Wednesday
July 30, 2014

Posts by Reiny


Total # Posts: 26,915

Algebra
let's work on the bottom 6^(2n+1) = 3^(2n+1)* 2^(2n+1) = 3^n * 3^(n+1) * 2^n * 2^(n+1) = 3^n * 2^n * 6^(n+1) now the 3^n would cancel the 3^n on top, leaving you with 1/(2^n * 6^(n+1) )

Math; Alegbra
If r = 3 Volume of sphere = (4/3)π r^3 = 36π volume of a cone = (1/3)π r^2 h =3π h 3π h = 36π 3h = 36 h = 12

mathematics
H = (1/28)L L = 28H L + H = 116 28H + H = 116 29H = 116 H = 4 then L = 112 one number is 16 let the other number be 4x then : 16 = 4*4 4x = 4*x 16x = 112 x = 7 and 4x= 28 The other number is 28 check: 16 = 2*2*2*2 28=2*2*7 LCF = 2*2 = 4 HCM = 2*2*2*2*7 = 112 is 4 equal to 1/28...

early morning oops - Math
But .... if the second derivative is linear, the original function must be a cubic. y'' = 6x y' = 3x^2 + a at x = 1 we have y = 5 - 3x is a tangent, so y' = -3 when x=1 -3 = 3(1) + a a = -6 y' = 3x^2 - 6 then y = x^3 - 6x + b at (1,2) 2 = (1)^3 - 6(1) + b b...

Math
ARrgghhh, really? Matrices for such a simple system? ok .... we need the inverse of 4 -2 7 1 I will assume you know how to find the inverse of a 2by2 I get 1/18 2/18 -7/18 4/18 now if we multiply that by 4 -2 7 1 we get 1 0 0 1 on left and the column matrix 33/18 3/18 on the r...

Algebra
from 3x = 4y ---> x = 4y/3 from 12y = 5z --> z = 12y/5 so z/x = (12y/5) / (4y/3) = (12y/5)(3/4y) = 9/5

Calculus
direction of the given line is (1,1) so if Ø is the angle it makes with the x-axis, then tanØ = 1/1 Ø = 45° so a line which makes an angle of 60° with the given line would have an angle of (45°+60°) or 105° or -15° now tan 105° ...

Calculus
A normal to r is (0,1,1) cross (-1,0 3) or (3, -1, 1) , (I assume you know how to find a cross-product) So the plane must look like, 3x - y + z = c , where c is a constant from the line (x-3)/2 = (y+1)/-3 , z=1 the point (3,-1 ,1) must lie on the line, so it must also lie in t...

Math
Ok, starting to make sense now So I will assume you are given: sin(alpha+beta)=(sin alpha)(cos beta)+(cos alpha)(sin beta) and cos(alpha+beta)=(sis alpha)(cos beta)+(sin alpha)(sin beta) I will use A and B for easier typing You must also know that 1. sin(-A) = -sinA 2. cos(-A)...

Math
That's not what you said originally, look at your post. So which identity are we deriving ?

Math
so you want us to use the identity: sin(A - B) = sinAcosB - cosAsinB to prove sin(A - B) = sinAcosB - cosAsinB ? mmmhhh? did you mean sin(A+B) ??

Math
let the time taken since 10:00 am till they meet be t hrs at 10:00 am , train will have already gone 130 miles when they meet, they both will have traveled the same distance, so ... 90t = 130 + 65t 25t = 130 t = 5.2 hrs or 5 hrs and 12 minutes that would put the time at 10:00 ...

Math
1 ---> 4 = 2^2 2 ---> 8 = 2^3 3 ---> 16 = 2^4 4 ---> 32 = 2^5 mmmhhh, look at the exponent of 2 and compare it to your input value. isn't it always one greater ? so .....

error - Algebra
Whoahh there Sheenybeany if the inequality is y/6 > 10 then y > 60 Why did you reverse the inequality sign? It is reversed only if you multiply or divide by a negative. Since we simply multiplied by 6, it stays the same. Since y > 60 is not one of the choices, we eith...

geometry
mmmh, I guess that explains why he is still a bachelor

arggg! ... Geometry
How did I possible see 4 of equal sides ? but... my algebra worked out sooo nice! Reminds me of the classic StarTrek episode where Cpt Picard is tortured by the Kardashians and sees 4 lights. https://www.youtube.com/watch?v=moX3z2RJAV8

Geometry
let the sides be a, b, and c We know: 4a +4b + 4c = 24 ----> a+b+c = 6 and 4ab + 4ac + 4bc = 22 2ab + 2ac + 2bc = 11 The length of the diagonal is √(a^2 + b^2 + c^2) by algebra, we know (a+b+c)^2 = a^2 + b^2 + c^2 + 2ab + 2ac + 2bc subbing in 6^2 = a^2 + b^2 + c^2 +11...

math
The way it is written, I must agree with Steve

Math
start at (-3,-4) and mark it since slope = rise/run = 2/3 the rise is 2 and the run is 3 so from the point (-3,-4) go to the right 3 (run of 3), then go up 2 (rise of 2) mark this new point, join with a line and you are done Easy, eh ??

Math
you replaced the y with -8 , but not the x with -3 Why not? -8 = -2(-3) + b -8 = 6 + b -14 = b so y = -2x - 14

Math
done below

math
1. can you think of two numbers which when multiplies yields -36 and when added is 16 how about 18 and -2 ???? (x+18)(x-2) 2. can you think of two numbers which when multiplies yields 9 and when added is -10 how about -1 and -9 (x^2 - 1)(x^2 - 9) now we have the difference of ...

Math
Natalie, use the method I showed you in your previous post slope of lines parallel to 8x + 4y = 7 = -8/7 slope of perpendicular lines = + 7/8

math
profit = 12.50 - 8.00 = 4.5 percentage profit = 4.5/8 = .5625 or 56.25%

math
I will assume from your poorly worded question that the sale price is $10.00 so if the original is $x .8x = 10 x = 10/8 = 12.50 Now, do you need the profit percentage before or after the sale? You decide

Math
use a two step process 1. take all terms except the y term to the right side 4x + 5y = 3 ----> 5y = -4x + 3 2. divide each term by the coefficient of the y term 5y = -4x + 3 y = (-4/5)x + 3/5 now you have it in the form y = mx + b, where m is the slope, so the slope is -4/5

Calculus
if F' (x) = -7x then F(x) = -(7/2)x^2 + c but F(0) = 1 1 = 0(-7/2) + c c = 1 F(x) = (-7/2)x^2 + 1

math
Johnny, looks like "homework dumping to me" How about showing us what steps you have taken in these problems or indicate where your difficulties lie.

math
I suppose we could do this .... 12V = 3W V = 3W/12 = W/4 then 2W - 8V = 2W - 8(W/4) = 2W - 2W = 0

Geometry
I agree with Bob My understanding of a trifoil has been this: http://www.google.com/imgres?imgurl=http://upload.wikimedia.org/wikipedia/commons/9/9d/Trefoil-Architectural.png&imgrefurl=http://commons.wikimedia.org/wiki/File:Trefoil-Architectural.png&h=218&w=231&tbnid=8TWnpqXUo...

general math
This is how I would have expected my students to write up the solution to this equation 5x − 2 = 2x + 7 5x - 2x = 7 + 2 3x = 9 x = 3

Maths (differentiation)
the way you typed it, Wolfram read it as http://www.wolframalpha.com/input/?i=+Y+%3D+1%2FSinX%5E2 and y = (sinx)^-2 dy/dx = -2(sinx)^-3 (cosx) = -2cotx /sin^2 x or = -2cotx csc^2 x if you meant: y = 1/ sin(x^2) then y = sin(x^2)^-1 dy/dx = -1sin(x^2)^-2 cos(x^2) (2x) = -2x cot...

Math
number of tests before the last one ---> x total marks at that point = 84x then (84x + 100)/(x+1) = 86 86x + 86 = 84x + 100 2x = 14 x = 7 So there were 8 tests, including his perfect test at the end.

Maths
Kelvin --- x Ken ----- x+6 average of Kelvin and Ken = (2x+6)/2 = x+3 David = (x+3) + 6 = x+9 (x + x+6 + x+9)/3 = 42 3x + 15 = 126 3x = 111 x = 111/3 = 37 David is 37+9 = =46 check: Kelvin --> 37 Ken----> 43 David ---> 46 average of Kelvin and Ken = (37+43)/2 = 40 Is ...

math
number of girls = 3x number of boys = 4x (check: total is 7x) total weight of all children = 7x(36) = 252x total weight of all the girls = 3x(32) = 96x so the weight of all the boys = 252x-96x = 156x average weight of boys = 156x/(4x) = 39 kg

Maths
Did you make a sketch? If so, you can see that cosØ = 2/6 = 1/3 Ø = cos^-1 (1/3) = appr 70.5°

math
Let the salaries of A, B, and C be 2x, 3x, and 5x respectively. then 3x + 5x = 8000 8x=8000 x = 1000 A's is 2000 C's is 5000 we don't really have to find their actual salaries amount that C has more than A is 5x-2x = 3x Percentage of that of A = 3x/2x = 3/2 = 1.5 o...

math
breadth --- x length ---- 1.2x 2(x+1.2x) = 88 x+1.2x = 44 2.2x = 44 x = 20 area = x(1.2)x = 1.2(20^2) = 480 m^2

correction - calculus 2
∆x = (6-1)/3 = 5/3 , so ∆x/3 = 5/9 should be ∆x = (6-1)/10 = 5/3 , so ∆x/3 = 5/30 = 1/6 and the 5/3 in front of the big brackets should be 5/30 or 1/6

calculus 2
I assume that you know the formula .... in case you don't, here is the method http://www.mathwords.com/s/simpsons_rule.htm ∆x = (6-1)/3 = 5/3 , so ∆x/3 = 5/9 interval = (6-1)/10 = 1/2 then we have (5/9)[ f(1) + 4f(1.5) + 2f(2) + 4f(2.5) + 2f(3) + 4f(3.5) + 2f(4...

calculus 2
fix your equation first

math
since the function is linear, the slope must be constant for any pair so (12-a)/(1-0) = (b-12)/(2-1) 12-a = b-12 24 = a+b

Math
number of increases of one unit of money (pesos ? or dollars ?) be n price = 10+n number sold = 200-10n revenue = R = (10+n)(200-10n) = 2000 + 100n - 10n^2 completing the square = -10(n^2 - 10n + 25 -25) + 2000 = -10(n-5)^2 + 2250 vertex is (5,2250) price should be 15 max reve...

math
so -9x^2 + 9x + 5 = 0 9x^2 - 9x - 5 = 0 Don't see any obvious facors, so let's use the formula x (9 ± √261)/18 = appr 1.4 or -.4 looks like d)

Calc
let each of the 2 equal sides by x let yeach of the 3 equal sides by y xy = 1,500,000 y = 1500000/x let the length be L L = 2x + 3y = 2x + 4500000/x dL/dx = 2 - 4500000/x^2 = 0 for a min of L 2x^2 = 4500000 x^2 = 2250000 x = 1500 then y = 1500000/1500 =1000 so L = 2(1500) + 3(...

math
Since no choice of 3 points forms a straight line, you are simply finding the number of ways to choose 3 of the 5 points, which is C(5,3) or 5!/(3!2!) = 10

good observation - Trigonometry
Bosnian, thanks for catching that The question used feet as its units, and I just did the math without really thinking about that height. I think the linear units should have been metres and not feet. Both of our numerical values were correct, you also had 171.7 I recall takin...

Trigonometry
I use a slightly different method. In my sketch , I labeled the top of the monument P and the bottom Q By properties of the sum of angles in a triangle, in triangle ABP , angle A = 32°, angle ABP = 142, and angle APB = 6° using the Sine Law: BP/sin32 = 55/sin6 BP = 55s...

Math
I made a sketch, letting the top of the building A I drew in the tower, called the top P and the bottom Q I drew a line from A to B, AB parallel to the ground thus QB = 16 , the same height as the building. We now have two right angled triangles, ABP and ABQ in triangle ABQ, t...

maths
I know math is heavenly, but triangles have angels ?? If the smallest angle is x, then the largest is 5x If they are in AP, then the middle angle must be 3x (note: 3x - x = 5x - 3x , using the common difference relationship) then x + 3x + 5x = 180 9x = 180 x = 20 the angles ar...

math
pieces on disc = 3 + 4 + x = x+7 prob of picking one of the 4 ballads = 4/(x+7) but we are told 4/(x+7) = 1/4 x+7 = 16 x = 9

Math 221*revised*
This is a poorly worded question. " y=x+4 and the parallel must past through this given point (-7, 1) " y = x+4 does not pass through (-7,1) and you cannot make it do it, unless you change its slope or y-intercept. If you merely want a new line which is parallel to y...

MATH
He can use the 2 pennies in 3 ways, take none, take 1 or take 2 He can use the 3 nickels in 4 ways, take none, take 1, etc the dime in 2 ways, and the quarters in 3 ways total number of ways = (3)(4)(2)(3) = 72 but that includes taking none of any coins, so number of ways to u...

Math
1. find what percentage of the trip Keith drove, then his wife must have driven the remaining percentage 2. 1.5J = (1/2)K 3J = K divide by K 3J/K = 1 divide by 3 J/K = 1/3 3. with radius r, area = πr^2 reduce radius by 10% ---> new radius = .9r new area = π(.9r)^2...

MATH
What choices did you pick? Where are your difficulties? I will do the first one, you try the others If A is 125% of B ----> A = 1.25B B = (1/1.25)A = .8A so B is 80% of A

Algebra
When it hits the ground , h(t) = 0 , so -16t^2 + 40t + 5 = 0 16t^2 - 50t - 5 = 0 Now solve this quadratic using the method that you learned. One of the answers will be negative, you would reject that one.

math
8 hrs, 15 minutes = 315 minutes total minutes available for the experiments = 8(315) = 2520 minutes 84 experiments take 2520 minutes 1 experiment takes 2520/84 or 30 minutes

geometry
areas of similar figures are proportional to the square of their sides area1 : area2 = 3^2 : 9^2 = 9 : 81 = 1 : 9

math
You must have meant: area is 2x^3+5x^2-x-6 if so, then it factors nicely into (x-1)(x+2)(2x+3) and the width of 2x^2 + x - 3 factors to (2x+3)(x-1) then (2x^3+5x^2-x-6) ÷ (2x^2+ x-3) = (x-1)(x+2)(2x+3)/( (2x+3)(x-1) ) = x+2 or you could do a long algebraic division as i...

algebra 2
Is this supposed to be the solution to finding the inverse of y = 1/3x - 5 ??? I suggest a 2-step process 1. interchange the x and y variables ----> x = 1/3y - 5 (you had that) 2. now solve this new equation for y x = 1/3y - 5 x+5 = 1/3y times 3 3x + 15 = y so f^-1 (x) = 3x...

Algebra
what do you think ? I just answered it for you in your previous post

Algebra
I would say it is A it simplifies to -x + 3 = 0 , which is linear and not quadratic. If you force the issue and make it look like a quadratic, it would be 0x^2 - x + 3 = 0 so a=0 , b=-1 and c = 0 BUT, in the formula we are dividing by 2a which in this case would be dividing by...

math
if AP , then d = 2k/3 - k = 2k/3 - 3k/3 = -k/3 term 6 = a+5d = k + 5(-k/3) = -2k/3

Math
2160 = 2*2*2*2*3*3*3*5 1344 = 2*2*2*2*2*2*3*7 1440 = 2*2*2*2*2*3*3*5 HCF = 2*2*2*2*3 = 24 2. let their income be x x/10 + x/3 + x/5 + 1320 = x times 150 , the LCM 15x + 50x + 30x + 198000 = 150x 198000 = 55x x = 3600

algebra
(3+2x)^5 = 3^5 + 5(3^4)(2x) + 10(3^3)(2x)^2 + 10(3^2)(2x)^3 + 5(3)(2x)^4 + (2x)^5 =243 + 810x + 1080x^2 + 720x^3 + 240x^4 + 32x^5 by simple observation that a negative base raised to an odd exponent is negative .... (3-2x)^5 = 243 - 810x + 1080x^2 - 720x^3 + 240x^4 - 32x^5 (3+...

algebra 2
use your formula for S(n) S(n) = a(r^n - 1)/(r-1) 405 = a(3^4 - 1)/(3-1) 405 = a(81 - 1)/2 405 = 40a a = 405/40 = 81/8

math
8+4+2+1+1/2+1/4+...+1/32 = 1/32 + 1/16 + ... + 4 + 8 sum = ∑ 2^(n - 6) for n= 1 to 9

math
sum(n) = (n/2)(first + last) sum(11) = (11/2)(1+6) = 77/2

math
volume = lwh = 18(3)(1/3) = 18 cubic feet

coordinate algebra
I don't see any choices, but it would have to be c = 4h

trigonometry
write it as y = -3sec 2(x-π/6) period = 2π/2 = π no vertical translation phase shift π/6 units to the right

Maths
a = b+2 c = b-11 )a+b+c)/3 = 70 a+b+c = 210 b+2 + b + b-11 = 210 3b = 219 b = 73 a = 75 c = 62 check: (73+75+62)/3 = 70 all looks good

Math
the wonders of Wolfram http://www.wolframalpha.com/input/?i=pattern+%2831%2C30%2C27%2C22%2C15%29 actual work did you notice that consecutive differences are -1, -3, -5, -7 ? this forms an arithmetic sequence, so a quadratic will act as the defining function. let the sequence b...

Algebra
e.g. x^2 - 6x = 0 add 9 to both sides x^2 - 6x + 9 = 9 (x-3)^2 = 9 x-3 = ±3 x = 3 ± 3 = 6 or 0 check: by factoring, x(x-6) = 0 x = 0 or x = 6 , as above

Algebra
I betcha I can solve any quadratic equation by completing the square.

math
#2 number of green = x number of marbles after 5 reds are added = x+5 prob of picking red = 1/7 5/(x+5) = 1/7 x+5 = 35 x = 30 there were 30 marbles

math
#1 g/(b+g) = 1/3 3g = b+g b = 2g (g+1)/(b+g+1) = 3/7 7g + 7 = 3b+3g+3 4g - 3b = -4 4g - 6g = -4 g = 2 then b = 4 , which is choice d. #3 1 million is an even number all prime numbers are odd, except the first one, which is 2, thus even so we have the sum of 999,999 odd numbers...

math
looks like a typo in both functions. is it f(x) = x+2 or f(x) = -x+2 ? same for the other one.

Alegbra
If the expression is as you typed it, then -9x - 13x+7 is indeed equal to -22x + 7 and it is your professor who is in error.

Algebra
I will assume you meant to type 9(/x-1)*7/(x-3) which is 63/( (x-1)(x-3) ) or 63/(x^2 - 4x + 3)

math
Make a sketch and set up your ratio. I get height/(30+25) = 20/30 height = 55(2/3) =110/3 ft or 36 ft, 8 inches

math
dimes in box A originally --- x dimes in box B originally --- y case 1: after 25 moved from A to B box A has x-25 box B has y+25 but x-25 = y+ 25 ----> x = y + 50 case 2: after 100 dimes moved from B to A box A has x+100 box B has y-100 but (x+100)/(y-100) = 7/2 7y - 700 = ...

Trigonometry
No need for trig, just use a simple ratio ... height/60 = 5/10 height = 60(1/2) = 30 ft (did you notice the height of the man is 1/2 of his shadow, then the height of the pole must be 1/2 its shadow, or 1/2 of 60, which is 30 )

Trigonometry
done, see your other post above

statistics
prob defective = .05 prob of good = .95 So we want the prob that all are good = .95^14 = .48776... prob of at least one is defective = 1 - .48776.. = appr. .512 The 8000 does not enter the picture, since we have the percentage if we used it then we could proceed as follow numb...

Algerbra 1
again, you should type it as (y+5)/(x^2 + 4y - 32) , the way you have it, the only division is 5/y^2 = (y+5)/((y+8)(y-4)) so which values would make the denominator zero ?

algerbra 1
According to your given choices, I suspect you meant 2/( x(x-3) ) so the restrictions are, x = 0 x = 3 namely, those values which make the denominator zero, thus resulting in an undefined answer.

math
This is the best there is for these kind of questions Just fill in the data http://davidmlane.com/hyperstat/z_table.html

Math 221
2 < y and 7 ≥ y 2 < y and y ≤ 7 or 2 < y ≤ 7

mat/117
Use the formula like I showed you in your other post

mat/117
-3x^2+3x+9=0 x^2 - x - 3 = 0 x = (1 ±√13)/2

Algebra
The wording is poor. Did you mean: " The numerical value of the area of the rectangle is 25 more than the numerical value of 4 times the width" ? if so, then ... width --- x length -- x+4 x(x+4) = 4x + 25 x^2 + 4x = 4x + 25 x^2 = 25 x = 5 The width is 5 units (length...

Algebra
slope = (4 -(-9))/(-3 - (-2)) = 13/-1 = -1 Surely you must have the definition of slope in your notes or in your text.

Algebra
x - y ≥ 2 -y ≥ -x + 2 y ≤ x - 2 draw the line y = x-2 and shade in the region below the line. Since the line is included, make it solid (had it been y < x-2, you would have drawn a dotted line to show it is excluded.)

Math
double the first: 6x - 2y = -24 x + 2y = -18 add them: 7x = -42 x = -6 back into the second: -6 + 2y = -18 2y = -12 y = -6 x = -6 , y = -6

Algebra
I would use substitution, from the 1st: y = 5x-18 sub into the 2nd: -4x - 2(5x-18) = -6 -4x - 10x + 36 = -6 -14x = -42 x = 3 y = 5(3)-18 = -3 x=3 , y = -3

College math
let each of the two equal sides be x let the single side by y then y+2x = 5500 y = 5500 - 2x area = xy = x(5500-2x) = -2x^2 + 5500 Since you labeled it "college" math, I will assume you know Calculus d(area)/dx = -4x + 5500 = 0 for a max of area 4x = 5500 x = 1375 y ...

stats
must be an old-type "crank on the wall" from The Waltons era .... anyway .... I will assume that none of your 6 digit numbers can start with a zero, and that numbers may be repeated, so we can't have a number with no 8 prob of no 8 = 8 x 9^5/(9x10^5) so prob that...

math
i = .105/12 = .00875 n = 12(30) = 360 payment ( 1 - 1.00875^-360)/.00875 = 130000 payment = $1189.16

Math
In 1959 the inch was internationally defined in terms of the centimetre 1 inch = 2.54 centimetres So if you want any precision you have to go back to that basic definition. c) 80 in = 80(2.54) cm = 203.2 cm = 2.032 metres once you have converted to any of the metric units, the...

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