Thursday

July 24, 2014

July 24, 2014

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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