it was: mein Bruder und meine Schwester.

Algebra - Rational Exponents
Depends what you mean by raising a power to a power e.g. (3^2)^3 = (3^2)(3^2)(3^2) = (9)(9)(9) = 729 or = 3^6 = 729 if the two exponents are at the same "horizontal level" then you multiply the two or more exponents (a^x)^y = a^(xy) do not confuse that with (a^x)(a^y...

pre cal
I agree. What about it?

Math
What is 1/3 of 1/5 ? isn't that just 1/15 ??

Algebra
start with y = mx + b y = (4/5)x + b plug in the point ... -1 = (4/5)(3) + b -1 = 12/5 + b -5 = 12 + 5b ---- I don't like fractions 5b = -17 b = -17/5 y = (4/5)x - 17/5 easier way: y+1 = (4/5)(x-3) 5y + 5 = 4x - 12 4x - 5y = 17 mold this equation into any form you wish, on...

math
original price --- x (1/2)x - 6 = 88 x/2 = 94 x = 188

Maths
I am not familiar with a "balloon payment" since I am not from the US, but I will take a stab at the math. Amount owing after 30 years = 300000(1.07)^30 - 23500( 1.07^30 - 1)/.07 = $ 63,848.80 Is this the balloon payment? It is appr 3 times the annual payment of 23,5...

Intermediate Algebra
or y = (9/5)x + 4

Intermediate Algebra
The slope of the given line is -5/9 so the slope of the new line must be +9/5 and the new equation will look like 9x- 5y= c plug in the given point (0,4) 0 - 20 = c new equation: 9x - 5y = -20

Math
Using the same form of your given line, and since the slope is the same , m = 2 y-7 = 2(x-5) or y = 2x - 10 + 7 y = 2x- 3

math
What is 400(3) + 500(-2) ?

Calculus I
when x = 3 9+y^2 = 25 y^2 = 16 y = ±4 2x dx/dt + 2y dy/dt = 0 dy/dt = -x dx/dt/y = -3(-8)/±4 = ± 6

Geometry
40 cm : 18 mm = 40 cm : 1.8 cm = 40 : 1.8 = 400 : 18 = 200 : 9

Maths
Pay( 1.08^18 -1)/.08 = 160000 pay = $ 4272.34

math
45000(1.03)^n = 50000 1.03^n = 1.1111... n log 1.03 = log 1.111.. n = 3.5644.. about 3 1/2 years

Math
let the present value of the deposit be P P(1.075)^6 = 55000 p = 55000/1.075^+ = $35637.88 (elope, skip the expensive wedding, and use it as a downpayment for a house)

Algebra
What? No interest involved? So, let the number of months be n 500 + 95n = 800 + 75n 20n = 300 n = 15 check: 500 + 15(95) = 1925 800 + 15(75) = 1925

Bronies
Never heard of that, so I googled it. Does GOOGLE not work on your computer ?

Algebra (Age Problem)
present age --- x age five years ago --- x-5 age five years from now -- x+8 "Five years ago Rico's age was half of the age he will be in eight years" x-5 = (1/2)(x+8 times 2 2x - 10 = x + 8 x = 18 Rico is now 18 yrs old check: 5 years ago: 13 8 years from now: 26...

Math (Variation)
cost = k r^2 when r = 6, cost = 148 148 = k(36) k = 37/9 cost = (37/9) r^2 so when r = 11 cost = (37/9)(121) = 497.44 or cost1/cost2 = r1^2/r2^2 148/cost2 = 36/121 36cost2 = 148(121) cost = 148(121)/36 = 497.44

math
denominator --- x numerator ---- x-6 (x-6)/x = 3/4 4x-24 = 3x x = 24 check: (24-6)/24 = 18/24 = 3/4 , YUP

Pre-Alegebra
25/20 = 6/x 25x = 120 x = 120/25 = 24/5 or 4.8 ft

maths
time = distance / rate = 300 km/(60 km/h) = 5 hrs

algebra 2
since cotØ = 1/tanØ by definition, given the tangent of an angle, just take the reciprocal to find the cotangent of that same angle eg, given tanØ = 4/7 then cotØ = 7/4

Math
I would first of all change the ratio from 1/4 in : 6 ft , to 1 inch: 24 ft a) for 18 ft, x in/1 in = 18ft/24ft x = 18/24 = 3/4 inch b) x/1 = 66/24 = 11/4 inches or 2.75 inches c) you do it.

Maths
current: number of girls -- 3x number of boys --- 4x after change: number of girls -- 3x+3 numbr of boys --- 4x-1 new ratio of girls to boys = (3x+3) : (4x-1) more data needed to get numerical answer. e.g. if we let x = 5 we had 15 girls and 20 boys, notice 15:20 = 3:4 after c...

Probability
Assuming of course that he would try the same password more than once, we want success within 2 attempts ----> He could log in on his first try, or if that fails on his second try. FS for failure, then success is Prob(S) + Prob(FS) = 1/8 + (7/8)(1/7) = 2/8 = 1/4

Math
using my favourite normal distribution graphing calculator (same as tables in back of text books) http://davidmlane.com/hyperstat/z_table.html click on "value from an area" then enter: area = .9 (to be in top 10%, 90 must be "below" ) mean = 620 SD = 220 cl...

math
total now = 24 let the number of oranges to be added be x so (4+x)/(24+x) = 1/4 16 + 4x = 24+x 3x = 8 x = 8/3 8/3 buttons ??? Questions is flawed, check your data or your typing.

math
number of rooms rented = 450 - 7x price per room = 750 + 4x revenue = (450-7x)(750+4x) expand, then either find the vertex of the resultiong quadratic function, or differentiate, set equal to zero, and solve for x

MATH HELP!!!!!!!!
Do you know how to find the inverse of a 3by3 matrix? I got the following: 28 -51 1 40 -18 -26 4 27 7 each is divided by 192 so multiply the above inverse matrix by 46 12 60 then divide each result by 192 for your x1, x2, x3

Algebra 1 (Reiny!)
a) correct b) correct, but do you know why the volume is zero ? c) this will also answer part b) the given volume = c(8.5-2c)(11-2c) in expanded form notice if c = 4.25, the size of the cut-out, you would be cutting away 4.25 on each side of the width but the width is only 8.5...

math
do you know Calculus? If so, then dP/dx = -80x + 1000 = 0 for a max of P 80x = 1000 x = 1000/80 = 12.5 I assume you can't make a partial product , so either make 12 or 13 to get the same maximum profit If you don't know calculus .... the x value of the vertex is -b/(2a...

math
let magnitude 3 be represented by c then maginitude 4 would be 10c and magnitude 6 would be 10^2 x 10c = 1000c it would be 1000 times as great.

algebra
number of quarters --- x number of dimes ----- x + 6 25x + 10(x+6) = 165 solve for x, sub into my definition

math
let the amounts be 2x , 3x, and 5x solve 2x+3x+5x = 8000, then sub the x back into the three different definitions (hint: the largest share should be $4000 )

math!!!!
9 laps = 9(1/8) or 9/8 miles speed = (9/8) / 2.5 minutes = 1.125/2.5 mpm = .45 miles/min

MATH
yellow : red = (3/4) : (5/4) = 3 : 5 y:1 = 3:5 y/1 = 3/5 y = 3/5 He needs 3/5 L of red check: (3/5) : 1 = 3 : 5, the ratio as needed

Geometry
Area of a kite = (1/2)product of the diagonals So the width and height would be diagonals let the height diagonal be h (1/2)(15)h = 60 15h = 120 h = 8 , looks like C

Maths
I will assume you meant: x^2 = (y^2 - r^2)/y^2 , (or else it becomes a real mess involving a quadratic equation in y^4) Let me know otherwise on my assumption, x^2 y^2 = y^2 - r^2 y^2 - x^2 y^2 = r^2 y^2(1 - x^2) = r^2 y^2 = r^2/(1 - x^2) y = ± r/(√(1-x^2) , where...

math
Assume there were no babies in the group number of children --- x number of adults ----- y number of seniors ---- 6-x-y 17x + 27y + 25(6-x-y) = 115 17x + 27y + 150 - 25x - 25y = 115 -8x + 2y = -35 8x - 2y = 35 The left side of this equation is even, the right side is odd, this...

pre calculus
.72 = 1 (e^-.000124t -.000124t ln e = ln .72 but lne =1 t = ln .72 /-.000124 = appr 2649 years check my arithmetic

pre calculus
i = .10/12 = .008333.. n = ? months 5000(1.008333..)^n = 10000 1.008333..^n = 2 n log 1.0083333..= log2 n = appr 83.5 months or 6 years and appr 11.5 months

pre calculus
a) amount = 1000(1.025)^10 = 1280.08 b) amount = 1000 e^(5(.05)) = 1000 e^.25 = 1284.03

Math
cos 4Ø = 2cos^2 2Ø - 1) = 2(2cos^2 Ø - 1)(2cos^2 Ø -1) -1 = 2(4cos^4 Ø - 4cos^2 Ø + 1) - 1 = 8cos^4 Ø - 8cos^2 Ø + 2 - 1 = 8cos^4 Ø - 8cos^2 Ø + 1 now let cosØ = x and we have f(x) = 8x^4 - 8x^2 + 1

maths
number(baseball OR football) =number(baseball) + number(football) - number(baseball AND football) 29 = 21 + 12 - x x = 4 4 of them play both sports.

Math
And exactly what part of Steve' answer and mine did you not like ? http://www.jiskha.com/display.cgi?id=1391831037

statistics
W - wrong R - right a) prob RRR = (1/3)(1/3)(1/3) = 1/27 b) prob WWW = (2/3)^3 = 8/27 c) 2 right could be WRR, RWR, or RRW prob(of that) = 3 x (2/3)(1/3)^2 = 6/27 (notice the other case is 2 wrong prob of that = 3(1/3)(2/3)^2 = 12/27 and notice that 1/27 + 8/27 + 6/27 + 12/27 ...

Math
the first line of my explanation should have said: 72 = 2x2x2x3x3 = (2^3)(3^2) Looks like I had 12 on my mind

Math
To find the number of factors of a number, list its prime factors. e.g. 12 = 2x2x2x3x3 = (2^3)(3^2) so now we argue as follows: the 2's can be used in 4 ways: that is, we can use none, one, two , or all three of them. similarly the 2's can be used in 3 ways, none, one ...

statistics
I use this fantastic webpage for these kind of questions http://davidmlane.com/hyperstat/z_table.html enter the mean and SD, click on "between" and enter 69 and 70 to get .1779

LINEAR EQUATIONS
Noting to "solve" here, since you have 2 unknowns there would be an infinite number of solutions. What can you do with it? - perhaps graph it, by ... sub in any x you feel like e.g. let x = 3, then y = -2) ---> point (3,-2) let x = 0 , then y = 4 ---------> poi...

math
let time taken until they meet be t hrs distance covered by first train = 115t miles distance covered by 2nd train = 105t miles 115t+ 105t = 1200 220t = 1200 t = 5.454545.. hrs or 5hrs and .4545..*60 min = 5hrs and appr 27 minutes (let's hope the trains are on different tr...

Math
I tried dividing the given number by number that reflect teenagers. That is, I started with 13 61150 = 13*47040 47040 = 14*3360 3360=15*224 224=14*16 so the factors are: 13*14*14*15*16 So there are 5 factors, thus 5 members in the club For the second part, start with 12, then ...

math
I must disagree with that answer. There are 2 pizzas, each cut into 10 pieces. So they had 20 pieces, and ate 14 part of the pizzas eaten = 14/20 = .7

Algebra 1 (Reiny)
both 8 and 27 are perfect cubes, so the cube root will be exact and 2. (8/27)^(1/3) = 2/3 for (8/27)^(2/3) = [(8/27)^(1/3) ]^2 = (2/3)^2 = 4/9

Math
889/12 = 74 with remainder 1 961/12 = 80 with remainder 1 1009/12 = 84 with remainder 1 1189/12 = 99 with remainder of 1 So 12 is it! I am not sure if you know anything about modular arithmetic, so I made up a silly little old-fashioned computer program. Here is a listing of i...

Algebra 1 (Reiny)
If you meant: the cube root ∛(8m^3) then you would have = 2m , not both 8 and m^3 are perfect cubes 2. very confusing way of typing it, if you represent the square root correctly with an exponent of 1/3, why not represent the cube root with an exponent of 1/3 so we have ...

Math:A.P.
for AP: term1 = a term3 = a+2d term9 = a+8d but term7 = 19 = a+6d so a = 19-6d so re-defining: term1 = 19-6d term3 = 19-6d+2d = 19-4d term9 = 19-6d + 8d = 19+2d these 3 are supposed to be a GP, so (19-4d)/(19-6d)= (19+2d)/(19-4d) 361 - 152d + 16d^2 = 361 -76d - 12d^2 28d^2 - 7...

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