Friday
December 19, 2014

Posts by Reiny


Total # Posts: 28,255

geometry
Go with MathMate, I misread the question
November 26, 2014

geometry
All angles in the equilateral triangle are 60° In the isosceles triangle the two base angles are 73 ° each ......... ( (180-34)/2 ) so angle ABD = 60+73 or 133°
November 26, 2014

Trig
1. can't see your diagram but will assume that the angle of 35° is between the two given sides, so ... R^2 = 98^2 + 55^2 - 2(55)(98)cos 145° 2. "each" vector ? , what vector 3. a = <9,8> b = <-8,7) a dot b = |a| |b| cosØ -72 + 56 = √...
November 26, 2014

analytic
duplicate post, see your other post
November 26, 2014

analytic
slope of first line = m1 = (6-9)/(2-1) = -3 slope m2 = (5-3)/(3+1) = 1/2 if Ø is the angle between them: tanØ = (m2-m1)/(1 + m2m1) = (1/2 - 3)/(1 + (1/2)(-3)) = (-5/2) / (-1/2) = 5 Ø = 78.7° to the nearest tenth
November 26, 2014

Statistics
z score = (your data value - mean)/sd I will do the first and fourth, follow the same procedure for the others 68, ? z = (68-70)/8 = -2/8 = -.25 ? 1.8 1.8 = (x - 70)/8 multiply by 8 14.4 = x-70 add 70 84.4 = x notice the z value may be ± but your data value must be ...
November 26, 2014

Math
10/12 = 50/60 = 25/30 = ... just multiply the numerator and denominator by the same non-zero constant e.g (5/6)*(2/2) = 10/12 etc
November 26, 2014

Trig
2csc^2x-8=0 csc^2 x = 4/2 = 4 then sin^2 x = 1/4 sinx = ±1/2 ---> so x can be in any of the 4 quads we know sinπ/6 = 1/2 so x = π/6 x = π - π/6 = 5π/6 x = π + π/6 = 7π/6 x = 2π - π/6 = 11π/6
November 25, 2014

Trigonometry
sin^2 x = 3/4 sinx = ±√3/2 I know sin 60° = √3/2 or sin π/3 = √3/2 so x = π/3, 2π/3 , 4π/4 , 5π/3 2 tan^2 x = √12 = 2√3 tan^2 x = √3 now you should know the trig ratios of the 30-60-90 triangle. once you ...
November 25, 2014

Brief Calculus
look at the graph first. http://www.wolframalpha.com/input/?i=plot+y+%3D+e%5Ex%2C+y+%3D+2x%2B1%2C+-2+to+1 I is obvious that y = e^x and y = 2x+1 intersect at the y-axis at (0,1). there is another intersection but it beyond x = 1, so of no concern to us So area = ∫ (e^x...
November 25, 2014

Geometry
In the actual case they had 18° So in the general case they now have x° So let's do exactly the same thing So if we have n sides and the exterior angle is x° then the interior angle is 180-x So (180-x)n = (180)(n-2) 180x - nx = 180n + 360 solving for n: 180x - ...
November 25, 2014

math show work please
Did you notice that x^2 + 8x + 15 = (x+3)(x+5) which happen to be the denominators on the left side So let's multiply everybody by (x+3)(x+5) (x+5) + 4(x+3) = 2 Now how easy is that from there ?
November 25, 2014

math show work please
1 - 11/x + 30/x^2 = 0 times x^2 x^2 - 11x + 30 = 0 (x-5)(x-6) = 0 x = 5 or x = 6
November 25, 2014

calculus
s = (3+6t)^(1/2) v = (1/2)(3+6t)^(-1/2) (6) = 3(3+6t)^(-1/2) a = (-3/2)(3+6t)^(-3/2) (6) = -9(3+6t)^(-3/2) when t = 1 a =-9(9)^(-3/2) = -9(1/27) = -1/3 you are correct!
November 24, 2014

trig
Oh my! I know that cos π/3 = 1/2 and cos π/6 = √3/2 (What is the matter with me ? )
November 24, 2014

trig
1. 4cosx = 2 cosx = 2/4 = 1/2 I know cos π/6 = 1/2 , so x = π/6 but the cosine is positive in quadrants I or IV so x is also 2π- π/6 = 11π/6 #2 sec^2 = 4/3 1/cos^2 x = 4/3 cos^2 x = 3/4 cos x = ± √3/2 so x could in any of the 4 quadrants ...
November 24, 2014

MATH
I got 12 Make a Venn diagram consisting of two intersecting circles, one called M, the other called L Put a rectangle around the circles. place 5 in the intersection of M and L since M contains 18 , but 5 are already written down, place 13 in the M only part of the circle. ...
November 24, 2014

Math
What is 10000(1.01)^72 ?
November 24, 2014

calculus
dy/dx = 2x - 6 = 0 for horizontal tangent 2x-6 = 0 2x=6 x = 3 , which is choice a)
November 24, 2014

algebra
ratio of x and y coefficient of first = 2 : 5 ratio of x and y coefficients of 2nd = 4 : 10 = 2:5 but the constants are not in that ratio, so you have two parallel lines
November 24, 2014

Math
This is my interpretation of the question: R-- right W -- wrong there are 8 ways for the selection to take place (or there are 2 ways to pick the first cheese, right or wrong, 2 ways to pick the 2nd, and 2 ways to pick the third: 2x2x2=8 ) WWW WWR ** WRW ** WRR RWW ** RWR RRW ...
November 24, 2014

math
let the acceleration be a , (I expect a to be negative) v = at + c when t = 0 , v = 8 8 = 0+c ---> c = 0 so v = at + 8 when t = .36, v = 0 0 = a(.36) + 8 a = -8/.36 = appr -22.2 m/s^2
November 24, 2014

Precalc 2
Can't see your diagram, but it looks like a straightforward cosine law R^2 = 1600^2 + 3200^2 - 2(1600)(3200)cos 135° R = ....
November 23, 2014

Math (trigonometry)
1. angle A = 180-17.9-108.1 = 54° now by the sine law: AB/sin17.9 = 472/sin54 AB = 472sin17.9/sin 54 = .... 2. (9,2)dot((-3,3) = √85√18cosØ , where Ø is the angle between them (-27 + 6)/(√85√18) = cosØ I got Ø = 122.5°...
November 23, 2014

Calculus
Of course ! For some reason I was thinking x = 0. Ignore my silly comment , ( I will blame it on "old-timers syndrome" )
November 23, 2014

Calculus
What about the constraint of y = 0 wouldn't that restrict the volume to the part on the left of the y-axis ? and using washers, we would get only v = π∫[-2,0]((2-x)-(-2x)) dx = 2π
November 23, 2014

maths
eh?
November 22, 2014

mathematics of investment
I = PRT 8000(.09)T = 180 T = .25 years or 91 days I will leave it up to you to calculate what date that is
November 22, 2014

Math
counting the first bounce at up and down ... we have 144 + 144(2/3) + 144(2/3)^2 + ... which is an infinite geometric series where a = 144 , r = 2/3 sum(all terms) = a/(1-r) = 144/(1-2/3) = 144/(1/3) = 432 cm
November 22, 2014

Maths
then (3x+10)/(7x) = 6:7 42x = 21x + 70 21x=70 x = 70/21 = 10/3 so the number of reds originally was 3(10/3) = 10 the number of blues originally was 7(10/3) = 70/3 ????? how can we have partial balls ? I think there is something very wrong with your question. notice that "...
November 22, 2014

Maths
original red --- 3x original blue --- 7x number of reds added -- a number of blues added -- 10-a (3x+a)/(7x + 10-a) = 6/7 42x + 60 - 6a = 21x + 7a 21x - 13a = -60 I think you have something missing in your problem, maybe a typo We have to know how the 10 balls are distributed ...
November 22, 2014

Math Check please
your equation of c = 36/d^2 is correct so your constant of proportionality is 36 (your k value) now just plug in d = 5 c = 36/25 or 1.44
November 21, 2014

Math
the diagram looks rather routine draw the smaller building and mark is as 12 m high draw the other building a bit taller . draw a horizontal from the smaller to the taller, label the difference in height as x draw in your cable, Don't you have a right-angled triangle with ...
November 21, 2014

Math
(4^x)-(2^x)=56 (2^2)^x - 2^x - 56 = 0 (2^x)^2 - 2^x - 56 = 0 let 2^x = t , we get t^2 - t - 56 = 0 (t-8)(t+7) = 0 t = 8 or t = -7 if t = -7 2^x = -7 , no such x exists or if t = 8 2^x = 8 -----> x = 3
November 21, 2014

Math
3^(2c+1)=28*(3^c)-9 3^(2c)*3^1 = 28*3^c - 9 3(3^c)^2 - 28(3^c) + 9 = 0 let 3^c = x 3x^2 - 28x + 9 = 0 (3x - 1)(x - 9) = 0 x = 1/3 or x = 9 if x = 1/3 3^c= 1/3 = 3^-1 -----> c = -1 if x = 9 3^c = 9 = 3^2 ----> c = 2
November 21, 2014

Math
a) is correct b) since the S and L are defined variables, taken the inverse in the usual way changes their definitions. We could just follow the usual steps ... if S = 2√(5L) , the inverse is obtained by interchanging the variables, so inverse is L = 2√(5S) we ...
November 21, 2014

Math Question
-1500/360 = -4 with a remainder of -60° So we would have 4 clockwise rotations with and angle of 60 into quadrant IV
November 21, 2014

Math
f(f(x)) = f(6/(5+x) ) = 6/(5 + 6/(5+x) ) = 6/( (25+5x+6)/(5+x) ) = (30 + 6x)/(31 + 5x) = g(x) let y = (30+6x)/(31+5x) inverse is : x = (30+6y)/(31+5y) 31x + 5xy = 30 + 6y 5xy - 6y = 30 - 31x y(5x - 6) = 30-31x y = (30-31x)/(5x-6) = g^-1 (x)
November 21, 2014

Math
81^x = 64 log 81^x = log 64 x log81 = log64 x = log64/log81 27^(log64/log81 + 1) = 610.940...
November 21, 2014

typo - Algebra
forgot the zero in the first line , should read: as x is hugely negative, 2*51^x ----> 0
November 21, 2014

Algebra
as x is hugely negative, 2*51^x ----> so f(x) ----> 3 - 0 or 3 as x becomes hugely positive -2*51^x --->- ∞ do the range is y < 3 I will let you use whatever notation you have learned
November 21, 2014

Math
P(1.04)^10 = 5000 solve for P
November 21, 2014

Math
Rachel, Rachel ! Since both Damon and I went farther than the question asked for and also found the value of a .... all you needed is r = 1/2 (the value of a indeed has √2 in it, but your teacher was not referring to a but rather to r . Note we both had that √2 in ...
November 21, 2014

Math
ahh, so we have two ordered pairs (2,1) and (32, 4) that satisfy our equation ----> 1 = a(2)^r ----> 4 = a(32^r a(32)^r = a(2)5r so a(2)5r = 4 and a(2)^r = 1 divide them 2^(5r-r) = 4 2^4r = 2^2 then 4r = 2 r = 1/2 back into the first: a(2)^(1/2) = 1 a√2 = 1 a = 1...
November 21, 2014

Math
where does r come in ? did you mean , find a ?
November 21, 2014

Algebra Help please!
amount owing at 12% compounded annually in 4 years = 6000(1.12)^4 = 9441.12 amount owing at 12% per annum compounded quarterly in 4 years = 6000(1.03)^16 = 9628.24 Now subtract them as Henry told you to do.
November 21, 2014

math please help!!!!!
Since you are telling me that 4i = k then f(x)=x^3+(12-4i)x^2+(32-48i)x-128i =x^3 + (12 - k)x^2 + (32 - 12k) - 32k and since k is a zero, then (x - k) is a factor by synthetic division: f(x)=x^3+(12-4i)x^2+(32-48i)x-128i = (x-k)(x^2 + 12x + 32) = (x - 4i)(x^2 + 12x + 32)
November 21, 2014

Algebra 2
I will assume that you have (√5 + i)/(√5 - i) those brackets are absolutely essential. I will also assume that you want this rationalized. (√5 + i)/(√5 - i) = (√5 + i)/(√5 - i) * (√5+i)/(√5 + 1) , I am merely multiplying by 1, ...
November 21, 2014

Math Help!!!
If you meant √-75 , then you can't have a real number thus to ask for the nearest integer would be silly So you must have meant -√75 = -8.66025... = -9 to the nearest integer (look at the number on a number line)
November 21, 2014

Math
Brackets are essential here .... h(x) = (3x+2)/(7x-6) or y = (3x+2)/(7x-6) step 1 of finding the inverse is to interchange the x's and y's x = (3y + 2)/(7y - 6) 7xy - 6x = 3y + 2 step 2 : solve this for y 7xy - 3y = 6x + 2 y(7x - 3) = 6x + 2 y = (6x + 2)/(7x - 3) , ...
November 21, 2014

Algebra 2
from the type of problem that you posted, you surely MUST know how to solve quadratic equations. Steve took you as far as 5x^2 - 16x + 6 = 0 and made the same assumption I made. I suggest using the quadratic formula. (you will get two irrational answers)
November 21, 2014

MATH
proceed this way: f(g(x)) = f(2x^2 - 1) = 2/(2x^2 - 1) test it for some number e.g. let x = 3 g(3) = 18-1 = 17 f(g(3)) = f(17) = 2/17 in my answer: 2/(2x^2 - 1) = 2/17 This does not 'prove' that my answer is correct, but there is high probability that it is. Had my ...
November 21, 2014

math
old rate --- $x new rate --- $ x+2 wage per week at old rate = $ 32x wage per week at new rate with more hours = 40(x+2) 40(x+2) - 32x = 200 easy to solve
November 20, 2014

Math Help
Think about it .... if perimeter of little square is 16, each side is 4 for the larger, each side is multiplied by 7, or , each side is 28 so perimeter of larger is .....
November 20, 2014

algebra. help!
How can I check your work if you did not supply any of your choices
November 20, 2014

math
your solution is correct to check, you must go back to the original equation LS = log4 (19-3) = log 4 (16) = 2 -----> what must be exponent on 4 to get 16 ? = RS so x = 19
November 20, 2014

Math
Let his original number of pens be x then his original number of pencils is 30 - x So for every pen he gets 2 pencils so x pens will yield him 2x pencils but he already had 30-x pencils, so 2x + 30-x = 48 x = 18 So, originally he had 18 pens and 12 pencils check: 12+18 = 30 , ...
November 20, 2014

math
of course not distribute ... -36 - 6x - 6x - x^2 = .... add like terms
November 19, 2014

math!!!!!!
just distribute ... x(x+y+2) = x^2 + xy + 2x
November 19, 2014

Algebra
I will assume you mean (1/25)^(x+2) = 125^-x or else we got ourselves one doosey of a problem (5^-2)^(x+2) = (5^3)^-x 5^(-2x-4) = 5^(-3x) then -2x-4 = -3x x = 4
November 19, 2014

Algebra
m-7 < 6 add 7 to both sides, (just like you would for an equation) m < 13 Do the other two the same way
November 19, 2014

math
P(1 + .07/4)^28 = 30000 solve for P
November 19, 2014

math!
GCD(722,2413) = 19 then GCD(19,209) = 19 so GCD(722,2413,209) = 19
November 19, 2014

Algebra Help! Please
Did you not read the 3 conditions I outlined for you? Especially this one: "- if the variable drops out, and you get a true statement, there will be an infinite number of solutions " so you got 0=0, which is true, thus there will be an infinite number of solutions
November 19, 2014

ALGEBRA Help Please
1st: 2(x-3) = 2x 2x - 6 = 2x -6 = 0 -----> contradiction, thus no solution 4th: 4(x+3) + 2x = x - 8 4x + 12 + 2x = x - 8 5x = -20 x = -4 -----> One solution in general - if you get ?x = ? , there will be one solution - if the variable drops out, and you get a true ...
November 19, 2014

Math
#1, you can decide for yourself if (-5,-1) is correct by subbing in those values into both equations. You should be able to do this mentally. -- A quick mental calculation shows that your answer does not work in either equation from the 2nd: x = 2y + 10 plug that into the 1st...
November 19, 2014

MATH HELP
When testing if a number is prime, you would only try primes as divisors until you reach the last prime < √(the number) e.g. is 71 prime try: 2, 3, 5, 7 none divided exactly, so 71 is prime (did not have to go for 11 , since 11 > √71 so for 1881 ... √...
November 19, 2014

maths
Once around is one circumference. The circumference of a circle is 2πr or πd, d the diameter. So 5 times around would be ...... Plug in your values
November 19, 2014

math
I assume you meant to say, " ... travels 180 cm farther than ... " let the distance to the point of the minute hand be r cm In one hour the minute hand has gone around one rotation or 2πr in one hour the 'hour hand' has gone (1/12)(2π60)) or 10π...
November 19, 2014

Maths
Take a sheet of printer paper and try it. Doesn't the circumference of your tube equal the long side ? So.... 2πr = 20 r = 10/π
November 19, 2014

Math- Combinations
You are choosing 4 from 19 = C(19,4) = 19!/(15!4!) = 3876
November 18, 2014

Math
correct
November 18, 2014

Math
Retype in English please, and tell me what C is.
November 18, 2014

AP CALC
let the point of contact on the cosine curve be (x,y) So the perimeter of the rectangle = P = 2x + 2y = 2x + 2cos 2x dP/dx = 2 - 4sin 2x = 0 for a max/min of P 4sin 2x = 2 sin 2x = 1/2 I know sin π/6 = 1/2 so 2x = π/6 x = π/12 then y = cos π/6 = √3/2 ...
November 18, 2014

algebra
Let Jena time alone be x hrs let Cindy's time alone be 2x hrs let the two rates be 1/x and 1/(2x) combined rate = 1/x + 1/(2x) = 3/(2x) 1/(3/(2x)) = 10 2x/3 = 10 hrs = 2x = 30 or x = 15 Jena will take 15 hrs to do the house alone
November 18, 2014

ap calc
There are many variations of this same question,. Hint: let TP = x then OP^2 = x^2 + 64 OP = (x^2 + 64)^(1/2) I think you are missing the length of TR, we need that to find PR Just for arguments sake, lets say TR = 12 miles then PR = 12-x cost = 90000(x^2+64)^(1/2) + 54000(12-...
November 18, 2014

ap calc
Your graph looks like a W and I assume you want the rectangle placed inside the centre part. Let the two other vertices be (x,y) and (-x,y) So the length is 2x and the height is y Area = 2xy = 2x(x^4 - 2x^2 + 1) = 2x^5 - 4x^3 + 2x d(area)/dx = 10x^4 - 12x^2 + 2 = 0 5x^4 - 6x^2...
November 18, 2014

sixth grade ratios and rates
Here is another way of looking at Morgan's solution. Morgan found the percentage to be 25% or 1/4 of the marbes are blue. So 1/4 of Jasper's marbles must be blue , it said they have the same percentage of blue marbles. Let the total of Jasper's marbles be x then (1...
November 17, 2014

Math
f(x)= -x^2 + 2x = -1(x^2 - 2x +1 - 1 ) = -( (x-1)^2 - 1) = - (x-1)^2 + 1
November 17, 2014

college, math
If I were Sears I would sue the publisher of this textbook for associating their name with such a fraudulent practice . Anyway, according to this criminal plan .... cost after sales tax = 1656.9 "add-on interest" = 1656.90(.12)(3) = 596.484 amount to be "...
November 17, 2014

algebra
let's just plug in t = 10 T(10) = 65 + 115 e^-.42 = 140.56 = 141° to the nearest degree. b) we want 110 = 65 + 115 e^(-.042t) e^(-.042t) = (110-65)/115 = .391304... take ln of both sides -.042t = ln .391304.. t = 22.34 minutes or 22.3 minutes
November 17, 2014

math
x^2 = (-16 ± √196)/10 = (-16 ± 14)/10 x^2 = -1/5 or x^2 = -3 x = ± i/√5 or x = ± √3 i All four roots are imaginary
November 17, 2014

Math
only x= 0 so y= 0 x= 1 so y= -3 is correct, the others are not Perhaps, if you show how you are doing the calculations, I can see where you are going wrong. I will do one for you ... if x = -4 y = (-4)^2 - 4(-4) = 16 + 16 = 32
November 17, 2014

Math
So this question is essence establishes the quadratic equation formula hint: give yourself an equation such as 3x^2 + 12x + 2 = 0 and whichever step you perform on this equation, do the same thing for a parallel solution to ax^2 + bx + c = 0 Of course you know what you are ...
November 17, 2014

Algebra Work Check
correct or (x^2+4)(x^2-4) = 0 x^2 + 4 = 0 --> no real solution or x^2 - 4 = 0 (x+2)(x-2) = 0 x = ±2
November 17, 2014

Pre-Calc/Trig
let f(x) = 5x^3 - 119x^2 - 10x + 16 now try some f(x) , where x = ±1, ±2, ±4, ±8 ... hopefully to get a zero took some some, but f(8) = 0 so (x-8) will be a factor now by synthetic division , I got 15x^3-119x^2-10x+16 = (x-8)((15x^2 + x - 2) = 0 ...
November 17, 2014

algebra
speed of current --- x mph time to go 217 miles with the current = 217/(29+x) time to go 189 againts current = 189/(29-x) 217(29+x) = 189/(29-x) cross-multiply, solve for x
November 17, 2014

Calculus
everything happens starting at t=.5 a = -10 v = -10t + c when t = .5 , v = 20 20 = -10(.5) + c c = 25 v = -10t + 25 , for t ≥ .5 s = -5t^2 + 25t + k when t = .5 , the car goes goes another 20(.5) or 10 m so when t = .5, the remaining distance is 20 m 20 = -5(.5)^2 + 25(....
November 17, 2014

maths
original number --- x after epidemic --- .98x are left 14% of those leave, leaving (.86)(.98x) .86(.98x) = 2107 x = 2107/(.86(.98)) = 2500
November 17, 2014

maths
I am sure you meant A=p(1+r/n)^(nt) for yours r/n = .12/12 = .01 and nt = 12t (our unknown) so 500000(1.01)^(12t) = 1000000 1.01^(12t) = 2 take log of both sides log 1.01^(12t) = log 2 12t log1.01 = log2 12t = log2/log1.01 = 69.6607 t = 5.8 years
November 17, 2014

math
If I understand correctly there would have been 4 transactions. let the amount that each child has originally be x first transaction: 1st child -- x-9 each of remaining 9 children has x+1 2nd transaction: 1st child -- x-9 2nd child -- x+1 - 8 = x-7 each of remaining 8 children...
November 17, 2014

proportion test
new machine, defect rate is 85/820 = .1037 or 1037% draw you conclusion from that
November 16, 2014

Math
The question was to "find all possible roots" so you would try f(1), f(-1) , f(2) ...., f(±12) so you must try all of these unfortunately, none are equal to zero, so you have no rational roots.
November 16, 2014

Math
It is a 4th degree equation, so at most you could have 4 roots How can you possible get 6 of them ?
November 16, 2014

math
√(31-9x) = 5 - x square both sides 31 - 9x = 25 - 10x + x^2 x^2 - x - 6 = 0 (x-3)(x+2) = 0 x = 3 or x = -2 BUT, since we squared, we must verify ALL answers if x = 3 LS = 3 + √4 = 5 RS = 5, YEahh if x = -2 LS = -2 + √49 = -2 + 7 = 5 = RS, YEAHH x = -2 or x = 3
November 16, 2014

MATH 101
using the difference of cubes factoring x^2 - 8 = 0 (x-2)(x^2 + 2x + 4) = 0 x = 2 or x = (-2 ±√-12)/2 = (-1 ± 2√3 i )/2 = -1 ± √3 i for 3 solutions, one real, two complex
November 16, 2014

MATH 101
not enough information. is f(x) linear ? we must assume that, since you only have 2 points, namely, (3,0) and (-4,0) slope = 0/-7 = 0 so we have a horizontal line and f(x) = 0 f(x) is the x-axis
November 16, 2014

math
let's look at x^2 + 2x + 4 = 0 by completing the square, (in this case the easiest way to solve it) x^2 + 2x = -4 x^2 + 2x + 1 = -4+1 (x+1)^2 = -3 but anything squared cannot be negative, so there is no real solution consider y = x^2 + 2x + 4 this parabola never touches or...
November 16, 2014

Math
let f(x) = 3x^3 + 2x^2-1 f(1) = 3 + 2 - 1 ≠ 0 f(-1) = -3 + 2 - 1 ≠ 0 f(1/3) = 1/9 + 2/9 - 1 ≠ 0 f(-1/3) ≠ 0 So there are no "nice" roots looking at the graph, there appears to be a real solution at appr x = 0.5 and two complex roots (the graph...
November 16, 2014

CAL
y = x^3/x- x would reduce to y = x^2 - x and (1,-2/3) would NOT lie on this curve. So there is something wrong with the way you typed it Use brackets to establish the correct form Otherwise this question is bogus.
November 16, 2014

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