Saturday

July 4, 2015

July 4, 2015

Total # Posts: 30,323

**Math**

test for AS: .8-1.6 = -.8 .4-.8 = -.4 , so not AS test for GS: .8/1.6 = .5 .4/.8 = .5 .2/.4 = .5 , YUP, its GS
*February 2, 2015*

**Math**

yup, #3 has all 3 points satisfying the equation (I did not check any of the others)
*February 2, 2015*

**math**

net discount price = (.93)(.9)(.97)(250) = 202.97 or equivalent discount = 1 - .93(.9)(.97) = .18811 or 18.811% net discount price = 250 - .18811(250) = 202.97
*February 2, 2015*

**maths help please**

#1 multiply both sides by x 6x^3 + 5x^2 = 21x x(6x^2+ 5x - 21) = 0 x=0 or x= -5±√529)/12 = (-5 ± 23)/12 = 3/2 or -7/3 but x ≠ 0 in the original equation, we can't divide by zero x = 3/2 or x = -7/3 B) multiply each term by 2x x^2 + 12x = -20 x^2...
*February 2, 2015*

**math**

success could be : basketC, orange basketD, orange prob = (1/2)(26/39) + (1/2)(18/33) = 20/33
*February 2, 2015*

**math**

x/1= 16/12 x= 16/12 = 4/3 inch
*February 1, 2015*

**Math**

Wow, that is fast. What is it ? .85km/s = 850 m/s = 850 m/(1/60) min = 850(60) m/min = 51000 m/min btw, that would be 3060 km/h
*February 1, 2015*

**Math**

Micah : Sue =2 : 5 or 2x : 5x Let Will's share by y total bill = y + 7x Sue - Will = 6 5x - y = 6 or y = 5x-6 Will = (1/3)(total) y = (1/3)(y+7x) 3y = y + 7x 2y = 7x ---> y = 7x/2 in y = 5x-6 7x/2 = 5x-6 7x = 10x - 12 3x=12 x=4 then y = 5(4)-6 = 14 So the dinner cost y...
*February 1, 2015*

**Algebra**

Your dealing with parabolas and quadratic equations. If you have never learned this, I don't see how you can help him. He must know how to find the vertex of the above parabola, either by completing the square or a short formula which he must memorize. h(t) = -16t^2 + 96t...
*February 1, 2015*

**Algebra**

Basic algebra question: let the large number be x let the smaller number be y x - y = 12 x + 3y = 20 subtract them 4y = 8 y = 2 in x-y=12 x -2=12 ---> x = 14 the larger number is 14, the smaller is 2
*February 1, 2015*

**jiskha review**

Thank you Jam. I have been a volunteer on Jiskha for many years and do it for several reasons 1. I love mathematics 2. In my retirement and "old" age, it keeps my mind active 3. I live in Canada and life has been very good to me, so I enjoy giving back some of it.
*February 1, 2015*

**Algebra**

using 1 bill: 1, 5, 10, 20 using 2 bills 6, 11 ,21 15, 25, 30 using 3 bills : 16, 26, 31, 35 using 4 bills : 36 For a total of 15 different costs Notice Madison missed a few Or the number of subsets of 4 things = 2^4 = 16 but that includes the null set , or not using any bills...
*February 1, 2015*

**Math**

assume 2^(1/2) is a rational number in the form a/b, where a/b is reduced to lowest terms 2^(1/3) = a/b cube both sides 2= a^3/b^3 2b^2 = a^3 the left side of this equation is even then the right side of the equation must be even Properties of integers: if you cube an even ...
*February 1, 2015*

**Stats**

Think about how you obtained that mean? didn't you add the total of the 10 children and divide by 10 ? so the total must have been 172 Let the new kid's score be x then (172+x)/11 = 18 172+x = 198 x = 26
*January 31, 2015*

**Math**

Elis --- y Samuel --- y-10 David --- y+20 y+y-10+y+20 = 140 3y = 130 y = 130/3 = 43 1/3 newspapers ???? Something is rather bogus about your question. Notice mathematically my answer is correct: Elis sold 43 1/3 Samuel sold 33 1/3 David sold 63 1/3 43 1/3 + 33 1/3 + 63 1/3 = 140
*January 31, 2015*

**Math**

women --- x children --- x+6 men ---- (1/3)(x+6) total passengers = x + x+6 + (1/3)(x+6)
*January 31, 2015*

**math**

original number: men -- 3x women -- 4x 3x+4x = 126 7x=126 x = 18 so we had 54 men and 72 women new count: men = 56 women = 80 new ratio : men : women = 56:80 = 7 : 10
*January 31, 2015*

**Math**

let the height be x cm original volume = (45)(25)x cm^3 = 1125x cm^3 remember 1L = 1000 cm^3 (the beauty of the metric system) volume removed = (45)(25)(x-4) which is 22500 1125(x-4) = 22500 1125x - 4500 = 22500 1125x = 27000 x = 24 the height was 24 cm
*January 31, 2015*

**Add maths form 4**

that's not what you had, so make the necessary changes in my solution.
*January 31, 2015*

**Add maths form 4**

I will assume that you meant the equation to be 2qx(x+1) - 8x^2 - 1 = 0 2qx^2 + 2qx - 8x^2- 1 = 0 x^2(2q - 8) + 2qx - 1 = 0 a quadratic with a = 2q-8 b=2q c=-1 to have no real roots, b^2 - 4ac < 0 4q^2 - 4(2q-8)(-1) < 0 4q^2 + 8q - 32 < 0 q^2 + 2q - 8 < 0 (q+4)(q-2...
*January 31, 2015*

**Math**

let the cost price be x original selling price = x + .4x or 1.4x after 20% discound ... final selling price = (.8)(1.4x) = 1.12x which looks like a 12% profit based on cost b) if x = 448 If by "marked" price you mean final selling price, then 1.12(448) = 501.76 ...
*January 31, 2015*

**Trigo**

The angle of "elevation" means it was measured from ground level up So angle QPB = 54 angle QPA = 46 leaving you with 54-46 or 8° or angle APB = 8° In the right-angled triangle APQ, angle P = 54° so angle B = 90-54 = 36°
*January 31, 2015*

**Trigo**

Did you make your sketch? On mine, I labeled the bottom of the building Q, the top of the flagpole B and its bottom A I have a right-angled triangle APQ and a scalene triangle ABP. Angles can be easily found In triangle ABP, I have angle BPA = 8° angle PBA = 36° angle ...
*January 31, 2015*

**algebra**

old price --- x new price ----x+9 increase in old price = (4/5)(x+9) new price = x+ (4/5)x+9) x+9 = x + (4/5)(x+9) 9 = (4/5)(x+9) 45 = 4x + 36 4x = 9 x = 9/4 cents ?? or 2.25 cents check: old price -- 2.25 cents new price --11.25 cents other way to get new price: increase in ...
*January 31, 2015*

**Calculus**

And Math should be and is fun.
*January 31, 2015*

**Calculus**

or let x = 2.44535353.. times 100 100x = 244.535353.. subtract them 99x = 242.09 x = 242.09/99 = 24209/9900 or 2 4409/9900
*January 31, 2015*

**Trigo**

make your sketch let the point below the ballon be P let the distance from the 60° position to P be x then the other distance is 350-x You have two right-angled triangles let the height be h m (the common side to the two triangles) for the 1st triangle: tan60 = h/x h = ...
*January 31, 2015*

**Calculus**

To be concave up the 2nd derivative must be positive, so -x^2 + x + 6 > 0 x^2 - x - 6 < 0 (x-3)(x+2) < 0 looking at y = x^2 - x - 6 , we see from our solution above that it has x-intercepts of 3 and -2, thus it is above ( greater than zero) for x < -2 or x > 3
*January 30, 2015*

**math**

very similar to the other question you had http://www.jiskha.com/display.cgi?id=1422645251 10!11!/(7!13!) = (10x9x8x7! 11!)/(7! 13x12x11x10!) = 10x9x8/(13x12x11) (after the 7!10! cancel) = 60/143
*January 30, 2015*

**math**

you are correct in the final answer, but I object to your "work" the statement 121a^2b^2 = 11ab is wrong it should be 121a^2b^2 = (11ab)^2 same for your next line you could have checked your answer ... (11ab + 2b)^2 = 121a^2b^2 + 44ab + 4b^2
*January 30, 2015*

**college Algebra**

let the sales over $7000 be x 2150 + .08x = 3120 .08x = 970 x = 12125 so he must have sales of 12125+7000 or $19,125
*January 30, 2015*

**MATH**

automatically rule out A and D, last terms are not perfect squares Also rule out B, since both front and back must be positive. So it could only be C , if any at all. take √ of both first and last, multiply those results, then double to get the middle term. looks like C ...
*January 30, 2015*

**math**

btw, this is true for all values of n, not just positive integers. e.g. let n = 2.3 (2/3)^2.3 (3/2)^(2.3-1) = (2/3)^2.3 (3/2)^(1.3) = (2/3)^2.3 (2/3)^-1.3 = (2/3)^(2.3 - 1.3) = (2/3)^1 = 2/3
*January 30, 2015*

**math**

(2/3)^n (1 1/2)^n-1 =(2/3)^n (3/2)^(n-1) = (2/3)^n (2/3)^(1 - n) = (2/3)(n + 1-n) = (2/3)^1 = 2/3
*January 30, 2015*

**Algebra 2**

No, Jasmine I gave you the solution and the answer.
*January 30, 2015*

**Algebra 2**

really quite simple, just subtract them f(x) - g(x) = -2x+4- (-6x-7) = -2x+4 + 6x+7 = 4x + 11
*January 30, 2015*

**math**

quick way: on your calculator find a key usually labeled n! (on mine to find 6!, I keystroke like this: 6 2ndF n! = to get 720 so for (6!8!)/(9!5!) you should get 2/3 or .6666... or use the definitions: also recall that the concept that 9! = 9x8! since this suits our ...
*January 30, 2015*

**Math- check my answers pls**

Was told I had to log in to view.
*January 30, 2015*

**math**

first term: a common difference = 2 sum of first 3 terms = a + a+d + a+2d = 3a + 6 sum of first 9 terms = (9/2)(2a + 8(2)) = 9(a + 8) = 9a + 72 so 3a+6 = ar and 9a+72 = ar^2 square 3a+6 = ar^2 9a^2 + 36a + 36 = a^2r^2 r^2= (9a^2 + 36a + 36)/a^2 from the other equation, r^2 = (...
*January 30, 2015*

**algebra**

first of all, if you are going to factor an equation, get the RS equal to zero x^2 + 5x + 6 = 0 Now can you think of 2 number, which when multiplied gives you 6, and which when added give you 5 ?? How about 2 and 3 ---> 2+3 = 5 and 2x3 = 6 so (x-2)(x-3) = 0 then x-2=0 or x-...
*January 30, 2015*

**Math**

Picking up the equation found by Bosnian at A = 12t + 18t^2 dA/dt = 12 + 36t ---> the instantaneous rate of change for any t when t = 2 dA/dt = 12 + 36(2) = 84 cm^2/second
*January 30, 2015*

**math**

w = 5/8 L wl = 360 (5/8)L^2 = 360 L^2 = 576 L = √576 = 24
*January 30, 2015*

**math**

Same type of problem as the one I just did for you above this post.
*January 30, 2015*

**business math**

single equivalent discount = 1 - .9(.8)(.7) = .496 = 49.6% 49.6% off 9500 = 4712 final price = 9500-4712 = 4788 or , the long way 10% of 9500 = 950 after 1st discount: 9500-950 = 8550 20% discount on 8550 = 1710 after 2nd discount:8550-1710 = 6840 30% of 6840 = 2052 after 3rd ...
*January 29, 2015*

**Mathh**

10/13 = .7692.. or 77% I don't see that answer
*January 29, 2015*

**algebra**

In that case (1/8 + (x+4)/16 )/( (x+4)/x + 4/x ) = ( (2 + x+4)/16) / ( x+4 + 4)/x) = (x+6)/16 * x/(x+8) = x(x+6)/(x+8)
*January 29, 2015*

**algebra**

Was it perhaps (1/8 + (x+4)/16 )/( (x+4)/x + 4/x ) ??
*January 29, 2015*

**algebra**

ok, taking it the way you typed it (1/8 + x + 4/16)/(x + 4/x^2 + 4/x) = (1/8 + x + 1/4)/(x + 4/x^2 + 4/x)*(16x^2/(16x^2) = (2x^2 + 32x^3 + 4x^2)/(16x^3 + 64 + 64x) which does not come close to any of the given answers, so the original is missing some important brackets
*January 29, 2015*

**algebra**

You MUST include brackets to establish the correct order of operation. I will assume you meant: 6/(x-6) + 3x/(x+5) - 1/( (x-6)(x+5) ) notice that the common denominator is (x-6)(x+5) so ... ( 6(x+5) + 3x(x-6) - 1)/( (x-6)(x+5) ) = (6x + 30 + 3x^2 - 18x - 1)/((x-6)(x+5)) = (3x^...
*January 29, 2015*

**math**

Daniel -- x John --- x+30 David --- 3(x+30) solve for x, the plug into my definitions x + x+30 + 3(x+30) = 400
*January 29, 2015*

**math**

make a rough sketch, let D be (x,y) vector AC = vector AB + vector AD <5,0> = <3,2> + <x-1,y-2> <5,0> = <x+2,y> x+2 = 5 ---> x = 3 y = 0 D is (3,0)
*January 29, 2015*

**math**

5 minutes depletes 3% of water 1 minute depletes 3/5 % of water 50 minutes depletes (3/5)(50) % or 30% of water We can't answer the number of gallons, unless we know how many gallons we started with
*January 29, 2015*

**Algebra**

written as 4x = y^2, you should realize that you have a parabola, with its axis of symmetry the x-axis, vertex as (0,0), opening to the right. domain: x ≥ 0 range : any real number btw, it is not a function e.g. both (4,4) and (4,-4) lie on it, so we have 2 different y ...
*January 29, 2015*

**Algebra**

looks like an AS a = 9 , d = 1 , n = ? a + (n-1)d = 87 9 + (n-1) = 87 n = 87-8 = 79 sum(79) = (79/2)(first + last) = (79/2)(9+87) = 3792 or sum = sum(all of 87) - sum(all of 8) = 87(88)/2 - 8(9)/2 = 3792
*January 29, 2015*

**math**

When the x = 0 in any point, that point lies on the y-axis Janine's error is probably not studying or not doing her homework
*January 29, 2015*

**Math**

You have made a contradictory statement. Is there a question?
*January 28, 2015*

**mixed number**

But he did tell you that in the first place. Did you not look at his solution? Looks pretty straight forward and correct to me.
*January 28, 2015*

**Geometry midpoint formula**

midpoint of diameter = ( (6+15)/2 , (8+8)/2) = ( 21/2 , 8) equation: (x-21/2)^2 + (y-8)^2 = r^2 plug in (6,8) 81/4 + 0 = r^2 (x-21/2)^2 + (y-8)^2 = 81/4 any other point? how about the y-intercept, let x = 0 441/4 + (y-8)^2 = 81/4 y-8 = ±√90 = ±3√10 y...
*January 28, 2015*

**Math**

Wow, 10 in a row without a single sign from you that you tried or where your difficulty lies. Where are you having difficulties, or did you just assume that we would do this assignment for you?
*January 28, 2015*

**Math**

you know A = π r^2 replace r with 2t^2 + 1 and expand differentiate to find the rate of change plug in t = 2
*January 28, 2015*

**Math**

rate of change of volume = change in volume / change in time = (30-0)/(5-0) = 6 cm^3 /second so if it fulls up at 6 cm^3 in 1 second , how much will there be in 12 seconds ?
*January 28, 2015*

**math**

-32 ≤ 24-2f 2f ≤ 24+32 2f ≤ 56 f ≤ 28 5 + c/9 ≥ -31 c/9 ≥ -31-5 c/9 ≥ - 36 c ≥ -324
*January 28, 2015*

**Geometry**

Let's assume that you are hanging the picture vertically, that is, the width is 20 and the length vertically is 25. so you want to maintain the ratio of height : width right now, height : width = 25 : 20 = 5 : 4 new width = 20+10 = 30 new height = x x/30 = 5/4 4x = 150 x...
*January 27, 2015*

**math**

number of pages ---- x (5/12)x = 24 x = 24(12/5) = 57.6 ??? You have confusing information. According to your wording the 24 pages he read on Monday were 5/12 of the total, but that came out to a partial page. Is that what you wanted? Were there perhaps 3 days?
*January 27, 2015*

**algebra**

2l + 2w = 22 l + w = 11 ---> l = 11 - w area = 30 lw = 30 (11-w)(w) = 30 11w - w^2 = 30 w^2 - 11w + 30 = 0 (w-5)(w-6) = 0 w = 5 or w = 6 if w = 5 , l = 11-5 = 6 if w = 6, l = 11 - 6 = 5 the dimension is 5 by 6 mm
*January 27, 2015*

**Math**

If you haven't already done so, you must memorize the basic trig rations of the 30-6-90° right-angled triangle, as well as the 45-45-90 triangle I often make a quick sketch of those and it is then easy to get those trig ratios you should recognize that tan60° = &#...
*January 27, 2015*

**math**

base will be 20-2x by 20-2x, and the height will be x Volume = x(20-2x)(20-2x) or x(20-2x)^2 clearly each of the dimensions must be positive, so 20-2x > 0 -2x > -20 x < 10 In my notation, 0 < x < 10, I will let you change it to yours.
*January 27, 2015*

**Calculus**

cost to produce 120 units = C(120) = 1000+5.7(120) + .7(120^2) = = 11764 cost to produce 100 units = C(100) = 8570 rate of change = (11764-8570)/(120-100) = 3194/20 = 159.70 dollars/unit repeat the process for 100 to 101
*January 27, 2015*

**algebra 2**

You have a typo and don't state how high above the water the diving board is. I will give it an arbitrary value of 6 ft. So the equation of height is h = -16t^2 + 10t + 6, where h is in ft and t is in seconds , where t ≥ 0 for a max height, we need the vertex of that...
*January 27, 2015*

**physics- vectors**

You must have meant, "What are (a) the magnitude and (b) the angle (relative to +x) of Vector C " A = (11.6cos36.5 + 11.6sin36.5) = (appr 9.32, 6.90) B = (14cos17.1 + 14sin17.1) = (appr13.38 , 4.12) vector C = (22.71 , 11.02) magnitude = √22.71^2 + 11.02^2) = ...
*January 27, 2015*

**algebra**

Algebaric expressions: algebraic expressions that are just plain barbaric.
*January 27, 2015*

**Kate**

I made a rough sketch of triangle JKR and filled in the angles. A basic property of triangles is that in any triangle, the smallest side is opposite the smallest angle, and the largest side is opposite the largest angle Since angle J of 75° is the largest, side RK must be ...
*January 27, 2015*

**math**

or, stated another way if x = 0 , y = -16 let's plug it in.... 0 + k(-16) + 15 = 0 k = 15/16
*January 26, 2015*

**math**

let's just look at the antifreeze, right now the volume of antifreeze is .7(4) L or 2.8 L Let the amount of the current fluid we are draining be x L Now 70% of that is antifreeze, so the amount of antifreeze we lose is .7x So the actual amount of antifreeze left in the rad...
*January 26, 2015*

**Math**

co-workers check -- x your check ------- .7x x + .7x = 695 1.7x = 695 x = 408.82 co-wks = $408.82 yours = .7(408.82) = $286.18 add them up to verify my answer
*January 26, 2015*

**Math**

Do you have a typo? You said, "What is P ?" but you said P = {1,2,3,4} , so we know it
*January 26, 2015*

**Math**

yes, the correct answer is 7/9 I was just objecting to the messy way that Kudum was writing the expression. Please read my answer to Kudum carefully
*January 26, 2015*

**@ Kudum - Math**

the expression 2/3/6/7 is in very bad form You MUST use brackets to establish the proper order of operations. the question was (2/3) ÷ (6/7) = (2/3)(7/6) = 7/9 but if you type in your expression 2/3/6/7 into any modern calculator, which are designed to follow the ...
*January 26, 2015*

**math**

Are you reading my replies to your posts? http://www.jiskha.com/display.cgi?id=1422288228
*January 26, 2015*

**math**

I will assume you are trying to type: A 6 cylinder car has cylinders with ..... volume of one cylinder = π(2.22^2)(3.25) = 50.3198..... so the engine is 6(50.3198..) = 301.9 cubic inches
*January 26, 2015*

**math**

same thing again, plug in the straight line equation, and solve
*January 26, 2015*

**math**

You could but you don't have to recall that x = (-b ± √(b^2 - 4ac)/(2a) Judging from the type of question you have been asking, I trust you have learned the properties of the "discriminant" b^2 - 4ac I gave them to you in one of the posts.
*January 26, 2015*

**math**

Same thing as your last post Just evaluate b^2 - 4ac and decide
*January 26, 2015*

**math**

intersect the line with the parabola kx^2 - 5x + 2 = -3x + 4 kx^2 - 2x - 2 = 0 Looks like you are studying the nature of the roots, remember that if b^2 - 4ac > 0 you will have two solutions b^2 - 4ac = 0 you will have 1 solution (2 equal ones) b^2 - 4ac < 0 , there is ...
*January 26, 2015*

**Maths**

Outer dimension of the picture : 44 by 34 area whole thing including the frame = 44x34 = ... area of picture = 40x30 so area of frame = ???
*January 26, 2015*

**Math**

Perhaps I am missing something, but if we fill each of the labeled bottles just once, the big bottle can contain as little as 18 L 1 x (4L + 6L + 8L) = 18L
*January 26, 2015*

**Math**

The is a quadratic equation: sin^2 x - sinx - 2 = 0 (sinx - 2)(sinx + 1) = 0 sinx = 2 , which is not possible or sinx = -1 x = 3π/2 or x = 270° location on unit circle --- (0,-1) period --- 2π general solution x = 3π/2 + 2kπ
*January 26, 2015*

**Add maths form 4**

using the properties dealing with the nature of the roots, if there are two equal roots, then b^2 - 4ac = 0 so in hx2 _ 4kx + 9h = 0 16k^2 -4(h)(9h) = 0 16k^2 = 36h^2 4k = 6h h/k = 4/6 So h : k = 4 : 6 = 2 : 3 They should have reduced their answer to 2:3
*January 26, 2015*

**algebra 1**

Yes, your question was answered. http://www.jiskha.com/display.cgi?id=1422242533 Always check back to avoid un-necessary duplication of answers such as this. Secondly it does not help if you switch names.
*January 26, 2015*

**Math**

let the angles in order of size be x , a , b, 2x "The difference between the smallest and second smallest angles" ---> a-x "the difference between the biggest and second biggest angles" ---> 2x-b 2x - b = a - x 3x = a+b also we know x + a + b + 2x = ...
*January 26, 2015*

**TO REINY**

check our previous post for the explanation
*January 25, 2015*

**ALGEBRA**

you showed this: x+0.05<632 x<632/0.05 x<??????? following my argument, you should have had x + .05x < 632 x is a common factor x(1 + .05) < 632 x(1.05) < 632 ahhh, now you see where that 1.05 comes from, right ?
*January 25, 2015*

**ALGEBRA**

When you pay for an item with sales tax of 5% you pay the price + the sales tax = 100% + 5% = 1 + .05 = 1.05 similary a sales tax of 7% ---> you pay 1.07 etc
*January 25, 2015*

**ALGEBRA**

1.05x = 632 x = 632/1.05 = 601.90 The machine should cost less than 601.90
*January 25, 2015*

**Calc**

I agree with SJ but I would look at the backend of this thing first. Consider 1/x As x --->0 , 1/x becomes infinitely large but we are taking cos(???) and the result of cos(anything) is a number between -1 and 1 so e^(cos(1/x)) lies between e^-1 and e^1 or between 1/e and e...
*January 25, 2015*

**algebra**

let the first odd integer be n then the next even integer is n+1 3n < 4(n+1) by 11 3n = 4(n+1) - 11 3n = 4n + 4 - 11 7 = n the first odd integer is 7, then next even one is 8 check: 3 times the first = 21 4 times the second = 32 Is 21 eleven less than 32 ??, YES
*January 25, 2015*

**calculus**

how about y = 7x^2/((x-7)(x-9))
*January 25, 2015*

**Calc 1**

1. lim ( √(x+4) - 2)/x , as x-->0 =lim ( √(x+4) - 2)/x * ( √(x+4) + 2)/( √(x+4) + 2) = lim (x+4 - 4)/(x(√(x+4) + 2) = lim 1/( √(x+4) + 2) , x --> 0 = 1/(2+2) = 1/4 #2. In any limit question, the first thing I do is to sub the approach ...
*January 25, 2015*

**Calculus**

1. y = x^3 , at x = 1, y=1, so we have the point(1,1) dy/dx = 3x^2 , which is 3, when x = 1 y-1 = 3(x-1) y-1 = 3x-3 3x - y = 2 or y = 3x - 2 2. Lim sinxcos 2x/(3x) = lim sinx/x * cos 2x/3, as x ---> 0 = (1)*(1/3) = 1/3
*January 25, 2015*

**Algebra**

original price = x sale price = .85x x - .85x = 180 .15x = 180 x = 180/.15 = 1200 $1200 for a cell phone ?? check: 15% of 1200 = 180
*January 25, 2015*