Tuesday
September 16, 2014

Posts by Reiny


Total # Posts: 27,117

math
avg rate of change = (23500 - 8750)/(8 = ...
March 27, 2014

Math
treat it as two ordered pairs (t, c) where t is temperature and c is consumption so we have (90,220) and (76, 178) slope = (220-178)(/(90-76) = 42/14 = 3 so: c-220 = 3(t-90) c = 3t - 270+220 c = 3t - 50 check: if t = 90, c = 270-50 = 220 if t = 76, c = 228 - 50 = 178
March 27, 2014

Math
no, 26x^2 ≠ x√26 Whatever made you think so. let x = 4 26(4^2) = 26*16 = 416 xV26 = 4√26 = appr 20.4 is 416 = 20.4 ???? However, you could write 26x^ as (x√26)^2
March 27, 2014

Math
Imagine "opening up" a cylinder, what would you get? 2 equal circles + a rectangle whose length is the circumference of the circle and whose height is the height of the cylinder. so SA = 2π(6^2) + 2π(6)(20) = 72π + 240π = 312π = appr 980 No ...
March 27, 2014

Math
I assume you pick a card, then throw the die primes from 1-10 : 2,3,5,7 , so 4 of them primes on a die: 2 3 5, so 3 of them prob(2 primes) = (4/10)(3/6) = 1/5 prob(not 2 primes) = 4/5 odds in favour of getting two primes = (1/5) : (4/5 = 1 : 4
March 27, 2014

2nd question - math help!!
(x+y)^2-x-y = (x+y)^2 - (x+y) = (x+y)(x + y - 1)
March 27, 2014

math help!!
To make it easier to see, let 2x^2 - x = a so you have 2a^2 - 3a - 9 = (a-3)(2a+3) put the original back in = (2x^2 - x - 3)(4x^2 - 2x + 3) = (x + 1)(2x - 3)(4x^2 - 2x + 3)
March 27, 2014

Math
cosine law .... 5.4^2 = 6.2^2 + 3.6^2 - 2(6.2)(3.6)cosR cosR = 22.24/44.64 = .4982.. R = 60.1°
March 27, 2014

Math
direct application of the sine law: x/sin41 = 96/sin71 x = 96sin41/sin71 = ....
March 27, 2014

Calculus Help Please!!!
According to Newton's Law of Cooling T(t) = roomtemp + (37 - 20)e^(-kt) , where t is the time in hours and k is a constant so we get two equations: 32.5 = 20 + 17e^(-kt) ---> 12.5 = 17e^(-kt) and 30.3 = 20 + 17e^(-k(t+1)) ---> 10.3 = 17e^(-kt - k) divide them: 115/...
March 27, 2014

Algebra
did you try factoring both expressions? They factor quite easily. Then divide out the common factor, don't forget to state the restriction.
March 27, 2014

trig
Not sure what notation you are using when you say "blowing in at 53° " is North your 0° and you are going clockwise, or is 0° your positive x - axis and you are going counterclockwise ?
March 27, 2014

Calculus
just using ln a^b = b ln a ln (243^3/5 *32^4/5) = ln ( (3^5)^(3/5) * (2^5)^(4/5) ) = ln ( 3^3 * 2^4) = ln (27*16) = ln(432) 1/5 ln (243^3 * 32^4) = ln [ (243^3 * 32^4) ^(1/5) ] = ln (243^(3/5) * 32^(4/5) ) = .... = ln(432)
March 27, 2014

Calculus
I agree with Damon's "huh" since ln (243^3/5 *32^4/5) = 1/5 ln (243^3 * 32^4)
March 27, 2014

FINANCE
choice A: pay 3100(.85) or 2635 now choice B: pay 12 payments of 270 present value of the 12 payments at a monthly rate of i = 270( 1 - (1+i)^-12)/i= 2635 hard to solve, let Wolfram do it for us (I changed the i to x, since Wolfram thinks i = √-1 ) http://www....
March 26, 2014

math 2
let E(x,y) be your point use ratios ... for the x: (x-3)/(11-3) = 3/8 8x-24 = 24 8x = 48 x = 6 for the y: (y-4)/(3-4) = 3/8 8y - 32 = -3 8y = 29 y = 29/8 E is (6,29/8)
March 26, 2014

math
y - 6 = .5x - 3.5 y = .5x - 3.6 + 6 y = .5x + 2.5
March 26, 2014

math
slope of AB = 4/-2 = -2 so slope of new line = +1/2 new line: y-6 = (1/2)(x-7) expand and doctor it up any way you want.
March 26, 2014

argggh - Calculus
messed up in my expansion volume should have been 4x^3- 120x^2 + 800x and V' = 12x^2 - 240x + 800 = 0 3x^2 - 60x + 200=0 to get x = 4.23
March 26, 2014

Calculus
First things first: width --- s length ---- 2s 2s^2 = 800 s^2 = 400 s = 20 so the piece of metal is 20 by 40 let the side of the square to be cut out be x so the width is 20-2x the length is 40-2x the height is x Volume = x(20-2x)(40-2x) = 2x^3 - 120x^2 + 800x d(Volume)/dx = ...
March 26, 2014

Algreba
What about it ?
March 26, 2014

Calculus
you should have recalled that sin (-x) = -sinx so that sin(-.1) could not have been positive. did you mean -.1 ?
March 26, 2014

Math
slope of new line must be -2 so y =-2x + b plug in the given point (2,-7) -7 = -2(2) + b -3 = b y = -2x - 3
March 26, 2014

Calculus
yes v(t) = h ' (t) = -16t + 5 so v(0) = -16(0) + 5 = 5
March 26, 2014

math
times 8 8B = 3(A-10) 8B = 3A - 30 8B+30 = 3A A = (8B+30)/3
March 26, 2014

Math
divide the fist equation by 2 to get y = 9x now plug that into the second: 9x - 6 = 2x 7x = 6 x = 6/7 then y = 9(6/7) = 54/7 x = 6/7 y = 54/7
March 26, 2014

math
I suspect that your equation is C = 6u^2 v (usually they would not separate factors of 6 and 2 like you did, and would have C = 12uv instead) Please confirm.
March 26, 2014

Math
prob(2dimes) = (8/14)(7/13) = 4/13
March 26, 2014

Math
consider the equation of the circle with centre (1,2) and radius 10 Its equation is (x-1)^2 + (y-2)^2 = 100 (7, 10) satisfies that equation, (7-1)^2 + (10-2)^2 = 100 6^2 + 8^2 = 100 36+64 = 100 100=100 so it is (7,10)
March 26, 2014

College Calculus
let Ø be the angle between them the angular velocity of the minute hand = 2π/60 rad/min = π/30 rad/min the angular velicity of the hour hand = 2π/(12(60)) or π/720 rad/min then, so dØ/dt = (π/30 - π/720) rad/min dØ/dt = 23&#...
March 26, 2014

Math
looks like a combination recursion let term(n) be the nth term, term(1) = 2 if n is odd: term(n) = 3term(n-1) if n is even: term(n)= term(n-1) - 2 so the next terms are: 26, 78, 76, 228, 226, 678 .....
March 26, 2014

integer Math
Since they gave the answer as 7 , I am taking a guess that they wanted √52
March 26, 2014

Math
x( 1.07^27 - 1)/.07 =25000 x(74.483823..) = 250000 x = $ 3356.43
March 26, 2014

Precalculus II
don't you just love Wolfram http://www.wolframalpha.com/input/?i=plot+sec%5E2%28x%29%2B+3+tan%28x%29%3D5%2C+-2π+%3C+x+%3C+2π
March 26, 2014

math
Steve, that is really scary.
March 26, 2014

math
period of first = 2π/(12π) = 1/6 period of 2nd = 2π/(18π) = 1/9 1/3 is a factor of both, so the period = 1/3 verification: http://www.wolframalpha.com/input/?i=10+sin%2812+pi+t%29%2B4+cos%2818+pi+t%29
March 26, 2014

Finance
300( 1 - 1.01^-n)/.01 = 2000 300(1 - 1.01^-n) = 20 1 - 1.01^-n = 1/15 14/15 = 1.01^-n ln both sides and use rules of logs ln 14 - ln15 = -n ln 1.01 n = (ln 15 - ln 14)/ln 1.01 = 6.934 appr 7 months of course I could have used log 15 etc. and obtained the same result.
March 26, 2014

math
Who makes up these questions or what kind of strange paint is this? To paint a ceiling of that size should take about 1/2 gallon ( I know, I have too much time on my hand)
March 26, 2014

Math
number of adults --- A number of kids ----- C A + C = 35 12A + 7C = 315
March 25, 2014

calcules
Just noticed that both Damon and I answered a very similar question in the first of the Related Questions below http://www.jiskha.com/display.cgi?id=1268848081 I suggest you print it out , and change the numbers, and units.
March 25, 2014

math
solve 2 = e^(.07t) hint: take ln of both sides and use your log rules remember ln e = 1
March 25, 2014

math
what is 48000( 1.0105)^40 ?
March 25, 2014

Trigonometry
tan Ø = -√3 I know that tan 60 = +√3 and Ø could be in II or in IV in II , Ø = 180-60° = 120° or 2π/3 in IV, Ø = 360-60 = 300° or 5π/3
March 25, 2014

Calculus
let the number be x, and the sum as stated be S S = x^2 + 1/x dS/dx = 2x - 1/x^2 = 0 for a max/min 2x = 1/x^2 2x^3 = 1 x^3 = 1/2 x = (1/2)^(1/3) or the cube root of 1/2
March 25, 2014

Math
Brady, after all that work, you blew the final answer x+3x+6x = 180 10x=180 x = 10 but I called the angles x, 3x, and 6x so the angles are 18° , 54° , and 108° and of course 108° is the largest angle
March 25, 2014

Math
let the angles be x , 3x and 6x x + 3x + 6x = 180 take over ....
March 25, 2014

Grade 12 Calculus
I hope your function looks something like this: R(x) = (5000 - 100x)(30 + x) = 150000+ 5000x - 3000x - 100x^2 = -100x^2 + 2000x + 150000 this is a standard parabola opening dowwards , so it will have a maximum the x of the vertex is -b/(2a) = -2000/-200 = 10 So there should be...
March 25, 2014

Trigonometry
if sinx = -2/√5 in III y = -2, r = √5 , by Pythagoras, x^2 + 4 = 5 x = -1 in III cosx = -1/√5 tanx = sinx/cosx = (-2/√)/(-1/√5) = 2 sin 2x = 2sinxcosx = 2(-2/√5)(-1/√5) = 4/5 cos 2x = cos^2 x - sin^2 x = 1/5 - 4/5 = -3/5 tan 2x = 2tanx...
March 25, 2014

math
spent on perches --- x litter -------------- x -326 litter and perches combined = 2x - 326 nesting = 2(2x-326) 2x-326 + 2(2x - 326) = 4050 should be relatively easy to solve for x I get x = 838
March 25, 2014

Algebra 2
help with what? you didn't ask a question. your function simplifies to ... d(x) = 54x^10/(24x^8) = 4x^2 / 9 surely that wasn't your question, was it ?
March 25, 2014

MATH
so 2 + 4 + 8 + 16 + ... = 178 sum(n) = a(r^n - 1)/(r-1) 2(2^n - 1)/1 = 178 2^n - 1 = 89 2^n = 90 I know 2^6 = 64 2^7 = 128 2^8 = 256 So I agree with your answer , at the end of 7 you only have 128 but you need 178 so it must be the 8th month how did they come up with 10? ...
March 25, 2014

Math
first tell me what you got for your inverse matrix
March 25, 2014

Geometry B
x^2 + y^2 − 2x + 2y − 1 = 0 , notice how we indicate exponents complete the square x^2 + y^2 − 2x + 2y = 1 x^2 - 2x + 1 + y^2 + 2y + 1 = 1+1+1 (x-1)^2 + (y+1)^2 = 3
March 25, 2014

math
http://www.wolframalpha.com/input/?i=y+%3D+1%2F%283-x%29 asymptote at x = 3
March 25, 2014

discrete mths
(white, red) ----> 12 13 14 15 16 (5 of them ----> 23 24 25 26 (4 of them) ----> 34 35 36 (3 of them) ----> 45 46 (2 of them) ----> 56 just one so 5+4+3+2+1 = 15 prob(your event) = 15/36
March 25, 2014

algebra 2
complete the square ... y = -4(x^2 - (3/4)x .....) - 6 , (we usually don't say +-6 to adding a negative 6 ) = -4(x^2 - (3/4)x + 9/64 - 9/64) - 6 , ( take 1/2 of 3/4 to get 3/8, now square that ----> 9/64 = -4( (x - 3/8)^2 - 9/64) - 6 = -4(x-3/8)^ + 9/16 - 6 = -4(x - 3/8...
March 25, 2014

Trigonometry
http://www.wolframalpha.com/input/?i=y%3D2sin%28x-2pi%2F3%29 for x-intercepts, y = 0 2sin(x-2pi/3) = 0 sin(x-2pi/3)=0 but sin 0 = 0 and sin π =0 and sin 2π = 0 so x - 2π/3 = 0 and x -2π/3 = π and x - 2π/3 = 2π x = 2π/3 or x = π + 2...
March 24, 2014

math
amount in B ---- x amount in A -----x - 8000 .04x + .08(x-8000) = 1040 times 100 4x + 8(x-8000) = 104000 I am sure you can finish it
March 24, 2014

Algebra
-5 + 2x^2 = -6x 2x^2 + 6x - 5 = 0 x = (-6 ± √(36 - 4(2)(-5))/4 = (-6 ± √76)/4 = (-6 ± 2√19)/4 = (-3 ± √19)/2
March 24, 2014

Implicity
1 + 4x dy/dx + 4y (1) = 2y dy/dx 1 + 4y = 2y dy/dx - 4x dy/dx dy/dx(2y - 4x) = 1 + 4y dy/dx = (1+4y)/(2y-4x)
March 24, 2014

Calculus A
I will assume you meant: h(x) = x^2 + 5x + 4/(x-1) h ' (x) = 2x + 5 - 4/(x-1)^2 = 0 for max/min 2x + 5 = 4/(x-1)^2 (2x+5)(x^2 - 2x + 1) = 4 2x^3 - 4x^2 + 2x + 5x^2 - 10x + 5 = 4 2x^3 + x^2 - 8x + 1 = 0 hard to solve, Wolfram has this http://www.wolframalpha.com/input/?i=2x...
March 24, 2014

math
after 1st round 7 people receive email after 2nd round 7^2 or 49 receive email after 3rd round 6^3 or 343 receive email after 4th round 7^4 or 2401 receive email after 5th round ...........16807 receive email number receiving email in 5th round = 7^5
March 24, 2014

math
correct, so .....
March 24, 2014

math
what is √(300^2 + 50^2 ) ?
March 24, 2014

Maths
in groups of 4 with 2 left over: 6 10 14 .... 94 98 102 106 110 114 in groups of 5 with 1 left over : 6 11 16 21 .....96 101 106 111 116 .... looks like 106 or 4a + 2 = 5b + 1 4a = 5b - 1 a = (5b-1)/4 but 5b+1 > 100 5b > 99 b > 99/5 or 20, 21, ... let b = 21, then a= ...
March 24, 2014

Algebra 1 Answer Evaluation
check by expanding your answer, you will see that the first one is wrong you probably meant a^3 - 5a^2 + 2a -10 , says by grouping, so do that ... = a^2(a-5) + 2(a-5) = (a-5)(a^2 + 2)
March 24, 2014

Algebra
17*w*(2w+4) = 2720 2w^2 + 4w = 160 w^2 + 2w + 1 = 80+1 , I completed the square (w+1)^2 = 81 w+1 = ± √81 w = -1 ± 9 = 8 or some negatiave, which I will reject the width = 8 inches
March 24, 2014

Math
general equation of a conic: Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0 we can eliminate the xy term by finding the angle of rotation Ø , so that tan (2Ø) = B/(A-C) and replacing the x and y with a new X and Y, so that x = XcosØ - YsinØ and y = XsinØ...
March 24, 2014

Algebra
If x=-4 and x = -1 are zeros to one or more of the given functions, then dividing them by both x+1 and x+4 should yield a remainder of zero. I divided x+1 into each of the given functions (I used synthetic division), each yielded a remainder. So x+1 did not divide into any of ...
March 24, 2014

good catch , Calcules
yup, looked over my work and found an error in my SA substitution. SA = 2(4xy) +2(x)(4x) + 2(xy) .... = 10x(231/x^2) + 8x^2 ---->10x(231/(4x^2)) + 8x^2 to produce your answers
March 23, 2014

Calcules
let the height be x then the width is 4x , (the height is 1/4 of the width, this way I have no fractions ) let the length be y volume = (x)(4x)(y) = 4x^2 y 4x^2 y = 231 y = 231/(4x^2) SA = 2(4xy) +2(x)(4x) + 2(xy) = 8xy + 8x^2 + 2xy = 10xy+8x^2 = 10x(231/x^2) + 8x^2 = 2310/x...
March 23, 2014

MATH HELP!!
from the 2nd: 2c + 6d = -34 c + 3d = -17 c = -3d-17 plug into the 1st: 3(-3d-17) - 7d = -3 -9d - 51 - 7d = -3 -16d = 48 d = -3 then c = -3(-3) - 17 = -8 c = -8 , d = -3
March 23, 2014

Algebra II
double the 2nd c - 6d = 16 add to the first 3c = 30 c = 10 back into the 1st 20 + 6d = 14 6d = -6 d = -1 c = 10 , d = -1
March 23, 2014

algebra 2
what is 3500(1.025) ?
March 23, 2014

trig
sin(anything) lies between -1 and +1 so -18sin(71π t) lies between -18 and +18 then p lies between 83-18 and 83+18 or between 65 and 101 period of your function = 2π/(71π) = 2/71 min or appr 1.69 seconds 1.69 seconds = 1 beat 1 second = 1/1.69 beats 60 seconds...
March 23, 2014

maths
distance along flight path = (3/4)(220) = 165 km measured horizontally: cos 25° = x/16 x = 165cos28 = 49.54 km
March 23, 2014

Math
Just noticed that Steve answered the same question when you reposted it just a few entries above this Please avoid reposting the same question, especially when it still shows near the top of the list of questions like it did here. It avoids unnecessary duplication of solutions.
March 23, 2014

Math
vector ab = (-3,4,1) vector dc = (3, -4, -1) = vector cd since their magnitude is the same, and they simply have opposite direction they must be equal and parallel So the figure is a parallogram vector cb = (0,-2,6) area = cross product of ab and cb = (-3,4,1) x (0,-2,6) = (26...
March 23, 2014

Math
loan at 2.8% --- $ x loan at 4.5 % ---- $ 31000-x solve for x .... .028x + .045(31000-x = 1024.40 times 1000 28x + 45(31000-x) = 1024400 etc
March 22, 2014

Algebra
Just noticed a typo (sticking 3 key) <taking the first 3 I got: a = 5.5 , b=-12.5 , c = 12> should say: taking the first 3 I got: a = 53.5 , b=-12.5 , c = 12 btw , I did not show how I solved those 3 equations in 3 unknowns, I used a webpage for that http://www.1728.org/...
March 22, 2014

Algebra
I did the usual analysis and found the first differences to be 145, 250, 358, and 465 and the second differences to be 105, 108, and 107 which appear to be relatively constant at appr 106, so I suspect a quadratic. let N = ad^2 + bd + c, where d is the number of days, and N is...
March 22, 2014

Math (help)
So the punch contained 1 gal of fruit juice and 1 gal of ginger ale, for a total of 2 gallons percentage of fruitjuice = 1/2 * 100% = 50% I have no clue how they get 25%, did you check the wording of the problem?
March 22, 2014

Math
66 2/3 of 39 = (200/3)(39) = 7800/3 = 2600
March 22, 2014

Math
If you have consecutive values of x, like in both your cases, in general if the first differences in the y's are constant, you have a linear function if the 2nd differences in the y's are constant, you have a quadratic function, (as your case above) if the 3rd ...
March 22, 2014

Math
I took first differences and got 2.8 , 8.4 , 14, and 19.6 second differences yielded: 5.6 , 5.6 , 5.6 which tells me that the relationship is a quadratic function. so let y = ax^2 + bx + c, giving us 0 = c 2.8 = a + b + c 11.2 = 4a + 2b + c we know c = 0 so if we double the ...
March 22, 2014

math
sinhx = (e^x - e^-x)/2 and coshx = (e^x + e^-x)/ , by definition. then: 5coshx + 3sinhx = 4 5(e^x + e^-x)/2 + 3(e^x - e^-x)/2 = 4 5e^x + 5e^-x + 3e^x - 3e^-x = 8 8e^x + 2e^-x = 8 times e^x 8 (e^x)^2 + 2 = 8e^x a quadratic, let a = e^x 8a^2 - 8a + 2 = 0 4a^2 - 4a + 1 = 0 (2a - ...
March 22, 2014

maths
The correct answer to your question is: It is a quadratic equation. If you want the solution ... it factors: (3x-1)(3x + 2) = 0 x = 1/3 or x = -2/3
March 22, 2014

precal
from sin 2x = 1/2 2x = π/6 or 2x = π-π/6 = 5π/6 x = π/12 or 5π/12 but the period of sin 2x is π so we get 2 more solutions: x = π/12 + π = 13π/12 or x = 5π/12 + π = 17π/12 in [ 0 , 2π] x = π/12 , 5π...
March 21, 2014

Math - PreCalc (12th Grade)
First of all , I am sure you meant: s(t) = 2t^2 + 3t s(2) = 2(4) + 3(2) = 14 s(4) = 2(16) + 3(4) = 44 total distance = 44-14 = 30 m total time = 4-2 seconds = 2 seconds average velocity = total distance / total time = 30 m/2 seconds = 15 m/s
March 21, 2014

Math - PreCalc (12th Grade)
very similar to http://www.jiskha.com/display.cgi?id=1395410253
March 21, 2014

Math - PreCalc (12th Grade)
Use you "sense" of numbers to see what happens to the fractions as n gets larger. (I think your last term should read 15/(3n^2) or else it becomes large as n gets large) e.g. look at 5/n suppose n = 100,000, then 5/n = .00005 , which is close to zero suppose n = 1,...
March 21, 2014

Math and Music
Perhaps you will find it fascinating to see the relationshipe between music and the Fibonacci Numbers and the Golden Ratio ( google Fibonacci numbers to see thousands of webpages, here is probably one of the best: http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/...
March 21, 2014

arithmetic
interest = 2000(1.0155)^20 - 2000 = 720.37 or "appr" $ 720
March 21, 2014

Math - PreCalc (12th Grade)
spread = 5-2 = 3 if cut into n pieces, each base = 3/n endpoint of 1st rectangle = 2 + 3/n endpoint of 2nd rectangle = 2 + 2(3/n) ... endpoint of kth rectangle = 2 + k(3/n) = 2 + 3k/n f(2+3k/n) = 2(2 + 3k/n) + 1 = 5 +6k/2 I see you have two other questions above that follow ...
March 21, 2014

MATHS
Steve's answer and mine seem to contradict each other, but we defined x differently. Steve defined x as his usual time, so the answer of 7.5 is correct for his usual time I defined x to be the usual speed, and got x = 2/15 so to go 1 km would take 1/(2/15) = 15/2 = 7.5 , ...
March 20, 2014

MATHS
usual speed --- x km/h time at usual speed to go 1 km = 1/x hrs time at 3/4 his normal speed = 1/(3x/4) = 4/(3x) 4/(3x) - 1/x = 2.5 times 3x 4 - 3 = 7.5x 7.5x = 1 x = 1/7.5 = 2/15 km/h
March 20, 2014

Trigonometry
r^2= 7^2 + (-3)^2 = 58 r = √58 since (7,-3) is in IV, cosØ = 3/√58 secØ = √58/3 cotØ = -7/3
March 20, 2014

CORE MATHS
Unless the x term had a coeffecient of zero, then of course you wouldn't count it, so 5a + 10b = 0 ---> a = -2b and 45/2 a^2 + 45b^2 = 90 (45/2)(4b^2 + 45b^2 = 90 90b^2 + 45b^2 = 90 135b^2 = 90 b^2 = 90/135 = 2/3 b = ±V2/√3 if b = +√2/√2 then a...
March 20, 2014

CORE MATHS
(1+ax/2)^10 + (1+bx)^10 = (1 + 10(ax/2) + (10)(9)/2 (ax/2)^2 + ... ) + (1 + 10bx + (10)(9)/2 (bx)^2 + ...) = 2 + (5ax + 10bx) + (45/4) a^2 x^2 + 45b x^2 + .. = 2 + (5a+10b)x + (45/2 a^2 + 45b^2)x^2 + ... first term matches your given, but the 2nd only contains first degree x...
March 20, 2014

math
roughly plot the points to see that you have a rectangle of base = 30 height = 2 area = 2x30 = 60 square units
March 19, 2014

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