Sunday
September 21, 2014

Posts by Reiny


Total # Posts: 27,130

Math
You are welcome
August 13, 2014

Math
You are just finding the radius of circle with a circumference of 27 inches 2πr = 27 r = 27/(2π) = appr 4.30
August 13, 2014

math
so you want to set the area equal to the circumference .. πr^2 = 2πr r^2 - 2r = 0 r(r-2) = 0 r = 0 , the trivial case or r = 2 so the diameter is 4 inches
August 13, 2014

math
A = (5/4)B 4A = 5B B = (4/5)A B = 80% of A looks like B is 20% less than A
August 13, 2014

Math
You keep repeating the same question, which I answered for you, and which does not make sense.
August 13, 2014

mathematics
Artem! The bell will ring at 0:00 , 0:02 , 0:04 , 0:06 , 0:08, ... The bird will chirp at 0:00 , 0:03 : 0: 06 < 0:09 , ... Can you not see that your choices of answers make no sense ? I don't know of any way to make it more obvious.
August 13, 2014

mathematics
Something wrong with your problem As you stated it, they will occur together in 6 seconds
August 13, 2014

fractions/math / Help!
8 3/7-2 1/2 = 59/7 - 5/2 = 118/14 - 35/14 = 83/14 or 5 13/14 93 = 3x31 524 = 2x2x131 both 31 and 131 are primes
August 12, 2014

Algebra
let the smaller be x then the larger is 9-x " Four times the larger number plus three times the smaller number is 48" ---> 4(9-x) + 3x = 48 36 - 4x + 3x = 48 -x = 12 x = -12 The smaller is -12 and the 21 check: -12 + 21 = 9 , check! 4(21) + 3(-12) = 48 , check!
August 12, 2014

Math
-2/5+(-1/10) = -2/5 - 1/10 = -4/10 - 1/10 = -5/10 = -1/2
August 12, 2014

algebra
For a polygon of n sides, the sum of the interior angles = 180(n-2)°
August 12, 2014

algebra
probably: 1/3 + 5/(s-4) = 2 time 3(s-4) 1(s-4) + 5(3) = 2(3)(s-4) s-4 + 15 = 6s - 24 35 = 5s s = 7
August 12, 2014

algebra
I assume from your 2nd line that your 1st line should have been n/4=(n+1)/(3n) 3n^2 = 4n+4 3n^-4n-4=0 (3n + 2)(n - 2) = 0 n = -2/3 or x = 2
August 12, 2014

algebra
Is your first line, 20/(x^2 + 4x) = 3/(x+4) + 1/x ?? I will assume that, then 20/(x(x+4)) = 3(x+4) + 1/x your LCD is x(x+4) , so let's multiply each term by that ... 20 = 3x + x+4 16 = 4x x = 16/4 = 4 The rest of your post has no relation to your first equation. If it is a...
August 12, 2014

Math
So we need 2 widths and 1 length let the width be x and the length be y 2x + y = 2400 y = 2400-2x Area = A = xy = x(2400-2x) = 2400x - 2x^2 dA/dx = 2400 - 4x = 0 for a max of A 4x = 2400 x = 600 then y = 2400-1200 = 1200 field is 600 ft by 1200 ft
August 12, 2014

math
let the width of the base be x let the length of the base by y 2x + 2y = 50 x + y = 25 ---> y = 25-x volume = V = 5xy = 5x(25-x) = 125x - 5x^2 dV/dx = 125 - 10x = 0 for a max of V 10x = 125 x = 12.5 y = 12.5 the box is 12.5 by 12.5 by 5 cm
August 12, 2014

math
"..having all the digits odd except 9.." but 9 is odd Typo?
August 12, 2014

maths
number of selections without conditions = C(15,6) number of selections as stated = C(6,2) x C(9,3) Problem with your question ..... 2 men and 3 women adds up to only 5 people chosen, but you are choosing 6. Fix your problem and I will continue
August 12, 2014

ramjas
in the original number let the unit digit by x and the tens digit be y the number is 10y+x x+y = 13 then the number reversed is 10x + y 10x + y - (10y + x) = 27 9x - 9y = 27 x-y = 3 add the two equations: 2x = 16 x = 8 then y = 13-8 = 5 the number is 58 check: 85-58 = 27 , all...
August 12, 2014

2nd: Algebra
sale price = 40 - .25(40) = 30 or sale price = .75(40) = 30 (your statement of s = p - .25 makes no sense)
August 12, 2014

Algebra
1st question: not sure if you mean: 5^2 - 4/5 + 2 or (5^2 - 4)/5 + 2 or .... can you see why you might want to use brackets to establish the correct order of operation so, if 5^2 - 4/5 + 2 then 25 - 4/5 + 2 = 27-4/5 = 131/5 if (5^2 - 4)/5 + 2 then (25-4)/5 + 2 = 21/5 + 2 = 31/5
August 12, 2014

mathhhhhhh!
Since it asked for substitution, why not just sub the 2nd into the 1st 5x = 4x - 4 x = -4 now back into the 2nd: y = 5x= 5(-4) = -20 so the intersection point is (-4,-20)
August 11, 2014

Algebra
1. width --- w length -- w+14 w(w+14) = 1632 w^2 + 14w = 1632 w^2 + 14w + 49 = 1632 + 49 I completed the square (w+7)^2 = 1681 w+7 =±41 w = -7 ± 41 = 34 or a negative the width is 34 ft and the length is 48 ft or it factors to (x-34)(x+48) = 0 x = 34 or x = -48 2...
August 11, 2014

math
x^4 - 13x^2 + 36 = 0 (x^2 - 4)(x^2 - 9) = 0 (x - 2)(x + 2)(x - 3)(x + 3) = 0 so x = ±2, ±3 or x = -3, -2, 2 3
August 11, 2014

math
let the load be x N 10x = 5(200) + 2(300) 10x = 1600 x = 160 N
August 11, 2014

Precalculus
First of all I will assume that your equation is in polar form, so it should have been r = 4/(2 - cosØ) converting: r = 4/(2 - x/r) 2r - x = 4 2r = x+4 square both sides 4r^2 = x^2 + 8x + 16 4(x^2 + y^2) = x^2 + 8x + 16 3x^2 - 8x + 4y^2 = 16 3(x^2 - (8/3)x + 16/9) + 4y^...
August 9, 2014

math
so πr^2 = 2πr divide by π and bring the 2r over r^2 - 2r = 0 r(r - 2) r = 0 or r = 2 r = 0 would be no circle r = 2, then diameter is 4
August 9, 2014

co-ordinate geometry
slope between the points (2,4) and 2,-1) = (-1-4)/(3-2) =-5 / 1 so the other line must have slope 1/5 (3k-0)/(2-k) = 1/5 15k = 2-k 16k = 2 k = 1/8
August 9, 2014

math
2nd term is 81 ---- ar = 81 4th term is 9 ----- ar^3 = 9 divide second equation by the first r^2 = 9/81 = 1/9 r = ± 1/3 so ar = 81 a(1/3) = 81 a = 243 ii) you have a type, but now that you have a and r, whatever the question should be simple iii) sum of infinite =a/(1-r...
August 9, 2014

math
There is an infinite number of these, as long as they look like y = (-3/2)x + b , where b is any constant, it would be perpendicular to your given line notice I made my new slope the negative reciprocal of the given one. e.g. y = (-3/2)x + 56 would do
August 8, 2014

Maths - Optimisation
since we had y^2 subbing in 2x for y would give us (2x)^2 = (2x)(2x) = 4x^2 notice it was 4x^2 and not 4x like you stated
August 8, 2014

Maths - Optimisation
Let's put the rectangle on the x-y grid so that A is (0,0) and B is (3,6) the equation of the line from A to B is clearly y = 2x d = √(x^2 + y^2) = (x^2 + 4x^2)^(1/2) = √(5x^2) = (√5)x dd/dx = √5 So for each unit of x, the length changes by √5...
August 8, 2014

Math
-3x^2 – x = 10 3x^2 + x + 10=0 the discriminant is b^2 - 4ac = 1 - 4(3)(1) which is negative, so there are two complex solutions, and the statement is false 2. again it is false, it would be true if the right side = 0 and not 8 or take one the answers, x+5 = 8 x = 3 sub ...
August 8, 2014

Algebra
They double in number every 2 hours 8:00 -- 100 10:00 -- 200 12:00 -- 400 2:00pm -- 800 4:00 pm -- 1600 6:00pm -- 3200
August 7, 2014

ogive-maths
I did not know what ogives are, so I googled it. I can't see why you could not do likewise.
August 7, 2014

geo
slope of the line going through the first two points = (-7-9)/(-12-8) = -16/-20 = 4/5 so going through new point (-5,-15) with the same slope y+15 = (4/5)(x+5) do whatever you have to do further, but that is in point-slope form
August 7, 2014

Maths
5 kg cost 65 1 kg cost 13 500 g or 1/2 kg cost 6.50 ahh , the simplicity of metric!
August 7, 2014

math
Let P be the foot of the tower, and h be the height of the tower let AP = x , then BP = 80-x I see two right-angled triangles tan21 = h/x ---> h = xtan21 tan46 = h/(80-x) --> h = (80-x)tan46 xtan21 = (80-x)tan46 xtan21 = 80tan46 - xtan46 xtan21 + xtan46 = 80tan46 x(tan21...
August 7, 2014

trigonometry
1 km = appr 3280.84 feet 2 km/h = 2(3280.84/3600) ft/s = 1.82269 ft/s let r be the resultant velocity r^2 = 2^2 + 1.82269^2 r = √7.32219.. = appr 2.7 ft/s tanØ = 1.82269/2 , where Ø is in my right-angled triangle Ø = appr 42.34° his direction is ...
August 7, 2014

Maths
my little BASIC program gave the following: Chipmunk BASIC v3.6.5(b3) 4 possible cases: 135 175 518 598 testing for 518 518 ---> 5 + 1^2 + 8^3 = 5+1+512 = 518 YUP! I ran the following little program Chipmunk BASIC v3.6.5(b3) >10 for a = 1 to 9 >20 for b = 0 to 9 >...
August 7, 2014

MATH
The following site takes the place of tables in a textbook http://davidmlane.com/hyperstat/z_table.html click on: Value from an area enter: area 0.7 mean 2.9 sd .6 click on 'below' to get3.214
August 7, 2014

math
mmmmhhh ? Did you try plugging in 8 for t in your given formula ? - remember you would have to square first
August 6, 2014

Math
1/4(8y+4)-18<-1/2(4y-6) times 4, ( so < sign stays the same ) 8y + 4 - 72 < -8y + 12 add 8y+68 to both sides, (no change in the < ) 16y < 80 divide by 16, (no change in < ) y < 5
August 6, 2014

Math- urgent
speed of hockey-puck ---- x (10/7)x = 170 10x = 1190 x = 119 mph
August 6, 2014

math test review
w=7r+6r+5r+4r+3r w = 25r the next multiple of 7r would be 28r for any positive integer of r so we need to add 3r
August 6, 2014

math corrections
that would make it 900/300 = 3 a gear with 3 teeth ????
August 6, 2014

math corrections
2. x = .75x + 6 .25x = 6 x = 24 4. outer radius = .75/2 = .375 inner radius = .625/2 = .3125 so thickness of wall = .375-.3125 = .0625 14. no diagram 24. Think of the teeth laid out linearly For the first gear in 1 minute would cover 30x30 or 900 teeth for the 2nd gear, let ...
August 6, 2014

Geometry
Yup, I was so totally distracted by the second part of his post, that I completely missed and ignored the actual question. Another senior moment!!! but... wasn't that a great explanation?? reminds me of my teaching years, when during an exam a student replied to a certain ...
August 6, 2014

Geometry
both are variations of the relation cos 2A = cos^2 A - sin^2 A or cos 2A = 2 cos^2 A - 1 or cos 2A = 1 - 2sin^2 A We use this to either find trig ratios of double an angle or 1/2 an angle e.g. if we know sin 50° , I could now find ratios for 25° or 100° e.g. you ...
August 6, 2014

math
x^2 + 12x + 4 = 0 does not factor, so I will complete the square, easiest way for this one. x^2 + 12x + 36 = -4+36 (x+6)^2 = 32 x+6 = ±√32 = ±4√2 x = -6 ± 4√2
August 6, 2014

math
Must be mathemagics
August 6, 2014

math
Your post makes no sense to me How is this related to the binomial theorem? 32 ÷ 7 = 4 with a remainder of 4
August 6, 2014

college algebra
number of gallons of the 30% stuff --- x .3x + .14(60) = .2(60+x) 30x + 14(60) = 20(60+x) 30x + 840 = 1200 +20x 10x = 360 x = 36
August 5, 2014

geometry
I interpreted " two of its interior angles are 127 degrees and 135 degrees, and the remaining interior angles are 173 degrees each. " the wrong then. so I should have had 130 + 130 + 130 + 127 + 135 + 173(n-5) = 180(n-2) which gives 652 + 173n - 865 = 180n - 360 n = ...
August 5, 2014

geometry
But Damon's answer contradicts the sum of the inside angles property if n = 21 the sum of the interior angles = 127+135 + 19(173) =3949 which must be a multiple of 180
August 5, 2014

geometry
sum of interior angles of an n-gon = 180(n-2) 127 + 135 + 173(n-2) = 180(n-2) 262 + 173n - 346 = 180n - 360 276 = 7n n = 39.4.. , but n must be a whole number so the question is bogus. Check your wording and typing
August 5, 2014

Math
done
August 5, 2014

algebra
huh? I see no x in a^2 + b^2 = 2014
August 5, 2014

Math
If you want that sum to be less than 7000 x + x+2 + x+4 + x+6 + x+8 = 7000 5x = 6980 x = 1396 so 1396 + 1398 + 1400 + 1402 + 1404 = 7000 but you want the sum to be < 7000 so 1394 + ... 1402 = 6990 if you want the numbers to be less than 7000 6998 + 6996 + 6994 + 6992 + 6990...
August 5, 2014

Math
You have to give more information. It is not arithmetic , nor is it geometric I can make it a quadratic .... term(n) = 3n^2 - 10n + 10 and the three terms you gave me will match. so term(15) = 3(225) - 10(15) + 10 = 535 or a cubic or ....
August 5, 2014

advance algebra
ditto what Steve said in your previous post on this.
August 5, 2014

math test review
I do not understand your m<C=2m<b,m<A=6m<B. In our general usage of angles and sides, a capital letter usually stands for an angle, a small letter stands for the length of the opposite side to that angle, there also seems to be a missing equal sign. If you are ...
August 4, 2014

math
what is 2 more than p ? isn't it p+2 ? area = p(p+2) p^2 + 2p = 8 p^2 + 2p - 8 = 0 which factors to (p+4)(p-2) = 0 p = -4, which is not admissable or p = 2 so the table is 2 m by 4 m check: what is 2 x 4 ?
August 4, 2014

math
done! patience!, you posted the same question only about 8 minutes before this one.
August 4, 2014

math
I assume you meant: If b is a positive integer < 200 a/b = 2/9 9a = 2b a = 2b/9 So b must be a multiple of 9 to have a as an integer the smallest value of b is 9 and the largest value of b is 198 so we have: 9 18 27 .... 180 189 198 to find out how many terms are in this ...
August 4, 2014

MA 1310
rewrite it in the more general form as y = (1/4) cos 3(x + 7/3) compared to y = a cos k(Ø + p) the amplitude is 1/4 the period is 2π/3 the phase shift is 7/3 to the left for your equation in the original form a common mistake would be to state that the sphase shift...
August 4, 2014

geometry
should be 19 cm^3 x/19 = 3^3/2^3 x/19 = 27/8 8x = 513 x = 64.125 cm^3
August 4, 2014

math 4
Value of loan = $300 let the monthly rate be i then 34*(1- (1+i)^-10)/i = 300 hard to solve this type of equation but I have some methods and it gave me i = appr .02343 so the annual rate compounded monthly is 28.1 % check: 34(1 - 1.02343^-10)/.02343 = = 299.9988 , not bad I ...
August 4, 2014

Ha ha - algebra
got me, ( I think 15/60 = 1/3 in non-metric) anyway... Thank you Steve
August 4, 2014

algebra
15/60 or 1/3 chose an hour lunch with no breaks for in 500 people we would expect 1/3 of 500 or 167 to choose the above option
August 4, 2014

math
let Jim's distance be x miles then John's distance is 3-x miles Jim's time = x/4 John's time = (3-x)/5 when they meet, they will both have paddled the same time so ... x/4 = (3-x)/5 5x = 12 - 4x 9x = 12 x = 12/9 miles so Jim's time = (12/9) /4 = 1/3 hour or...
August 4, 2014

geometry
radius of base = 3√3 height^2 + (3√3)^2 = (6√3)^2 find the height, now you have everything needed in the formula for the volume of a cone
August 4, 2014

math
follow the same steps I just showed you in your previous post. Let me know what you got
August 4, 2014

math
let f(x) = 4x^2 - 3x - 8 and use the Remainder Theorem, f(a) = 4a^2 - 3a - 8 = 2 4a^2 - 3a - 10 = 0 (a-2)(4a + 5) = 0 a = 2 or a = -5/4 the 2nd is done the same way: f(3) = 81 + 9m + 3n + 5 = 128 9m + 3n = 42 3m + n = 14 f(-1) = -3 - m - n + 5 = 4 -m-n = 2 add them: 2m = 16 m...
August 4, 2014

Math
balance owing = 22000-5500 = 16500 We don't know the rate, but if the monthly rate is i , then 16500 = 406.69(1 - (1+i)^-48)/i Did some alternate numerical calculations and found n = .007083333.. which makes it an annual rate of 8.5% compounded monthly So balance owing ...
August 3, 2014

algebra
Number(Ipad or Car) = number(Ipad) + number(carss) - number(Ipads and cars) = 65 + 45 - 15 = 95 which leaves 5 unaccounted for from the 100 so .... a) 95 owned either Ipad or car b) 5 owned neither or you could get the same result by constructing a Venn diagram
August 3, 2014

math
In your text or in your notes you should find the following relationship between (r,Ø) and (x,y) x = rcosØ -->cosØ = x/r y = rsinØ --> sinØ = y/r r^2 = x^2 + y^2 and tanØ = y/x so in r = 1/(sinØ + cosØ) r(sinØ...
August 3, 2014

Proof: math
amount at end of t = 2 = 500(1.015)^8 = 563.25 add additional payment of 273.14 = 836.39 amount of that after 3 more years = 836.39(1.015)^12 =999.9986.. not bad, eh?
August 2, 2014

oops - math
I miscounted on my "time line" should have been: 500(1.015)^20 + x(1.015)^12 = 1000 ... x = $273.14
August 2, 2014

math
500(1.015)^20 + x(1.015)^16 = 1000 1.268985... = 326.572.. x = $257.35
August 2, 2014

maths
height/100 = tan 60° height = ..... ?
August 2, 2014

math
for Tia: distance = 29-75(t-1) for Kathie: distance = ..... (what do you think)
August 2, 2014

Math
log (10A)/(7B^2) = log(10A) - log(7B^2) = lof 10 + logA - (log7 + 2logB) = 1 + logA - log7 - 2logB
August 2, 2014

college math
From a Physics point of view, this question is really flawed. First of all, it should be -16t^ (gravity works downwards, not upwards) Secondly, at the moment of jettison of the tanks, the tank still has an upwards velocity, so there should be term in t after the -16t^2 anyway...
August 2, 2014

College math
-In45=3.80666249 this statement is false should say: In45=3.80666249 then e^3.80666249 = 45 again, I will assume you meant: Log sub.B T^5=W , I read that as: logB T^5 = W by definition: T^5 = B^W
August 2, 2014

College math
yes it is 1: y = x^3 - 27 ----> x = y^3 - 27 2: x = y^3 - 27 y^3 = -x - 27 y = (-x - 27)^(1/3)
August 2, 2014

College math
follow same steps as I showed you
August 2, 2014

College math
Inverse: step 1. switch the x and y variables y = 5/(x+3) -----> x = 5/(y+3) step 2: solve this new equation for y xy + 3x = 5 xy = 5-3x y = (5-3x)/x I was able to find the inverse, but both the original and the inverse have restrictions, so it is not a one-to-one function ...
August 2, 2014

Greg/kat - calculus
Please stick to one name done in previous post
August 2, 2014

Precalculus
All you want is the linear equation passing through the two points (0,20000) and (5,10000) slope = (10000-20000)/(5-0) = -2000 So if we let t be the time V = -2000t + 20000 the rate of depreciation is $2000/year
August 2, 2014

Math
well! , just set 164t - 16t^2 = 400 -16t^2 + 164t - 400 = 0 4t^2 - 41t + 100 = 0 (t-16)(4t - 10) = 0 t = 10 or t = 10/4 or 2.5 seconds So it will reach that height first at 2.5 seconds, (and again after 10 seconds on its way back down)
August 2, 2014

Math
As you can see from the many similar questions, this poorly worded question comes up again and again with just a change of numbers We must assume that the width is the same for the kitchen and the dining room let the dining room be x by x area of dining room = x^2 area of ...
August 2, 2014

math
let the mileage be m 65 + .7m < 114 + 0m .7m < 49 m < 70 so for m> 70 miles, company A is cheaper check: if m = 50 company A charges $114 company B charges 65 + .7(50) = 100 if m = 71 company A charges $114 company B charges 65+.7(71) = $114.70 . which is more btw...
August 2, 2014

math
assuming neither of the two given sides is the hypotenuse, make a sketch to see that tan B = 960/490 angle B = appr 63°
August 2, 2014

math
if GP , then (2x-4)/4 = (21x+2)/64 128x-256 = 84x + 8 44x = 264 x = 6 check: 4, 8, ... , 64, 128 YUP, common ratio of 2
July 30, 2014

typo - Math
In all that lengthy typing, I just noticed an error. When I stated De Moivre's Theorem, it should of course have been: then z^n = r^n( cos (nØ) + i sin (nØ) ) I did use it correctly in my work.
July 30, 2014

Math
How did I get 171.9 ? from tanØ = -1/7 I know that the tangent is negative in II and IV by the CAST rule but <-7,1> ends up in quadrant II so I took tan-inverse of 1/7 to get 8.13° , had it been in quad I in quad II we have 180-8.13 = appr 171.9
July 30, 2014

Math
Jane, you will have to be able to change a complex number from standard form to trig form in general a + bi = (√(a^2 + b^2) [cosØ + isinØ] where Ø is such that tanØ = b/a e.g. change 3 + 4i to trig form = √(3^2+4^2) (cosØ + isin&...
July 30, 2014

Math
2nd: let z = 0 + 8i = 8( 0 + i) we need 0+i in the form cosØ + isinØ we need Ø, so that cosØ = 0 and sinØ = 1 mmmmhhh, Ø = 90 comes to mind so z = 8(cos90° + isin90°) so the cube root, and using De Moivre's z^(1/3) = 8^(1/3...
July 30, 2014

Math
For the 2nd: are you familiar with D' Moivres Theorem? let me know, and I will go through with this one 3rd: make a sketch and use the cosine law 35.1^2 = 32.7^2 + 20.2^2 - 2(20.2)(32.7)cosØ ( see if you get Ø = 100.7° )
July 30, 2014

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