Tuesday
July 29, 2014

Posts by Reiny


Total # Posts: 26,897

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)

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°

Math
direct application of the sine law: x/sin41 = 96/sin71 x = 96sin41/sin71 = ....

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: 115/10...

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

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 ?

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)

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

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.wolframalph...

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)

math
y - 6 = .5x - 3.5 y = .5x - 3.6 + 6 y = .5x + 2.5

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.

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

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 = 6...

Algreba
What about it ?

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

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

Calculus
yes v(t) = h ' (t) = -16t + 5 so v(0) = -16(0) + 5 = 5

math
times 8 8B = 3(A-10) 8B = 3A - 30 8B+30 = 3A A = (8B+30)/3

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

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.

Math
prob(2dimes) = (8/14)(7/13) = 4/13

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)

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`...

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 .....

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

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

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

math
Steve, that is really scary.

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

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.

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)

Math
number of adults --- A number of kids ----- C A + C = 35 12A + 7C = 315

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.

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

math
what is 48000( 1.0105)^40 ?

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

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

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

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

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...

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...

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

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 ?

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? perh...

Math
first tell me what you got for your inverse matrix

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

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

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

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...

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&...

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

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

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)

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...

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

math
correct, so .....

math
what is √(300^2 + 50^2 ) ?

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= ...

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)

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

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...

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 ...

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

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 +...

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

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

algebra 2
what is 3500(1.025) ?

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 =...

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

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.

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...

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

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/...

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...

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?

Math
66 2/3 of 39 = (200/3)(39) = 7800/3 = 2600

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 differen...

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 2n...

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 - ...

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

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...

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

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

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 = 1,00...

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/fi...

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

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 th...

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 , t...

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

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

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 ...

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 ,...

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

math
term 11 = a+10d = 8+10d term 7 = a + 6d = 8+6d (8+10d)/(8+6d) = 5/8 64 + 80d = 40 + 30d 50d = -24 d = -24/50 = -.48 check: term 11 = 8 + 10(-.48) = 3.2 term 7 = 8+6(-.48) = 5.12 5.12 : 3.2 = 512 :320 = 8 : 5

Physics question - I NEED HELP PLEASE
need rules of physics here. volume of water if trough is full = (1/2)(3)(5)(8) = 60 cubic metres from here on it is physics

math
boys --- 4x girls ---- 5x 4x+5x = 54 take over....

Math
distance at 15 km/h --- x distance at 18 km/h ---- 136-x x/15 + (136-x)/18 = 8 multimply each term by 90 6x + 5(136-x) = 720 6x + 680 - 5x = 720 x = 40 distance at 15 km/h is 40 km distance at 18 km/h is 136-40 or 96 km check: 40/15 = 2 2/3 hrs 96/18 = 5 1/3 hrs , for a total ...

math
(1/8) of what number is 3 ?

derivatives
yup! sloppiness on my part

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