Thursday
July 24, 2014

Posts by Reiny


Total # Posts: 26,863

math
first day he ran 1.5 2nd day he ran 1.5(1.1) 3rd day he ran 1.5(1.1)(1.1) = 1.5(1.1)^2 .. on the 7th day he ran 1.5(1.1)^6 so we have: 1.5 + 1.5(1.1)+ 1.5(1.1^2 + ... + 1.5(1.1)^6 which is a geometric series whose sum is 1.5( 1.1^7 - 1)/(1.1 - 1) = 1.5(.9487171)/.1 = 14.230756...

Pre-calculus
your equation "falls apart" when p = 100 because you would be dividing by zero So mathematically, the cost would be infinitely large (that is, it is not possible) look at this graph and see what happens at p = 100 http://www.wolframalpha.com/input/?i=plot+C%3D80%2C00...

not Calculus Please help!
B) compounded quarterly ----> i = .07/4 or .0175, and n = 6(4) or 24 amount = 7000(1.0175)^24 = $ 10,615.10 Do A and C the same way D amount = 7000 e^(6(.07)) = $ 10,653.73

Calculus Please help!
-8x + 4x dy/dx + 4y - 6y^2 dy/dx = 0 dy/dx(4x - 6y^2) = 8x - 4y dy/dx = (4x - 2y)/(2x - 3y^2) plug in x = 1 and y = 3 to find the slope

Math
Let the dimensions of the box by x by y by z xyz = 80 z = 80/(xy) "least amount of plasic" implies least surface area SA = 2xy + 2xz + 2yz = 2xy + 2x(80/(xy)) + 2y(80/(xy)) = 2xy + 160/y + 160/x now we know that xyz = 80 and 80 = (2)(2)(2)(2)(5) combinations of x y z...

Math
For simplicity sake, let's assume that the temperature increase is a linear function, (which it isn't), we would solve 2t + 20 = 98 2t = 78 t = 39 seconds

Math! HELP!
(3/2b^4)^3 = (27/8)b^12 (3/5y^4)^-2 = 1/(3/5y^4)^2 = 1/( (9/25)y^8 = 25/(9y^8) or (25/9)y^-8

Algebra 1
5x^2 + 2x^2 = 7x^2 (5 apples + 2 apples = 7 apples) Steve had a typo, happens even to the best of us

Algebra 1
Your question was answered , go back and check

Intermediate algebra
let number of AC adapters be x let number of flashlights be y 7x + 2y = 86 3x + 4y = 84 double the first equation 14x + 4y = 172 3x + 4y = 84 subtract them 11x = 88 x = 8 sub back into 1st: 7(8) + 2y = 86 2y = 30 y = 15 so 8 adapters and 15 flashlights. Check my answer to see ...

Algebra 1 Answer Check
1. correct if you meant 49^(3/2) The way you typed it --- 117649/2 2. can't read the question 3. the leading term in standard notation would be 8x^2 so leading coefficient is 8 4. correct 5. the x is undefined in your problem 6. 7x^2 - 2x + 5, the exponent is not affected ...

algebra
Steve is right, go with x-8 ≥ 20

algebra
After trying to make sense of your garbled English, I would pick x-8 > 20

algebra
Visualize the candy cane made in the form of a paper cylinder. Cut the cylinder open, you will see that the "ribbon" around the candy cane or cylinder consists of 4 diagonals for 4 different rectangles. the height of each of those rectangles is 20/4 or 5 cm and the w...

math help
poorly written up you lost the ratio notation and lack the equal sign correct presentation: 18 : 0.6 = 180 : 6 = 30 : 1

Math
I suspect you mean (x+1)/(x-2) = 3/6 confirm before I proceed

Algebra
the first one is already factored, so how come you are stuck on it ? 2nd: get the equation = 0 then it factors quite easily 4a^2 - 11a + 6 = 0 and 9r^r - 30r + 21 = -4 have you not been taught some kind of a method to factor these kind of trinomials? A common method these days...

Probability
I will assume that you filled in the Venn diagrams correctly n(M upside down u W) ---> n(M and W) = 14 n(M' U S) ---> n(M' or S) Since S is the symbol used for the universal set, the count would be 49 P( both mice are short-tailed) --- where does the "both&q...

Algebra
Yeahhh! you got it

Algebra
4x^2 - 8x - 12 + 6x , looks like grouping works nicely = 4x^2- 8x+ 6x - 12 = 4x(x-2) + 6(x-2) = (x-2)(4x+6) = 2(x-2)(2x+3) 144 - 9p^2 , should have recognized difference of squares = (12-3p)(12+3kp) 5c^2 - 24cd - 5d^2 if it factors it must start with (5c ...)(c...) and end wit...

Algebra 1 (Reiny)
Perimeter = 2s^3+4 + 5s + 4s^2 + 1 = 2s^3 + 4s^2 + 5s + 5 Why was this question difficult for you? If you are given the three sides of a triangle, wouldn't you just add them up to find the perimeter ?

Math
6x-2 = 3x+1 OR 6x-2 = -3x - 1 3x= 3 OR 9x = 1 x = 1 OR x = 1/9

Math
Mandy ---- b jay ------- b-3 kareem --- 2b look at my definitions,

Algebra
#1 should be -3x^2 + 5x- 12 #2 3x^2+ 5x - 6x - 10 = 3x^2- x - 10 #3, good, yeahhh #4, -2p^2 + 27p #5, yeahhh #6 good grief!!! = 2m^3 + 4m^2 + 8m - 4m^2 - 8m - 16 = 2m^3 - 16 #7, correct

math
let f(x) = ax^4 + bx^2 + c f(-1) = 0 , since it is a factor but f(-1) = a+ b + c so a+b+c = 0

advanced functions
-2t^3+3t^2+149t+410 = 980 2t^3 - 3t^2 - 149t + 570 = 0 could try 1, 2, 3, 4, 5 ,6, 7, 8, 9 ,10 Well, what do you know, t=5 works and so does t = 6 so there has to be 3 factors, I know the first two are (t-5)(t-6)(? t + ?) = 0 by the "common sense" theorem, the third ...

Algebra
see http://www.jiskha.com/display.cgi?id=1392932194

Algebra
If you meant y = -7/(x-16), then the domain is any real number, x ≠ 16 and for every x you pick there is one and only one value of y , except x=16 so it is a function.

Algebra
5y = 2x + 9 y = (2/5)x + 9/5 or y = (2x + 9)/5 now write f(x) = ... either of the two versions, both are correct

Math Algebra
Nice, that's the way I would do it,

Algebra
1/A + 1/B + 1/C = 3400 , #1 1/A + 1/B = 1900 (A+B)/(AB) = 1900 1900AB = A+B 1900AB - B = A B(1900A - 1) = A B = A/(1900A - 1) , #2 1/A + 1/C = 2300 A+C = 2300AC ... C = A/(2300A - 1) , #3 SUB #2 and #3 into #1 1/A + 1/(A/(1900A - 1)) + 1/A/(2300A - 1)) = 3400 1/A + (1900A - 1)...

Algebra
just plug in k where you see an x

Algebra
done here http://www.jiskha.com/display.cgi?id=1392928082

Algebra
large frames ---- x small frames ---- 20-x 16x + 7(20 - x) = 176 solve, should be very straightforward

math
Pop(t) = 865 (1.15)^t , where t is the number of years

Pre algebra
There is no "answer" to y = 5x + 5 Your equation is represented by the graph of a straight line. The y-intercept is 5 , or the point (0,5) The x-intercept is -1 or the point (-1,0) Join these two points with a straight line and extend them in both directions. see: ht...

Math
umhhh, Kimberly's age : Halley's age = 3 : 1 or 3/1

MATH 12
ahhh, just tried it again without the "solve" http://www.wolframalpha.com/input/?i=8500%281%2B12x%29%5E34+%2B+200%28+%281%2Bx%29%5E408+-+1%29%2Fx+%3D+193215.33 and got x = .0031041 or i = .0031041 12i = .0372492 So the equivalent annual rate of return for his portfol...

MATH 12
So I will assume a total time of 34 years or 408 months amount 30 years from now = 8500(1.0545)^34 + 200( 1.0025^408 - 1)/.0025 = 51641.968 + 141573.33655 = $ 193215.33 b) is quite complicated. Let the monthly return be i then 8500(1+12i)^34 + 200( (1+i)^408 - 1)/i = 193215.33...

math
a) amount = 8000 e^(12(.02)) = 8500 e^.24 = $ 10805.62 repeat procedure for the others

math
a) amount = 3500 e^(3(.0625)) = ..... same for the others.

Math
I suspect you mean: n(t)=5600/(0.5+27.5e^-0.044t) confirm my assumption before I proceed.

College Algebra
PV = 100000( 1 + .08/12)^-60 = 100000( 1.0066666..)^-60 = ...

math
2300 ----> 4600 after 1 decade so, once more gives you ??? I think your question is the incomplete version of this one, which was answered by Steve http://www.jiskha.com/display.cgi?id=1358452964

Finance
Assume an investment of $1.00 First Simple Bank: amount after 6 years = 1 + PRT = 1 + 1(.06)(10) = 1.60 Complex Bank: 1(1+i)^10 = 1.6 take 10th root of both sides ( (1+i)^10)((1/10) = 1.6^(1/10) 1+i = 1.048122.. i = .048122.. or appr 4.81%

Finance
32000 = 620 + 620( 1 - (1+i)^-59)/i My favourite webpage, Wolfram, says http://www.wolframalpha.com/input/?i=32000+%3D+620+%2B+620%28+1+-+%281%2Bx%29%5E-59%29%2Fx i = .0052576 or 12i = .06309 which is 6.309% per annum , compounded monthly (look past all that messy output to w...

Algebra
volume of 15% OJ --- x L volume of 10% OH --- 5-x L .15x + .1(5-x) = .11(5) times 100 , don't like them decimals! 15x + 10(5-x) = 55 15x + 50 - 10x = 55 5x = 5 x = 1 So 1 L of the 15% stuff and 4 L of the 10% stuff

math(algebra)
if f(x) varies directly with x, then f(x) = kx, where k is a constant given: if x=9 , f(x) = 49 so 49 = 9k k = 45/9 = 5 f(x) = 5x f(3) = 5(3) = 15 or just use a ratio 9/3 = 45/f(x) 9f(x) = 135 f(x) = 135/9 = 15

phisecs
Are you telling me you could not follow my solution to the same problem ? All you did was change one number. http://www.jiskha.com/display.cgi?id=1392776318

phisecs
What is phisecs, some small unit of time? rowing rate --- x km/h current rate --- y km/h A girl rows 11 km downstream in 2 h ---> 2(x+y) = 11 2x + 2y = 11 "Her return trip takes 4 h" ---> 4(x-y) = 11 4x - 4y = 11 first times 2 4x + 4y = 22 add to the 2nd 8x = 3...

Math ~ Check Answers ~
Are you just guessing? Your second one happens to be correct, do you know why it is 2 ?

math
Poor wording of the problem. dy/dx = 8x^3 + 9x^2- 2x+ 5 y = 2x^4 + 3x^3 - x^2 + 5x + c but (2,3) lies on it 3 = 32 + 24 - 4 + 10 + c c = .... evaluate, plug c back into y = ....

math
slope of line is -1 dy/dx for y = 2/x+ k is -2/x^2 so -2/x^2 = -1 x^2= 2 x= ±2 if x = 2, 2+y = 1 ---> y = -1 so one point of contact is (2,-1) it must lie on y = 2/x + k -1 = 2/2 + k k = -2 you try the case where x = -2

algebra
x -28 + 7= 43 solve for x

math
nope consider a rectangle, with sides of width 4 cm and length 10 cm. I can also draw a parallelogram with opposite pair of sides of 4 and 10 cm. they are not congruent. I would go with "sometimes"

algebra
9|9-8 x|=2x+3 , x ≥ -3/2 |9-8 x|=(2x+3)/9 9-8x = (2x+3)/9 81 - 72x = 2x+3 -74x = -78 x = -78/-74 x = 39/37 or 9-8x = -(2x+3)/9 81 - 72x = -2x - 3 -70x = -84 x = 87/70 = 6/5 check: if x = 6/5 LS = 9|9-8(6/5)| = 27/5 RS = 2(6/5)+3 = 27/5 , so x = 6/5 if x = 39/37 LS = 9|9-...

Math
here is a nice youtube showing how it works http://www.youtube.com/watch?v=hJCHhWlyIws

Math
let f(x) = 2x^4 + 4x^3 + 3x^2 + 18 f(1) = 2+4+3+18 ≠ 0 f(-1) = 2 - 4 + 3 + 18≠0 f(2) ≠0 f(-2) ≠0 ... f(±9) ≠ 0 tried ±1, ±2, ±3, ±6, ±9, ±1/2, ± 3/2, ±9/2 none worked could not find an...

math
let the time taken be t minutes velocity = 265 ft/sec = 15900 ft/min distance traveled along the hypotenuse = 15900t ft Did you make a sketch of the right-angled triangle? I see it as ... sin 15° = 11000/15900t 15900t = 11000/sin15 t = 110/(159sin15) = 2.69 minutes

MATH
2(x-5) - 7 =2 2x - 10 = 9 2x = 19 x = 19/2

PRE-Algebra
tank A : tank B = 11:15 550/tankB = 11/15 11tankB = 8250 tankB = 750

back up - Geometry HELP HELP
oops, I misread the question, and got the wrong triangle (I used the y-axis, instead of the x-axis) so thepoints are (0,0), (2,2) and (5,0) same equation for the right-bisector of AB which is x + y = 2 the right bisector of line from A to (5,0) is x = 5/2 for centre: 5/2 + y =...

Geometry HELP HELP
Make a sketch, and by some simple preliminary algebra you can see that the triangle is A(0,0) , B(2,2) and C(0, 10/3) the centre of the circle lies on the right bisectors of any of these sides midpoint of AC = (0, 5/3) so right-bisector equation is y = 5/3 midpoint of B(2,2) i...

math
first vector = (530cos0, 530sin0 = (530,0) 2nd vector = (80cos220 , 80sin 220 = (-61.28355, -51.423 resultant = ((468.71644 , -51.423) maginitude = √((468.71644^2 + (-51.423)^2 ) = 471.529 direction: tan ฿ = -51.423/468.71644 = -.839.. ฿ = E 40° S

math
I have a strong feeling you meant: (1-tan^2 Ø)/(1 + tan^2Ø) + 2tan^2 Ø = (1 - sin^2 Ø/cos^2 Ø)/sec^2 Ø + 2sin^2 Ø/cos^2 Ø = (1 - sin^2 Ø/cos^2 Ø)(cos^2 Ø) + 2sin^2 Ø/cos^2 Ø = cos^2 &Osl...

pre-calc
Your given function will be the part of the parabola which lies to the right of the vertex (3, -9) so y = x^2 - 6x inverse is x = y^2- 6y y^2 - 6y = x complete the square: y^2 - 6y+ 9 = x+9 (y-3)^2= x+9 y - 3= ± √(x+9) y = 3 ± √(x+9) but we only used ...

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.

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