Thursday
July 24, 2014

Posts by Reiny


Total # Posts: 26,863

Math
That's better. multiply each term by 12 , the LCD 6x - 4 = 3x 3x = 4 x = 4/3 you are correct.

math
Proof of my answer: now ----- 3250 end of 1st year: 3250(1.06) = 3445 end of 2nd year: 3445(1.06) = 3651.70 end of 3rd year: 3641.70(1.06) = 3870.80 >> as I had before suppose they did 3250(1.06)3.5 = 3985.23 which is one of the choices, BUT contradicts the concept of &q...

math
Trick question? Since the compounding is annually, the amount at 3.5 years is the same as it was after 3 years amount = 3250(1.06)^3 = 3870.80

Math
you have a geometric series, where a = 6 , r = -4 I suspect you have a typo. S(1) to me means the sum of 1 term that would simply be 6

calc
y^3 = 16x^2 when x = 4 y^3 = 16(256) y = 16 3y^2 dy/dt = 32x dx/dt sub in our values 3(256) (-1) = 32(4) dx/dt dx/dt = -768/128 = -6

Math
You have no right side of an equation. There was no equation to solve. Retype your question please

Math
Write fractions this way: x/2 - 1/3 - x/4 LCD = 12 6x/12 - 4/12 - 3x/12 = (3x - 4)/12 Your answer makes no sense. (It doesn't even have an x term)

Math
2 = 1( 1.0275)^n log 2 = n log 1.0275 n = log2/log1.0275 = ....

Math question
Did you notice that each term is half of the previous one? Which type of sequence matches that property?

Inverse Trig
for both cases, since for any -π/2 < y < 0 the sine will be negative, we only have to concern ourself with angles in the first quadrant. so if y = arcsin (√3/2) then y = π/3 ( I know sin 60° = sin π/3 = √3/2 ) and for the second one y = ...

Inverse Trig
look at the sine curve, it is zero, or crosses the horizontal axis at 0 , ±π , ±2π .. or in general kπ , where k is an integer.

Inverse Trig
since sin(?) and arcsin(? are inverses of each other, arcsin( sin (6π) ) = 6π , but that is beyond your stated boundary. so arcsin(sin 6π) = arcsin 0 = 0 , π , 2π

Math
Each hour is equal to 30° or π/6 radians So to go from 3:00 to 5:00 would take 2π/6 or π/3 the arclength = rØ = 6(π/3) or 2π inches = appr 6.28 inches or circumference = 2π(6) = 12π the time from 3:00 to 5:00 represents 1/6 of a ro...

Math
add them: 17x = 16 x = 16/17 back in 1 9(16/17) + 2y = 8 2y = 8 - 144/17 y = -4/17 they intersect at the point (16/17 , -4/17)

algebra
centre would be the midpoint of the the two given points, which would be C(-3,3) so the equation is (x+3)^2 + (y-3)^2 = r^2 plug in one of the points given to find r^2

GRAPHING HELP
x = − 1/3^2+4 is a vertical line , (I don't see a y value) must be a typo

alg.
for y = ax^2 + bx + c the x of the vertex is given by -b/(2a) once you have that x, sub it back into the original equation to find the corresponding y of the vertex.

math
look below at the first of "Related Questions", Steve gave an answer to the same question.

trigonometry
3 sinØ = 1.5 , 0 ≤ Ø ≤ 4 sinØ = 1.5/3 = .5 the sine is positive in I or II Ø = π/6 or Ø = π - π/6 which is 5π/6 the period of sinØ is 2π, so adding another 2π to π/6 yields 13π/6 , wh...

math
If you are first of all looking for the integral of v=25sin50πt it should be -1/(2π) cos(50πt) + c the rest is physics, about which I know very little . from there the mean is usually found by ... 1/(10-0) ( -1/(2π) cos (500π - (-1/2π cos(0) ) = 1...

math
If it is right-angled, then x^2 + x^2 = (x^2)^2 x^4 - 2x^2 = 0 x^2(x^2 - 2) = 0 x = 0 , which is no good or x^2 = 2 x = √2 then the area = (1/2)(x)(x) = 1/2 (√2)^2 = (1/2)(2) = 1 square unit

math
7% per month ???? in the middle ages , they would burn folks on the stake for rates like that. It was called usury. anyway .... interest on balance = .07(1734.50) = $121.42 actual repayment from loan = 165-121.42 = $43.59 Balance next month = 1734.50 - 43.59 = $ 1690.92

math
prob(red, then blue) = (4/10(5/9) = 20/90 = 2/9 you do the rest

math
actually it is much bigger than that 1st place --- 10 different runners 2nd place ---9 3rd place ---8 ... last place --- 1 runner number of ways = 10*9*8*7*...*2*1 = 3,628,800 What your 10*9*8 is is the ways 1st, 2nd and third place could happen

Math
you have an arithmetic series: 4 + 6 + 8 + ... Easy to see that after 3 days, you will have already spent 18 hours, so you need one extra day of only 2 more hours to have a total of 20 hrs.

math
and g(x) is .... ??

math
current number of rooms = 30 current price per room = 12 let the number of additional increases of $1 be n numbers of rooms rented = 30 - 2n number of rooms not rented = 30 - (30-2n) = 2n price per room = 12 + n Profit = (12+n)(30-2n) - 4(30-n) - 1(2n) = 360 + 6n -2n^2 - 120 +...

Trig Maths
or from Steve's 5√3 sinθ = 21 cosθ sinØ/cosØ = 21/5√3 tanØ = 21/5√3 , and the tangent is + in I and III Ø = 1.18 in I or Ø = π + 1.18 = 4.32 in III

Math
number of 50's ---- x number of 10's ---- 2x number of 5's ----- 2(2x) = 4x Now, consider the value of those notes to form your equation. 50x + 10(2x) + 5(4x) = 1080 50x + 20x + 20x = 1080 90x = 1080 x = 12 we defined 10's as 2x so she has 2(12) or 24 $10 bills...

math
x + x(.08)(3) = 15000 1.24x = 15000 x = 12096.77

math
8. amount invested at 12% -- x amount invested at 8% --- 3000-x .12x + .08(3000-x) = 3200 times 100 12x + 8(3000-x) = 320000 4x = 29600 x = ??? (more than she invested!!!!) I think you have a typo, should the interest be RM 320 ?? That way it works out nicely, change the 3200 ...

Math
|3x+1|-|2-x|<3 Formal Way: Case 1 |3x+1| < 3 + |2-x| 3x+1 < 3 + |2-x| AND -3x-1 < 3 + |2-x| |2-x| > 3x-2 AND |2-x| > -3x-4 which leads to a) 2-x > 3x-2 OR -2+x > 3x-2 -4x > -4 OR -2x > 0 x < 1 OR x < 0 ----> x < 1 b) 2-x > -3x - 4 O...

maths
3x = 6y looks trivial, just divide by 6 y = (3/6)x + 0 y = (1/2)x + 0 for equations that contain all 3 terms, there is a two-step process 1. move all terms except the y term to the right side of the equal sign ----> 2y = 6x - 2 2. divide each term by the coefficient of the ...

math
a = 3 , d = 6 term(n) = a + (n-1)d 123 = 3 + (n-1)(6) 120 = 6n - 6 126 = 6n n = 126/6 = 21 there are 21 terms

naths
midpoint is (4,5) y - 5 = 2(x-4) arrange it any way you have to

Math
log2+ 3log1 = log 2 + 3(0) = log2 you SHOULD know that log 1 = 0

maths
from the 2nd: y = 5-x plug into the 1st: 2(5-x) - 5x = 3 I am sure you can finish that

geometry
ratio of corresponding sides = 7 : 5 since perimeter is a linear measurement, the ratio of perimeter is also 7 : 5 ratio of volumes = 6^3 : 5^3 = 343 : 125

Math
p% = p/100 so (p/100) ( ? ) =12 since we only want the 12 to remain on the left side my ( ? ) must be 100(12)/p or 1200/p check: (p/100) * (1200/p) = 12

Math
A - Give yourself an example and see which way is correct e.g. start with 5/8 now add 1 to both top and botto ---> 6/9 Is the value the same ???? B. Again, test with an example C. start with 5 , 5^2 = 25 mmmhh? how about 1/3 , what is (1/3)^2 or 1/9 compared with 1/3 Hint: ...

geometry
You are obviously looking at some circle diagram that I can't see. In BE , which is the centre, B or E ? Where does DC come from? Where does BD come from ? All I know so far is that AC is a chord.

calculus help
ignore the very last "the acceleration is 9.33" pressed "post answer" too soon so the acceleration is a = 13.59 ft/s^2 and v = 13.59t + 32.2667 a = 13.59 ft/s^2

calculus help
If the acceleration is a then v = at + c , where c is a constant: when t=0 , v = 22 mi/h = 32.2666.. ft/s 32.266.. = a(0) + c c = 32.2666.. when t = 3s , v = 50 mi/h = 73.333.. ft/s 73.333.. = a(3) + 32.26666... 3a = 41.06666.. a = 13.58888.. the acceleration is 13.89 ft/s^2 t...

elem algebra
let speed of boat in still water be x mph 17/(x-10) + 17/(x+10) = 10 time (x-10)(x+10) 17(x+10) + 17(x-10) = 10(x^2 - 100) 34x = 10x^2-1000 10x^2 -34x - 1000 = 0 x = 11.84 or some negative speed x = 11.84

maths
number of lunchers ---- x number of non-lunchers --- 30-x 5x + 3(30-x) = 110 5x + 90 - 3x = 110 2x = 20 x = 10 10 took their own lunch, 20 bought their lunch check: 10(5) + 20(3) = 110

Math
Steve gave a good example to Taylor here for the same question: http://www.jiskha.com/display.cgi?id=1360645422

math
Your mean is correct to get a mean of 72, let the extra score be x and he now has 10 scores to average (633 + x)/10 = 72 633 + x = 720 x = 720-633 = 87 he needs an 87 or, think of it this way. to have an average of 72 on 10 tests, he needs a total score of 720 so far he has 63...

maths
The question makes no sense to me. Are you saying that the angle has the same numerical value as the side BC ? Interesting mix of linear measurement and angle measurement. Are you using degrees or radians ? so you could use any 0 < x < 180 e.g. if x = 20 then angle ABC =...

Calculus Help Please Urgent!!!
I stand by mine and Damon's answer for a minimum area. I even ran a simple 1980's style "BASIC" program to show it 10 a = 5000 20 for x = 0 to 14 step 1.000000E-05 30 y = (14-4*x)/3 40 na = x*x+sqr(3)/4*y*y 50 if na < a then a = na : side = x 60 next x 70 ...

Calculus Help Please Urgent!!!
I also got 6.09 (actually 6.0895..) I defined the side of the triangle slightly different from Damon to avoid as many fractions as I could. let each side of the square be x m let each side of the equilateral triangle be 2y m that way I can say that the height of the triangle i...

Algebra
Sandra, the placing of brackets is crucial here The way you placed them makes them insignificant, it is the same thing as 3/2a + 5/2a According to the rules of operations, this is the same as (3/2)a + (5/2)a = (8/2)a = 4a so you must have meant: 3/(2a) + 5/(2a) , the way both ...

Math
multiply each term by z z^2 + 1 = 2z z^2 - 2z + 1 = 0 (z-1)^2 = 0 z-1 = 0 z = 1 you had that, good job

math
Make a sketch of your triangle in quadrant II to see that x = -3, r = 4 and from Pythagoras that y = √7 in II so sinØ = √7/4 sin 2Ø = 2sinØcosØ = 2((√7/4)(-3/4) = -3√7/8

MATH
Each side of the base will be (24-2x) v(x) = x(24-x)^2 Wolfram's magic done here: http://www.wolframalpha.com/input/?i=plot+y+%3D+x%2824-x%29%5E2

calculus
your equation came out looking rather jibberish on my computer, but I see it contans x's and y's I can give you the general method of doing this question .... Find the derivative with respect to t, then your result should contain dx/dt and dy/dt , as well as x and y yo...

Math
from the 2nd: x = 5y+7 plut into the first: x + 2y = -7 5y+7 + 2y = -7 7y = -14 y = -2 back in x = 5y+7 = 5(-2)+7 = -3 x = -3 , y = -2

Math
I understand bi-monthly to mean every other month, or 6 times a year. The main problem here is that the payment period does not coincide with the interest period, so my normal formula does not work so we will convert the 6% compounded bi-monthly to one of i compounded semi-mon...

precal
|y-8.0|<=1.5 y-8 ≤ 1.5 and -y+8 ≤ 1.5 y ≤ 9.5 and -y ≤ -6.5 y ≤ 9.5 and y ≥ 6.5 which can be written as 6.5 ≤ y ≤ 9.5 (or in words, y is between 6.5 and 9.5 inclusive

Math
each individual question has a prob of 1/2 of being correct so you want (1/2)(1/2) .... (1/2) --- (8 times) = (1/2)^8 = 1/256

Math
red from 1st ---> 8/18 = 4/9 red from 2nd ---> 10/13 prob(2res) = (4/9)(10/13) = 40/117

Math
Are we to assume that the other 9 customers did receive a star, thus are winners? If so, then the prob of winning = 9/156 = 3/52

Math
what is 10( 1.015^540 - 1)/.015 ? (don't be surprised if you get over 2 Million dollars)

Algebra 1
what you need is the vertex. for any parabola of the form y = ax^2 + bx + c the x of the vertex is -b/(2a) once you have the x of the vertex, plug into the original to get y y will be your maximum, and it happens at the x value. (make sure you get a max height of 156.25 ft )

Algebra 2
e^3x>e^x-1 you probably meant: e^(3x) > e^(x-1), (huge difference from what you typed) ln both sides ln (e^(3x)) > ln e^(x-1) 3x > x-1 2x > -1 x > -1/2 PROOF: http://www.wolframalpha.com/input/?i=plot+y+%3D+e%5E%283x%29+%2C+y+%3D+e%5E%28x-1%29+from+-1+to+0 -6...

Math (Probability)
to make a sum of 5 , the two dice would be : 1-4 , 2-3, 3-2, or 4-1 so 4 ways prob (sum of 5) = 4/36 = 1/9

Math
If what you want is the effective annual rate, all we need is the 6% per annum compounded monthly let the annual rate be i then 1+i = (1 + .06/12)^12 1+i = 1.005^12 = 1.0616778.. i = .0616778 the effective annual rate correct to 3 decimals is 6.168 % check: amount of 12300 at ...

Algebra
your LCD is 6x , so multiply each term by that 20 + 8x = 3(7+x) 20+8x = 21+3x 5x = 1 x = 1/5

Math
let the tens digit be x, let the unit digit be y the number is 10x+y (10x+y)/(x+y) = 2 + 2/(x+y) times (x+y) 10x+y = 2x+2y + 2 8x - y = 2 ----> y = 8x-2 (10x+y)(x+y) = 112 10x^2 + 11xy + y^2 = 112 sub in y = 8x-2 10x^2 + 11(8x-2) + (8x-2)^2 = 112 10x^2 + 88x - 22 + 64x^2 - ...

Algebra
anticipated cost/doz --- x anticipated number of dozen bought = 210/x actual cost/doz = x+3 number of dozen he bought = 210/(x+3) 210/x - 210/(x+3) = 1/2 multiply each term by 2x(x+3) 420(x+3) - 420x = x^2 + 3x x^2 + 3x - 1260 = 0 x = appr 34.03 or some negative value 210/34 =...

Math
A terminal position of ((-15/13),(12/13)) puts you in quadrant II and using similar triangles we could have the same angle for a terminal position at (-5,4) so r = √(25+16) = √41 x = -5, y = +4 , r = √41 sin è = 4/√41 ----> csc è = W...

math
prob(Ruben winning) = 16/24 = 2/3 prob(Ruben NOT winning) = 1/3 so prob(Manuel winngin) = 1/3 prob(Man not winning) = 2/3 odds in favour of Manuel winning = (1/3) : (2/3) = 1 : 2

math homework
Just add them up.

Algebra
What you meant was ... For what value of b is the expression undefined? when b = -4, the denominator is zero, and you would be dividing by zero. Division by zero is undefined, so b ≠ -4

statistics
what is .8^3 = ?

Algebra
I will assume you meant: 1/(2x) + 1/x = -12 times 2x 1 + 2 = -24x x = 3/-24 = -1/8 if you meant it the way it was typed: 1/2 x + 1/x = -12 times 2x x^2 + 2 = -24x x^2 + 24x + 2 = 0 x = (-24 ± √568)/2 = -12 ± √142

Calculus
let be base be x ft by x ft let the height be y ft (x^2)(y) = 3 y = 3/x^2 Cost = 3(x^2) + 2(4xy) = 3x^2 + 8x(3/x^2) = 3x^2 + 24/x d(cost)/dx = 6x - 24/x^2 = 0 for a min of cost 6x = 24/x^2 x^3 = 4 x = cuberoot(4) = appr 1.6 ft the base should be appr 1.6 ft by 1.6 ft (the heig...

Math
Forgot to mention that we could also have placed out third point on the left side of the y-axis, e.g. (-4,8) would work

Math
let's consider (0,1) and (0,6) to be the base, the the base is 5 units. let the height be h giving us a nice isosceles triangle (1/2)(5)h = 10 5h = 20 h = 4 so a possible third point is (4, 3.5) As a matter of fact, we could now take any point along the vertical line x = 4...

Math emergency I have 10 minutes to submit it.
did you not notice that the derivative of the denominator is sitting in the numerator ? and if y = ln(u) then dy/du = u'/u, exactly our pattern integral of e^x/(7+e^x) from 0 to 2 = [ ln (7 + e^x) ] from 0 to 2 = ln(7 + e^2) - ln(7 + e^0) = ln (7+e^2) - ln(7+1) = ln ( (7+e...

Algebra
3/(4x-36)- 5/(2x-4) - 2x/(x^2-11x+18) = 3/(4(x-9) ) - 5(2(x-2)) - 2x/( (x-9)(x-2)) so the LCD = 4(x-9)(x-2) = ( 3(x-2) - 5(2)(x-9) - 2x(4) )/(4(x-9)(x-2)) = (3x-6 - 10x + 90 - 8x)/(4(x-9)(x-2)) = (84 - 15x)/(4(x-9)(x-2))

Math
The standard 3by3 magic square is 8 1 6 3 5 7 4 9 2 --> notice ever row, column and diagonal adds up to 15 for a total of 45. Any 9 numbers in an arithmetic sequence can be arranged in the above order and you would have a magic square with the properties you want. change al...

Algebra 2
term1= 3(1) - 3 = 0 term2 = 3(2) - 3 = 3 term3( = 3(3) - 3 = 6 .... looks like an arithmetic sequence , with a=0 and d = 3 sum(1) = (10/2)(2(0) + 9(3)) = 5(27) = 135

@ Sandra - Algebra
Looks like Connexus is new to this site, looks like he just added his question to yours. about yours ..... (x^2 – 1) / (x^2 – x – 2) – (x-1) / (x-2) = (x+1)(x-1)/( (x-2)(x+1) - (x-1)/(x-2) = (x-1)/(x-2) - (x-1)/(x-2) = 0 , x ≠ -1

Rectangular coordinates to polar coordinates
remember that while rectangular coordinates define one and only point, the position of a point using polar coordinates is not unique. In general any point (r, Ø) can also be represented by (-r, π+Ø) e.g. (using degrees) look at the point defined by (6, 150&d...

mathematics
Did you notice that 1.4 = 7/5 ? log5 1.4 = log5 (7/5) = log5 7 - log5 5 = 1.209 - 1 = .209 A property of logs that comes in handy here is loga b = 1/logb a b) log7 75 = log7 (3*5^2) =log7 3 + 2log7 5 = (log5 3) / (log5 7) + 2/log5 7) = .683/1.209 + 2/1.209 = 2.683/1.209 = 2683...

math
log4(2x+4) - 3 =log4 3 log4(2x+4) - 3log44 = log4 3 log4(2x+4) - log4 4^3 = log43 log4[(2x+4)/64] = log43 (2x+4)/64 = 3 2x+4 = 192 2x=188 x = 94

calculus help please
let each side of the square be x m let each side of the equilateral triangle be 2x (that way, the height is √3y, from the ratio of the 30-60-90° triangle) a) for a max area, you are right, all should be used for the square b) 4x + 6y = 14 2x + 3y = 7 x = (7-3y)/4 OR ...

Algebra
For what value of b would you be dividing by zero ?

MAth
cos 31° = PQ/20

Math
the way you typed it, the entire bracket is divided by 2. 5(2x - 10)/2 + 14 = 19 5(x - 5) + 14 = 19 5x - 25 = 19-14 5x = 5 + 25 5x = 30 x = 6

Trig
ARggghhhh!!!!

Trig
we need cos 225° and sin225° 225 = 180+45 , it is in quadrant III and has the same numerical trig values as 45°, but in III both the sine and cosine are negative sin 225 = - sin 45° = -1/√2 cos 225 = - cos 45° = -1/√2 so 7(cos255degrees + isin25...

MATH
sin 10.5° = PR/120 PR = 120 sin 10.5° = ....

Math
P(x) = 1.3x-.01x^2-30 = -.01x^2 + 1.3x - 30 in more standard notation you will need the vertex. The x of the vertex is -b/(2a) = -1.3/(-.02) = 65 then P(65) = -.01(65)^2 + 1.3(65) - 30 = 12.25 when x = 65

geometry
surface area of box = 2(2.5)(7) + 2(2.5)(12) + 2(7)(12) = 263 inches^2 surface area of cylinder = 2πr^2 +2πrh = 2π(3^2) + 2π(3)(7.5) = 18π + 45π = 63π or appr 197.9 inches^2 so what do you think?

Math
I recommend getting rid of brackets first to get nice straightforward terms, then simplify, and then "move" terms from side to side. -5 - x = 2x - 4x - 6 -5 - x = -2x - 6 2x - x = -6 + 5 x = -1 (your -x on the right side should have been +x )

mathematics for management
I will assume they are the same x recall that loga b = log b/log a so logxy = logy/logx and logyx = logx/logy so your equation can be written as: logy/logx + logx/logy = 5/2 let logx/logy = a then we have 1/a + a = 5/2 times 2a 2 + 2a^2 = 5a 2a^2 - 5a + 2 = 0 (a - 2)(2a - 1) =...

mathematics for management
I saw this one pass by me before. Are you distinguishing between "x" and "X"? If so, you have 4 variables with only 2 equations.

math
first bounce --- 3 ft 2nd bounce = 2(1/4)(3) = 6(1/4) 3rd bounce = 2(1/4)(3)(1/4) = (6)(1/4)^2 4th bounce = ... = (6)(1/4)^3 .... so we have 3 + 6(1/4) + 6(1/4)^2 + 6(1/4)^3 + ... to infinity = 3 + 6(1/4) (1 + 1/4 + (1/4)^2 + ...) from the 2nd term on, we have a geometric seri...

Math
short leg --- x longer leg --- 2x-1 x^2 + (2x-1)^2 = 17^2 x^2 + 4x^2 - 4x + 1 = 289 5x^2 - 4x - 288 = 0 (x-8)(5x + 36) = 0 x = 8 or x is an inadmissable negative number short leg = 8 ft long leg = 15 ft area = (1/2)(8)(15) = 60 ft^2

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