Wednesday

April 16, 2014

April 16, 2014

Total # Posts: 25,975

**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

**derivatives**

I assume that you want the derivative, since you titles your post that way. if y = x^2cosx-2xsinx-2cosx dy/dx = (x^2)(-sinx) + 2x cosx - 2x(-cosx) - 2sinx + 2sinx = -x^2( sinx) + 4x( cosx) etc if needed

**Not so fast .....**

Since each flower needs 1 square foot, the flowers planted along the circumference will not have a complete square foot. To illustrate, take a grid paper, and draw a circle with radius 7. we will need x^2 + y^2 = 49 you only have to look at 1/4 of the circle and look at the nu...

**Calculus Help**

y = (e^-x) (cosx)^2 (x^2 + x + 1) take ln of both sides ln y = ln e^-x + ln (cosx)^2 + ln(x^2 + x + 1) = -x + 2 ln(cosx) + ln(x^2 + x + 1) now differentiate y' / y = -1 + 2(-sinx/cosx) + (2x+1)/(x^2 + x + 1) = -1 - 2tanx + (2x+1)/(x^2 + x + 1) y' = y(-1 - 2tanx + (2x+1...

**Math**

for any quadratic function f(x) = ax^2 + bx + c the x of the vertex is -b/(2a) sub that x value into the function to get the y of the vertex, so n(x) = -.3x^2 + 9x + 15 x of vertex is -9/(2(-.3)) = 15 n(15 = -.3(225) + 9(15) + 15 = 82.5 ticket sales will peak on day 15 and the...

**math**

TC = 5/9 (TF – 32) TF = 9/5 TC + 32 , converts between TF and TC TF is temperature in archaic Fahrenheit, TC is temperature in Celsius I + PRT, interest = principal x rate x time for simple interest D = R x T , distance = rate x time

**Math**

yes , the x-intercepts are 0 and 4, respectively confused about your second reply, the vertices are indeed (0,0) and (0,4) <<I mean 0 for -2x^2. Sorry about the 4, I didn't mean to put that. >> , don't even know what that is supposed to say. see, http://www...

**Math**

You talk about equations, but show no equation. You must have meant the equations to be y = -2x^2 and y = -2x^2 + 4 You are asking for the axes of symmetry but instead state the vertices. You were correct that the vertices are (0,0) and (0,4) respectively. so the axes of symme...

**Math**

Did you not notice that for every increase of 20 in the x's there is a decrease of 20 in the y's so the slope is (45-65)/(30-10) = -1 so y = -x + b using x=10, y = 65 65 = -10 + b b = 75 y = -x + 75

**trigonometry**

the formula you want is cos a + cos b= 2cos((a+b)/2) * cos((a-b)/2) so cos 5w + cos 2W = 2cos(7w/2) * cos(3W/2)

**Algebra**

I did this one last year http://www.jiskha.com/display.cgi?id=1362104847

**algebra 1**

first even : x 2nd even : x+2 now do it like the others

**PreCalc**

Andy, I have done quite a few for you now. Give this one a try, let me know what you get.

**uninhibited growth**

done, look back to your earlier post of this

**algebra 1**

done , look back

**interest**

we don't really need the amount at first rate: 2 = 1 e^(.05t) ln2 = .05t t = 13.86 ---> the doubling time at 2nd rate: 2 = 1 e^(.1t) you finish it.

**algebra 1**

1st number ---> x 2nd number -- > x+1 3rd number --> x+2 x+x+1+x+2 = -204 3x = -207 x = -69 largest is -67 or let the 3 numbers be (x-1) , x , (x+1) x-1 + x + x+1 = -204 3x = -204 x = -68 largest number is -68+1 = -67 notice that in my second solution, the equation wa...

**algebra 1**

what does (2/9)x = 24 sound like to you?

**algebra 1**

looks like (3/8)b = 14

**Math**

The ones digit is 5 less than 10. ---> xx5 The tens digit is 2 more than the ones digit -- x75 it must be less than 200 so it is either 175 or 75

**Precalculus**

I have now answered several question for you of this type. This is the easiest of the bunch Your turn ! let me know what you got

**PreCalculus**

amount = 100 (1/2)^(t/5730) b) 59 = 100 (.5)^(t/5730) .59 = .5^(t/5730) ln .59 = (t/5730) ln (.5) t/5730 = ln .59/ln .5 = .76121314 t = 4361.75 yrs

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