Wednesday
December 17, 2014

Posts by Reiny


Total # Posts: 28,220

math
let the height be x then the base is x area of triangle = (1/2)x^2 sum = 2x 2x = (1/2)x^2 - 16 4x = x^2 - 32 x^2 - 4x - 32 = 0 (x-8)(x+4) = 0 x = 8 or x = -4, the latter makes no sense, so if x=8, area = (1/2)64 = 32 check is their sum 16 less than the area? or is 16 less than...
October 22, 2014

algebra
3x^2 + x = 2 3x^2 + x - 1 = 0 no integer solution, (use the formula, it will not come out to be a whole number)
October 22, 2014

Math
2215.1( 1 - (1+i)^-72)/i = 135000 very nasty equation to solve, since there is no "formula" way to do this Wolfram is our saviour. (notice I changed the i to x) the reasonable answer is i = .00470829 for the monthly rate so annual rate = 12(.0047...) = .056499.. or ...
October 22, 2014

arithmetic
the minute hand rotates 360° in 60 minutes or 6° per minute or 3° in 30 seconds. area swept by minute hand in one rotation = π(19^2) = 361π mm^2 so by ratios: 3/360 = area/361π area = 361π(1/120) = 361π/120 mm^2 = appr 9.45 mm^2 check my ...
October 22, 2014

math
How about thinking like this: You want to hand out 1 1/2 dollars or 3/2 dollars in coins If you want to use only quarters (1/4 of a dollar), how many coins (quarters) will you need ? obvious 6 quarters so 1 1/2 ÷ 1/4 = 6
October 22, 2014

pre calc
h = -16t^2 + 16t + 370 -16t^2 + 16t + 370 ≥ 50 16t^2 - 16t -320 ≥ 0 t^2 - t - 20 > 0 (t-5)(t+4) > 0 since this makes sense only for t ≥ 0 you would have 0 ≤ t ≤ 5 ( your first inequality sign is incorrect)
October 22, 2014

pre calc
no big deal, so 1995 --- > 0 but what did he/she change 1990 to ? make the suitable changes
October 22, 2014

pre calc
at x = 0 --- we have 1975 R(0) = 3500 http://www.wolframalpha.com/input/?i=f%28x%29+%3D++-0.121x%5E5%2B2.952x%5E4%2B3500+for+x+%3D+0 http://www.wolframalpha.com/input/?i=f%28x%29+%3D++-0.121x%5E5%2B2.952x%5E4%2B3500+for+x+%3D+1 http://www.wolframalpha.com/input/?i=f%28x%29+%3D...
October 22, 2014

4th Grade math
3x2x1 = 6 different ways
October 22, 2014

7th grade math
2x+3≤-3 2x ≤ -6 x ≤ -3 AND 5x-2<3 5x < 5 x < 1 so -3 ≤ x < 1 looks like {-3, -2, -1, 0 }
October 22, 2014

algebra
yes, I hope you weren't just guessing.
October 22, 2014

metric conversion
kilogram kg = 1000 g hectogram hg = 100 g dekagram dg = 10 g gram g 1 decigram dg = .1 g centigram cg = .01 g milligram mg = .01 g kilometre km hectometre hm dekametre dm metre m decimetre dm centimetre cm millimetre mm same for litre , etc all you need is the prefixes each is...
October 22, 2014

Trigonometry
Ahhh, good observation bob I did a similar type the long way few posts back, could have done it this way as well, would have been shorter
October 22, 2014

Math
Think of it as money. Suppose 12 friends have $5 each how much total money would there be ? ...... $60 So if one person would get all that money, how much would he/she get? ..... $60 If you had to share all the money with 20 people, how much would each get ? ..... 60/20 = $3 ...
October 22, 2014

Trigonometry
I know, I was able to do my diagram. I want YOU to try it, let me know what you get
October 22, 2014

Trigonometry
Looks like a bit of "home-work " dumping here I have done 2 of them for you, you have shown no indication of any of your own work. You try this one. hint: make a diagram to show triangle ABC All the angles in the triangle can be found, and you know one side AB = 300 ...
October 22, 2014

Trigonometry
(cos^2 x - sin^2 x)(cosx) - (2sinxcosx)(sinx) = 0 divide by cosx cos^2 x - sin^2 x - 2sin^2 x = 0 cos^2 x = 3sin^2 x sin^2 x/cos^2 x = 1/3 tan^2 x = 1/3 tanx = ± 1/√3 so x could in in any of the 4 quadrants I know tan 30° = 1/√3 and 30° = π/6 ...
October 22, 2014

Trigonometry
3sinx = 1 + 3cosx square both sides 9sin^2 x = 1 + 6cosx + 9cos^2 x 9(1 - cos^2 x) = 1 + 6cosx + 9cos^2 x 9 - 9cos^2 x = 1 + 6x + 9cos^2 x 18cos^2 x + 6x - 8 = 0 9cos^2 x + 3x - 4 = 0 cosx = ( -3 ± √153)/18 = -.85385 or .5205 if cosx = -.85385 x = 148.6° or x...
October 22, 2014

Algebra
yes
October 21, 2014

math,algebra,fractions, decimals
1/2 = .5 2/3 = .66666.... so terminating decimal between is .58 repeating decimal between is .567676767...
October 21, 2014

math
then I am right check: area of one triangle = (1/2)(3.5)(10.7857 = 18.875 4 such triangle = 4(18.875) = 75.5
October 21, 2014

math
define what you mean by slant height.
October 21, 2014

math
Clearly the surface area would consist only of the 4 triangles. area of one of them = 75.5/4 or 18.875 m^2 area = (1/2)base x height 18.875 = (1/2)(3.5)h h = 2(18.875)/3.5 = appr 10.7857 clean up to whatever accuracy is expected I would say 10.8 , since the original data had ...
October 21, 2014

Algebra
the original value does not matter e.g. let's start with 100,000 after 3 years: value = 100,000(.9)^3 after 3 more years: value = 100,000(.9)^3 (1.1)^3 = 97,029.9 so what do you think? Here is a new question for you. Would it matter if the value first increased by 10% for ...
October 21, 2014

math
any number that can be expressed as a simple fraction of the form a/b, where b ≠ 0 is rational rational --- from ratio --- a: b or a/b A number which cannot be expressed as a simple fraction in the above form is irrational irrational --> not rational (irresponsible...
October 21, 2014

Calculus
f ' (x) = ( (x-2)(2x) - (x^2 + 1)(1) )/(x-2)^2 = (2x^2 - 4x - x^2 - 1/(x-2)^2 = (x^2 - 4x - 1)/(x-2)^2 so f ' (a) = (a^2 - 4a - 1)/(a-2)^2
October 21, 2014

math
correct
October 21, 2014

math
simple interest = PRT = 5000(.09)(2) = $ 900 compound interest = 5000( 1.09)^2 - 5000 = $ 940.50
October 21, 2014

math
-7x^2 + 4x + 9 = 0 7x^2 - 4x - 9 = 0 using the formula ... x = (4 ± √268)/14 = appr 1.455 or x = - .884 the only one that comes close is the last choice Do the other one in the same way
October 21, 2014

math
done, look at your other post
October 21, 2014

Maths
f' (x) = x^(2/3) + (2/3)x^(-1/3) (x-1) = (1/3)x^(-1/3) [ 3x - 2(x-1) ] = (1/3)x^(-1/3) [ x + 2] = 0 for a max/min x = 0 or x = -2 checking the f(x) for those and the endvalues f(0) = 0 f(-2) = (-2)^(2/3) (-2-1) = -3(-2)^(2/3) = appr 4.76 f(4) = 4^(2/3) (4-1) = appr 7.56 so...
October 21, 2014

algebra
amount at 4% --- x amount at 3% --- 15000 - x solve for x .... .04x + .03(15000-x) = 550
October 21, 2014

Algebra
if 9>-3w-51>60 add 51 60 > -3w > 111 divide by -3 -20 < w < -37 which of course is not possible, since we can't have a number which is greater than -20 AND less than -37 (try to place such a number on a number line)
October 21, 2014

Math
at a time of t minutes, let the height of the water be h ft V = π(6^2)(h) = 36π h dV/dt = 36π dh/dt subbing in our values 3 = 36π dh/dt dh/dt = 1/(12π) ft/min Did you notice that the rate was constant (it did not depend on what h was) ?
October 21, 2014

Math HELP!!!!!
????
October 21, 2014

Algebra
I do not understand your long first sentence. I will attempt to make sense out of it let number of 5 centavo coins be x let the number of 10 centavo coins be y let the number of 25 centavo coins be z "25 centavo coin is 3 times as many 5 coinand" ---- z = 3x "...
October 21, 2014

algebra
another ---- x one integer ---- 4x-3 x(4x-3) = 27 4x^2 - 3x - 27 = 0 (x-3)(4x+9) = 0 x = 3 or x = -9/4 but x was to be an integer so x =3 3 and 9
October 20, 2014

Math
Math is a language Just translate: 25 is --- "25 =" three times a number ---- "3w" , if w is the number decreased ---- " - " 8 --------- " 8 " so what do we have ?
October 20, 2014

math
let x be the total number of beads 2x/3 + 4x/21 + whites = x times 21 14x + 4x + 21whites = 21x 21whites = 3x whites = (1/7)x or (1/7) of the total
October 20, 2014

Pre-Calc
your given point is in quad II, so the cosine of the angle will have to negative. x = -1/5 , y = 1/2 r^2 = 1/25 + 1/4 = 29/100 r = √29/10 cosØ = x/r = (-1/5)/(√29/10) = (-1/5)(10/√29) = -2/√29 they might expect it to be rationalized and want the ...
October 20, 2014

calculus
your dy/dx should be -2sint + 2cos2t = 0 recall that one of the equivalents for cos 2t is 1 - 2sin^2 t so -2sint + 2(1 - 2sin^2 t) = 0 -sint + 1 - 2sin^2 t = 0 2sin^2 t + sint - 1= 0 (2sint - 1)(sint + 1) = 0 sint = 1/2 or sint = -1 but we want quadant I ,so sint = 1/2 t = &#...
October 20, 2014

geometry
You did not state which sides are parallel, so we can't tell If QT || RS, then obviously angle T = 180-23
October 20, 2014

Math
2z dz/dt = 2x dx/dt + 2y dy/dt when x=4 and y = 3 z^2 = 4^2 + 3^2 = 25 z = 5 Now that you have 5 of the 6 terms, just sub those in and solve for dz/dt
October 20, 2014

Calculus
I will guess you meant: f(x) = x^(1/6) - x^(-5/6) then f'(x) = (1/6)x^(-5/6 + (5/6)x^(-11/6) = 0 for critical values factor it .. (1/6)x^(-11/6)[ x + 5] = 0 x = 0 or x = - 5 sub those values back into the original function if you need the y values
October 20, 2014

Calculus
I will give you the derivative, you should be able to take it from there f ' (x) = (x^6(1/x) - lnx(6x^5) )/x^12 = (x5 - 6x^5(lnx))/x^12
October 20, 2014

Calculus
f'(x) = 12x^2 - 36x - 480 =0 for max/mins divide by 12 x^2 - 3x - 40=0 (x-8)(x+5) = 0 x = 8 or x = -5 You should know the general behaviour of cubic curve with a positive x^3 term and critical values at -5 and 8 I will give you the decreasing interval, it is between -5 and...
October 20, 2014

arithmetic
(7(9) + x)/8 = 6 63 + x = 48 x = -15 So you would have to add a negative number ?
October 20, 2014

Trigonometry
So A in in quadrant III tan 2A = 2tanA/(1 - tan^2 A) = 2(1/3)/(1 - 1/9) = (2/3) / (8/9) = (2/3)(9/8) = 18/24 = 3/4
October 20, 2014

Calculus
Your dy/dx should be (2y-4x)/(3y^2 - 2x) (the way you have it, only the -4x is divided by 3y^2 ) so when y = 2 , in the original, 2x^2 - 4x + 8 = 14 2x^2 - 4x - 6 = 0 x^2 - 2x - 3 = 0 (x-3)(x+1) = 0 x = 3 or x = -1 b) you probably meant to say: Find the equation of the tangent...
October 20, 2014

Math
You are right. It is not so much of an equation, but rather a statement. I would simply say: cost per child = 192/16 as the "equation"
October 20, 2014

math
let the sides be x , 3x , 5x, and 7x x+3x+5x+7x = 64 solve for x back-substitute to find any or all sides
October 20, 2014

calculus
Question makes no sense. It appears whole words are missing.
October 20, 2014

maths
term7 = a+6d = 6d-8 term9 = a+8d = 8d-8 (6d-8)/(8d-8) = 5/8 48d - 64 = 40d - 40 8d = 24 d = 3
October 20, 2014

Math
From the identity sin^2 x + cos^2 x = 1 if we divide both sides by sin^2 x , we get 1 + cot^2 x = csc^2 x so csc^2 x - 1 = cot^2 x RS = cot^2 x LS = csc^2(x)cos^2(x) = (1/sin^2 x)(cos^2 x) = cot^2 x = RS All done
October 20, 2014

Algebra
slope = (1-0)/(3-(-3)) = 1/6 so y = (1/6)x + b plug in (-3,0) 0 = (1/6)(-3) + b b = 1/2 y = (1/6)x + 1/2
October 20, 2014

math
since a = 2m/s^2 , note you have a typo there. v = 2t + c when t = 3, v = 6 6 = 2(3) + c c = 0 v = 2t so at top of hill, t = 0 then v = 0
October 20, 2014

algebra
3/(5-i) = 3/(5-i) * (5+i)/(5+i) = (15 + 3i)/(25-i^2) = (15+3i)/26
October 19, 2014

Math
contradiction: you say the diameter of the cone is the same as the diameter of the ice crream, but then you say 4 cm scoop of ice cream vs 7 cm of diameter of cone
October 19, 2014

math
Ø = tan^-1 (4/3) so you have right-angled trianle with opposite side = 4 and adjacent side = 3 You should recognize the 3-4-5 right-angled triangle, so sinØ = 4/5
October 19, 2014

algebra
Really ???? 10-4x = 0 -4x = -10 x = -10/-4 = 2.5
October 19, 2014

tech math
let the diameter of the small pulley be d let the diameter of the larger pulley be d+7 belt distance covered by smaller pulley in one minute = 136(πd) = 136πd by the larger pulley = 80(π)(d+7) so 136πd = 80π(d+7) divide out the π 136d = 80d + 560 ...
October 19, 2014

Business Math
work on the loan option: balance owing = 7200-720 = 6480 let the monthly rate be x then 205( 1 - (1+x)^-36)/x = 6480 205(1 - (1+x)^-36) = 6480x Equations of this type are very difficult to solve, since there is no "formula" to handle it. In the "olden" days...
October 19, 2014

Calculus
I would have taken the first derivative of -1/(1-x) and simplified it to 1/(x-1) or (x-1)^-1 (If my numerator or my denominator is a constant, I seldom use the quotient rule, since one part drops out anyway) y' = (x-1)^-1 y'' = -1(x-1)^-2 = -1(x-1)^2 f '' (...
October 19, 2014

Maths
recall two properties 1. for y = abc y' = abc' + acb' + bca' etc for multiple factors **** However, if any of the a, b, or c are powers such as (c-4)^4 , then that base of x-4 will appear in each of the terms of y'' ***** very important ! 2. if y'&#...
October 19, 2014

Steve or Damon or bobpursly or ... - Calculus
not quite, your brackets are very important what you have worked out is ... ln (x^x) which is x lnx etc, and your answer would be correct for that but you typed (lnx)^x which would be (lnx)(lnx)(lnx) ... (lnx) , x times we might apply the rule: extension of the product rule if...
October 19, 2014

AP Calc. AB
1. take the derivative of each, not that bad If you have a calculator, just plug in each given value and see what happens or make a sketch of y = sin^2 (x) and y = (1/2)x^2 from appr -1.6 to +1.6 take a few points using your calculator . 2. Did you get the actual derivative? I...
October 19, 2014

Maths
let's use an intuitive approach You might recall that lim (1 + 1/n)^n = e as n ---> ∞ or lim (1 + n)^(1/n) = e , as n ---> 0 now we have (1+sinx)^(1/tanx) now as x ---> 0 , sinx --->0 and 1/tanx ----> ∞ so we have (1 + really small)^really large ...
October 19, 2014

College Algebra (Word Problem)
What's an eld ? let the side parallel to the rive by y ft let the other sides be x ft each so xy = 1200 y = 1200/x cost of fence = 16y + 8(2x) = 16(1200/x) + 16x = 19200/x + 16x d(cos)/dx = -19200/x^2 + 16 = 0 for a min cost. 16x^2 = 19200 Can you finish it?
October 19, 2014

Math
What is 5x5x4
October 18, 2014

math
Use the distance between 2 points formula ... d = √( (4 - (-2))^2 + (-6-2)^2 ) = √(36+64) = √100 = 10
October 18, 2014

algebra
I will assume you want A(w) = √(w^2+13) then A(0) = √(0+13) = √13
October 18, 2014

algebra
wherever you see an x, plug in x+5 f(x+5) = 6(c+5)^2 + 7 = 6c^2 + 60c + 157
October 18, 2014

Math
amount of 36% solution -- x cc amount of 14% solution -- (25-x) cc .36x +.14(25-x) = .25(25) times 100 , (don't like decimals like to avoid them) 36x + 14(25-x) = 25(25) 36x - 14x = 625 - 350 22x = 275 x = 12.5 cc so it looks like 12.5 cc of each
October 18, 2014

math
let the number have the form abc "the first and second digits are multiple of 3 the first digit is greater than the second digit." ---> has to be 63c or 963, would also consider 30c "the sum of the first two digits is 7 more that the third digit " -->...
October 18, 2014

Algebra
difference of squares ... ( (y+2) + 9)( (y+2) - 9) = (y+11)(y-7)
October 18, 2014

Algebra
without "calculating", I can tell that the question is bogus, since only one point is given. Can't find slope if given only one point.
October 18, 2014

Intermediate Algebra
If they have to do their OWN homework, then the question really makes no sense. If it is an assignment type homework were both can work on the project, then beth's rate = 1/6 nina's rate = 1/9 combined rate = 1/6 + 1/9 = 5/18 time at combined rate = 1/(5/18) = 18/5 or ...
October 18, 2014

Algebra
2x^2-5x^3-20x^2+115x-52=0 -5x^3 - 18x^2 + 115x - 52 = 0 5x^3 + 18x^2 - 115x + 52 = 0 no obvious NICE factors the graph suggests 3 real roots, thus no complex zeros http://www.wolframalpha.com/input/?i=5x%5E3+%2B+18x%5E2+-+115x+%2B+52+%3D+0 I suspect a typo
October 18, 2014

Algebra Help
interpretation: 4 roots: 2+2i 2-2i -5 -5 the -5 root twice yields (x+5)^2 for the two complex roots: sum of those two = 4 product of those two = (2+2i)(2-2i) = 8 which gives us the trinomial x^2 -4x + 8 so f(x) = a(x^2 - 4x + 8)(x+5)^2 , where a is any non-zero constant
October 18, 2014

Scientific notation
correct, use 10^4 to show 10 raised to the fourth
October 17, 2014

Scientific notation
the format is to always have a single non-zero digit, followed by a decimal place time a power of 10 69,000,000,000 = 6.9 x 10^10 , exponent is 10 since we moved our decimal 10 places
October 17, 2014

finance
let the quarterly rate be i then 1(1+i)^12 = 3 (1+i) = 3^(3/12) = 3^(1/4) = 1.316 i = .316 or appr 31.6 % per quarter, or appr 126.4% per annum quickly, tell me who is giving us that, I have a few dollars to invest.
October 17, 2014

diff calculus
let the length of the rectangle parallel to the 160 ft side be x let its height be y I see 3 similar triangles, the original and the 2 smaller triangles by ratios: y/(160-x) = 120/160 = 3/4 4y = 480 - 3x y = 120 - 3x/4 area of rectangle = A = xy = x(120 - 3x/4) = 120x - 3x^2/4...
October 17, 2014

algebra 1
no first of all your answer, if that number is supposed to be the answer, is incorrect secondly, I do not like the way you present your answer proper way: 4 = 18 - 3w 3w = 18-4 3w = 14 w = 14/3 or 4 2/3
October 17, 2014

math
did you make a sketch? Isn't it just 5 km due west of where it started from without doing any calculations?
October 17, 2014

Algebra2
the given line has slope -2/3 so your perpendicular line has slope 3/2 new line must be y = (3/2)x + b passing through (-4,3) 3 = (3/2)(-4) + b b = 3 + 12/2 = 9 new line: y = (3/2)x + 9
October 16, 2014

Math
You want the sum of "all " the terms an infinite GS you have a GS, where a = 4/3, r = 1/2 sum(of all the terms) = a/(1-r) = (4/3)/(1-1/2) = (4/3)/(1/2) = 8/3 or 2 2/3
October 16, 2014

calculus
I will ignore the hint and use a very straight-forward method the shortest distance will of course be the normal to the plane going through (1,0,0) plane: 6x + 9y - z + 1 = 0 a normal to the plane is (6,9,-1) and passing through (1,0,0) would be the line x = 6t + 1 y = 9t z...
October 16, 2014

Math
That will depend on what type of sequence we are looking at Is it AS ? Is it GS ? or is it ...?
October 16, 2014

calculus
forget the very last line, I had made corrections, but forgot to delete that line
October 16, 2014

calculus
Last time I did this type of question was 55 years ago, so I hope I can remember. I think we first have to find the area intercepts between y = 25x^2 and y = 4 25x^2 = 4 x = ± 2/5 by symmetry we can go from 0 to 2/5 and double area = 2(integral) (4 - 25x^2) dx from 0 to...
October 16, 2014

Algebra2
were did you get 2^7i from ??? I thought we did 2 i^7 and I thought I did that for you. i^100 = (i^4)^25 = (+1)^25 = 1 I strongly suggest your write down the first 4 or 5 terms of the pattern I gave you and I strongly suggest you read my explanation of that pattern.
October 16, 2014

Algebra2
I assume you want to simplify each one the imaginary number i has very unusual properties watch this cyclic pattern: i i^2 = -1 i^3 = i(i^2) = -i i^4 = i^2 i^2 = (-1)(-1) = +1 i^5 = i i^4 = i(1) = i , and here we go round again notice every even power of i is either +1 or -1 ...
October 16, 2014

Algebra
actually the 2nd is a strange one, as it has an infinite number of solutions 3/x = 3x/x^2 the right side simplifies to 3/x so you have 3/x = 3/x, which of course is true for all values of x except x = 0 (remember, we can't divide by zero)
October 16, 2014

Math
correct
October 16, 2014

math
There were 23 marbles, of which 5 were blue 3 were removed, one of them blue so now there are 20 marbles, of which 4 are blue prob(blue) = 4/20 = 1/5 which is C
October 16, 2014

algebra
width --- x length -- 3x+5 area = x(3x+5) or 3x^2 + 5x
October 16, 2014

Math
yes
October 16, 2014

Math algebra Help please
original: base --- b, height --- h area = (1/2)bh = 24 bh = 48 new triangle: base ---6b, height ----6h new area = (1/2)(6b)(6h) = 18 bh = 864
October 16, 2014

Algebra
Let the time for the first train be t hrs 50t + 70(t-1) = 350 120t = 420 t = 420/120 = 7/2 or 3.5 hrs
October 16, 2014

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