Thursday

May 5, 2016
Total # Posts: 34,488

**Algebra**

speed of raft ---- x km/h speed of boat ----12 km/h when the boat caught up with the raft, they both had gone 20 km time for raft = 20/x time for boat = 20/12 20/x - 20/12 = 5 hrs, 20 min = 16/3 times 12x 240 - 20x = 64x 240 = 84x x = 240/84 km/h = 20/7 km/h check" time ...
*March 27, 2016*

**Calculus**

.638 = 1(1/2)^(t/5730) log .638 = (t/5730)log .5 t/5730 = log .638/log .5 = .64837... t = appr 3715 years
*March 27, 2016*

**maths**

If y = x/2 - 7/2 and it passes through C and E which are the x and y intercepts respectively, the for C, let y = 0 0 = x/2 - 7/2 x/2 = 7/2 x = 7, so C is (7,0) Why all that extra stuff about parabolas etc ?
*March 27, 2016*

**math**

Yesterday, I gave you this solution, but for some reason you didn't like it: See Related Question #1 below. "Let the amount of old stuff drained be x gallons so you have 4-x gallons left of 25% solution .25(4-x) + x = .5(4) 1 - .25x + x = 2 .75x = 1 (3/4)x = 1 x = 4/3...
*March 27, 2016*

**math**

so have a diamond, which means there are 51 cards left, of which 13 are still spades Prob(spade) = 13/51
*March 26, 2016*

**precal**

Always proofread your post before sending it, to make sure it makes sense.
*March 26, 2016*

**Calculus**

You probably expected this to come out as S = c/x^2 + k/(d-x)^2 = c x^-2 + k(d-x)^-2 dS/dx = -2cx^-3 - 2k(d-x)^-3 = 0 for a min c/x^3 = k/(d-x)^3 but k = 9c c/x^3 = 9c/(d-x)^3 1/x^3 = 9/(d-x)^3 (d-x)^3 = 9x^3 d-x = (9^(1/3))x d = x( 9^(1/3) - 1) x = d/(9^(1/3) - 1)
*March 26, 2016*

**Algebra**

400/s + 160/s + 240/(s-20) = 11 ok, hint: multiply each term by s(s-20) to get a quadratic. Hint: it comes out to be a nice whole number
*March 26, 2016*

**Algebra**

I did this for you here http://www.jiskha.com/display.cgi?id=1458920959 hoping you would be able to find the equation yourself then Steve finished it for you here: http://www.jiskha.com/display.cgi?id=1458939085
*March 26, 2016*

**math**

tan(t)=1/tan (t) tan^2 t = 1 tan t = ± 1 t = π/4, 3π/4, 5π/4, and 7π/4 2sin(t)cos(t) + sin(t) -2cos(t)-1= 0 by grouping: sint(2cost + 1) - (2cost + 1) = 0 (2cost+1)(sint-1) = 0 cost = -1/2 or sint = 1 I will let you finish that one 2cos3x = 1 cos3x...
*March 26, 2016*

**calculus2**

amount = a (1/2)^(t/74) where t is in years so when t = 10 amount = a(.5)^(10/74) = .91058.. a so appr 91% will be left
*March 26, 2016*

**Algebra 1**

corresponding function: y = x^2 - 9 which is a parabola opening upwards, centre at (0,-9) and x-intercepts of ±3 I assume you know how to graph a curve like this. solution : x = ±3
*March 26, 2016*

**contempory math**

I noticed the Fibonacci Number property, that is, adding the last two numbers produces the next number. note: 3+4=7 4+7=11 11+7=18 etc
*March 26, 2016*

**math**

Let the amount of old stuff drained by x gallons so you have 4-x gallons left of 25% solution .25(4-x) + x = .5(4) 1 - .25x + x = 2 .75x = 1 (3/4)x = 1 x = 4/3 so drain 4/3 gallon of the current solution, then top it up with pure antifreeze
*March 26, 2016*

**math**

easiest algorithm for area of any polygon: list the points in a column going counterclockwise, repeat the first point listed: area = (1/2)(downproducts - upproducts) 8 11 2 3 8 3 11 7 8 11 area = (1/2)(24+6+56+121 - (22+24+33+56)) = 36
*March 26, 2016*

**math**

could be AB or BA , but the order in which they are sold shouldn't matter, so prob(AB) = (1/9)(1/3) = 1/27
*March 26, 2016*

**math**

Prob(defect) = .2 prob(not defective = .8 prob(exactly 2 of 10 are defective_ = C(10,2) (.2)^2 (.8)^8 = .... 2. Use the "back-door" approach if 2 or more are defective, then we can't have: none defective or only 1 defective. = 1 - C(10,0) (.2)^0 (.8)^10 - C(10,1...
*March 26, 2016*

**maths**

what is 55-40 ? what is 15/40 ?
*March 26, 2016*

**mathematics-cubic equation**

They probably expect you to use factoring, so try factors of 8 so x = ±1, ± 2 , ± 4 would be values to start with, Sure enough on the third try, x = 2 works Thus x-2 is a factor and by synthetic division, 2x^3-11x^2+18x-8=0 (x-2)(2x^2 -7x + 4) = 0 so one ...
*March 26, 2016*

**Finance**

In order for the ordinary formulas to work, the interest period must match the payment period. In this question, the payment period is annually, but the interest period is semiannually. So we must first find what annual interest rate is equivalent to 4% per annum compounded ...
*March 25, 2016*

**Pre-Calc**

checking: from f(2) = 6 6 = a b^2 from f(0) = 54 54 = a b^0 so a = 54 ----> you had that back in 6 = 54 b^2 b^2 = 6/54 = 1/9 b = 1/3 ---> you had b = 33, which is close but not quite accurate enough then f(x) = 54(1/3)^x f(-3) = 54(1/3)^-3 = 54(3)^3 = 54(27) = 1458 ---&...
*March 25, 2016*

**Polynomials**

No idea what you are talking about.
*March 25, 2016*

**Probability**

prob(3 boys) = (1/2)^3 = 1/8 prob(at least 1 girl) = 1 - prob(all boys) = 1 - 1/8 = 7/8
*March 25, 2016*

**Algebra**

Steve did this yesterday http://www.jiskha.com/display.cgi?id=1458866531
*March 25, 2016*

**math**

done here http://www.jiskha.com/display.cgi?id=1458950977
*March 25, 2016*

**math**

What is C(43,9) ?
*March 25, 2016*

**Algebra**

amount at 6% --- x amount at 2% ---1900-x solve for x .06x + .02(1900-x) = 94
*March 25, 2016*

**Calculus**

Using common sense: for any value xy, where x + y is a constant, the largest value xy is obtained when xy is a perfect square, So the largest value of xy+xz+zy is obtained when all three are the same value but 10 cannot be split into 3 equal parts so the best we can do is ...
*March 25, 2016*

**Algebra**

First part of trip: distance = 400 km speed = x km/h time = d/r = 400/x hrs return trip 2/5 of 400 at x km/h, then 3/5 of 400 at x-20 km/h how far did the train go at x km/h ? how far did the train go at x-20 km/h ? What is the time for the first part of this return trip? What...
*March 25, 2016*

**Algebra**

Most of these distance-rate-time problems are basically the same. I did the last one for you, give this one fair try, and let me know at which point you get stuck. Hint: let the "certain" speed be x km/h then the slower speed is x-20 km/h
*March 25, 2016*

**Algebra**

I will assume that the speed of the raft is the speed of the current. Let the speed of the current be x km/h speed of boat against current = 12-x km/h time with boat = 25/(12-x) time on raft = 25/x 25/x - 25(12-x) = 10 divide by 5 5/x - 5/(12-x) = 2 multiply each term by x(12-...
*March 25, 2016*

**Trigonometry**

sin^2 Ø + cosØ -2 = 0 1-cos^2 Ø + cosØ - 2 = 0 cos^2 Ø - cosØ + 1 = 0 cosØ = (1 ± √-3)/2 which is not real you are correct, there is no solution.
*March 25, 2016*

**Math**

Would have been easier to type: 27.36 + 8.09 + 65.073 now just add them
*March 25, 2016*

**Math**

Not enough information. You will need an angle or the third side.
*March 25, 2016*

**Probability**

Since the order in which the numbers are chosen does not matter, it will be C(54,6) = 25,827,165
*March 25, 2016*

**math**

let the unit digit be x and the tens digit be y so x+y = 9 ---> y = 9-x the number is 10y+x the number reversed is 10x + y 3(10y+x) = 8(10x + y) 30y + 3x = 80x + 8y 22y = 77x 2y = 7x 2(9-x) = 7x 18 - 2x = 7x 18=9x x=2 y=7 the number is 72 check: number is 72 reverse is 27 ...
*March 25, 2016*

**Probability**

correct
*March 25, 2016*

**Math**

time walking = 4/8 hrs = 1/2 hr time jogging = 6/12 hrs = 1/2 hr total time = 1 hr avg speed = 10 km/1 hr = 10 km/h
*March 24, 2016*

**Maths**

suppose she had an original amount of x after giving to her brother she has 3x/4 left of that she spends (1/3)(3x/4) and (1/6)(3x/4) or (1/4)x + (1/8)x total amount spent = x/4 + x/4 + x/8 = (5/8)x so she has 3/8 of her money left, which she donated. check: suppose she has 24 ...
*March 24, 2016*

**Math**

You probably forgot to mention that those equal parts are sectors of the circle (like slices of pizza) each part would have a central angle of (360/9)° , so ...... carry on
*March 24, 2016*

**geometry**

area of one triangle = 37.2/5 = 7.44 cm area = (1/2)base x height 7.44 = (1/2)(base)(3.2) base = 2(7.44)/3.2) = ...
*March 24, 2016*

**Precalculus**

period = 2π/k k = 2π/44 = π/22 d = -88 sin ( (π/22)(t+11) ) must be a magic coiled spring, it never seems to lose its bounce.
*March 24, 2016*

**calc. 1**

let the width of the poster be x cm let the length of the poster be y cm then the width of the print area = x-10 and the length of the print area = y - 2 given: xy = 625 y = 625/x area of print = A = (x-10)(y-2) = xy - 2x - 10y + 20 = x(625/x) - 2x - 6250/x + 20 = 645 - 2x - ...
*March 24, 2016*

**prealgebra or algebra1**

Easiest way: since the lines are parallel, they would differ only in the constant so the equation is 4x + y = c plug in the given point to find c and you are done
*March 24, 2016*

**Trigonometry**

b) correct, the period would be 2π/60π = 1/30 c) when t = 3 d = (1/12)sin (180π) = 0 d) sin(60πt) = 0 when t = 0 , 1/30, 1/15 ... so the first positive value is 1/30
*March 24, 2016*

**math**

really ?
*March 24, 2016*

**Geometry**

The wording of this question is not clear It does not say if the sides of 15 and 18 are the parallel sides, or if they are adjacent sides. I must conclude that they are adjacent sides or else the height between them would be constant area of ||gram is base x height so 15(9) = ...
*March 24, 2016*

**Check Mathh Answers!!**

I agree with all you answers except #4 #4 , the outlier is 1.5
*March 24, 2016*

**Math**

I agree with what you have so far, other than skipping the integral sign and the dx from the last term. You seem to have the concept however. ∫e^(3x) sin(2x) dx = (-1/2)e^(3x)cos(2x) - ∫(-1/2)(3e^(3x))(cos(2x) dx = (-1/2)e^(3x)cos(2x) + (3/2)∫ e^(3x) cos(2x) ...
*March 24, 2016*

**trigonometry**

2sin^2 A + 5cosA = 4 2(1 - cos^2 A) + 5cosA - 4 = 0 2cos^2 A - 5cosA + 2 = 0 (2cosA -1)(cosA - 2) = 0 cosA = 1/2 or cosA = -2, the latter is not possible, so cosA = 1/2
*March 23, 2016*

**Algebra, functions**

to have one root, (actually two equal roots) b^2 - 4ac = 0 k^2 - 4(1)(5) = 0 k^2 = 20 k = ± √20 = ± 2√5 check: x^2 + 2√5x + 5 = (x + √5)^2 x^2 - 2√5x + 5) = (x - √5)^2
*March 23, 2016*

**math**

change in volume = 15x20x3 cm^2 which must have been caused by the volume of the rock.
*March 23, 2016*

**algebra**

your notation clearly did not show up as you intended. I will guess you meant: (b+7)/(b+4) = c/9 c = 9(b+7)/(b+4) I have this very old fashioned computer language called BASIC. I ran a stupid little program for b = -5000 to b = 5000 and it found the following pairs (b,c) >...
*March 23, 2016*

**Geometry**

Make a side-view of the pyramid, and drop a perpendicular. let the side of the base be 2x, (that way I don't have fractions in my variable) in the right-angled triangle tan 52° = 147/x x = 147/tan52 = ... then base side = 2x = ....
*March 23, 2016*

**Calculus**

You don't describe the diagram, but I am familiar with this type of question. Assuming there is a common width between the two fields let the width be x ft let the length of the combined field be y so 3x + 2y = 1200 y = 600 - (3/2)x area = xy = x(600 - (3/2)x) = 600x - (3/...
*March 23, 2016*

**Math**

Ruth's speed --- x km/h Tom's speed --- x+10 km/h in two hour: Ruth went 2x km Tom went 2(x+10) km solve for x 2x + 2(x+10) = 308
*March 23, 2016*

**trig**

No, it isn't the simplification of the expression is -1/sinx, as you can see from my steps however, if -1/f(x) = -1/sinx then f(x) = sinx
*March 23, 2016*

**trig**

I will "simplify and write the trigonometric expression in terms of sine and cosine" the part "=-1/f(x)=f(x)=____________ " makes little sense to me cot(-x)cos(-x)+sin(-x) = (cos(-x))/sin(-x))(cos(-x) + sin(-x) = (cosx/-sinx)(cosx) - sinx = - cos^2 x/sinx...
*March 23, 2016*

**math**

I certainly would not want to support laziness, so I will not answer you question. Why would you possible need papers to find 5/6 times 12 I did that in my head in about 3 seconds
*March 23, 2016*

**Bus. Math**

What is a rate of 9-15/18? Did you mean consecutive discounts of 9%, 15%, and 18% ? if so final percentage = .91(.85)(.82) = .63427 or 63.427% of the original price looks like b) is correct and you are right.
*March 23, 2016*

**Math**

A meaningless question. The value of c can be any real number to have a quadratic expression. "TheKnowItAll" found the value of c so that the expression becomes a perfect square, but that was not the question.
*March 23, 2016*

**math !**

surface area = 2lw + 2lh + 2wh = NOT 1134.375 , I get 731.5
*March 23, 2016*

**mathematics-slope of tangent**

differentiate implicitly, x^2 + xy + y^2 = 4 2x + x y' + y + 2y y' = 0 y' (x + 2y) = -2x - y y' = (-2x-y)/(x+2y) for (2,-2) y' = (-4 + 2)/(2 -4) = -2/-2 = 1
*March 23, 2016*

**Algebra II**

q = k(1/m^2)(rx) plug in the given values 2.5 = k(1/16)(8) solve for k
*March 23, 2016*

**Algebra II**

Did you find the equation for the flight path of the plane ? Did you find the equation of the parabola? Did you solve the two equations and got a real answer? If you have a solution, the the plane intersects the closed airspace. If you have no solution ...... etc
*March 23, 2016*

**MATH**

different shapes: 1 1 12 1 2 6 1 3 4 2 2 3 number of different bases for each one: 1 1 12 --->1 1 12, 1 12, 1 ----- 2 of them 1 2 6 ---> 1 2 6, 1 6, 2, 2 6 1 --- 3 of them 1 3 4 ---> 1 3 4, 1 4 3, 3 4 1 --- 3 of them 2 2 3 ---> 2 2 3, 2 3 2 ----- 2 of them 10 ...
*March 23, 2016*

**Math**

good job, they were all correct
*March 23, 2016*

**division and remainder...error ws from my teacher not me**

Sum(1) = 1 = 1mod5 sum(2) = 1 + 2^2 = 5 = 0 mod5 sum(3) = 5 + 3^3 = 32 = 2 mod5 sum(4) = 32 + 4^4 = 288 = 3 mod5 To divide by 5 all we need to do is look at the last digit. If the digit is form 0 to 4, then that digit is the remainder when dividing by 5 If the digit is from 5 ...
*March 23, 2016*

**maths**

for the additions, the common denominator is 60 grind out the sum of the inner bracket then multiply that by 5/8, simplify if needed finally multiply that by 8 let me know what you got, so I can check it for you btw, are you sure that -4/5 is not supposed to be +4/5 ?? It ...
*March 23, 2016*

**geometry**

None of the answers given are correct by the cosine law: f^2 = 8^2 + 13^2 - 2(8)(13)cos72° = 168.724... f = 12.989398... by sine law: sinG/8 = sin72/12.989... sinG = .58574... G = 35.86° correct to 2 decimals With modern calculators, there is no reason to round off ...
*March 23, 2016*

**@ Steve - trigonometry**

Steve, I worked on this for a while this morning, and I got that far as well. I also noticed that sinA = .618033989.. which is the decimal part of the golden ratio (1+√5)/2, ... interesting from xsinA= ycosA I had y/x = sinA/cosA = tanA from xsin^3A=y I had y/x = sin^3 A...
*March 23, 2016*

**trigonometry**

Did you mean: (tanA - sinA)/tan^2 A = tanA/(1+cosA) the way you typed it, it is not true LS = (tanA-sinA)/sin^2 A = (sinA/cosA - sinA)/sin^2 A = ( (sinA - sinAcosA)/cosA) /sin^2 A = (sinA(1 - cosA)/cosA)/sin^2 A = (1 - cosA)/(sinAcosA) RS = (sinA/cosA) / (1 + cosA) = (sinA/...
*March 22, 2016*

**Arithmetic progression**

S(n) = (n/2)(2a + (n-1)d) = 2n divide by n and double 2a + (n-1)d = 4 S(2n) = (2n/2)(2a + (2n-1)d) = n divide by n 2a + (2n-1)d = 1 subtract these two equations, (n-1)d - (2n-1)d = 3 nd - d - 2nd + d = 3 -nd = 3 nd = -3 S(4n) = (4n/2)(2a + (4n-1)d) = 2n(2a + 4nd - d) = 2n(2a -...
*March 22, 2016*

**math**

1st: Where did you get the denominator of 40 from, isn't it 9/20 ?? 2nd: correct 3rd: prob(odd and less than five) = 2/6 = 1/3 so out of 12 tries, (1/3)12 = 4 correct
*March 22, 2016*

**Math**

amount = 2000(1 + .05/4)^20 = ...
*March 22, 2016*

**Math Probability**

done, check further up in the listing for your later post
*March 22, 2016*

**Algebra**

amount invested in the 2% account --- x amount invested in the 4% account = 1500-x solve for x .02x + .04(1500-x) = 44
*March 22, 2016*

**probobility**

a) no condition: 7x7x7x7 = 7^4 = 2401 b) no repeats: 7x6x5x4 = 840 c) begin with A, can I repeat the others ? I will assume I can: 1x7x7x7 = 343 d) same as c) 7x7x7x1 = 343 e) 2nd letter is a vowel 7x2x7x7 = 686 In c), d) and e) I assumed that letters can be repeated, you did ...
*March 22, 2016*

**Math**

Your equation makes no sense to me at all An equation only is useful and meaningful if the variable has been defined. Let the number of nickels be x then the number of dimes is 21-x Now for the value of those coins: 5x + 10(21-x) = 165 5x + 210 - 10x = 165 -5x = -45 x = 9 then...
*March 22, 2016*

**math**

Number of possible pairs chosen = C(21,2) = 210 number of ways to choose 2 of the 3 friends = C(3,2) = 3 prob(of stated event) = 3/210 = 1/70
*March 22, 2016*

**math**

notice that 10 is added to a term to obtain the next one, so -1, 9, 19, 29, 39, 49, 59, ... none of the given choices is correct C has 69 instead of 59 at the end, unless you have a typo
*March 22, 2016*

**Algebra**

let the smaller be x then the larger is x+2 3(x+2) + (1/2)x = 34 3x + 6 + (1/2)x = 34 multiply each term by 2 6x + 12 + x = 68 7x = 56 x = 8 state your conclusion
*March 22, 2016*

**matth....**

√4 = 2 , so it is rational The other three are irrational
*March 22, 2016*

**math**

width ---- x length ----3x-4 perimeter = 2widths + 2 lengths 56 = 2x + 2(3x-4) carry on
*March 22, 2016*

**remainder help!@steve and damon**

Do you have a typo? your first 3 terms have exponents of 2, but the last term is 10^10. I will assume it is to be 10^2 sum of all squares up to n terms = n(n+1)(2n+1)/6 so if n = 10, sum = 10(11)(21)/6 = 385 which when divided by 5 leaves a remainder of zero
*March 22, 2016*

**Algebra 2**

Make sure you include brackets in your solution, at first look your equation made little sense. 4^(2b-3) = 8^(1-b) (2^2)^(2b-3) = (2^3)^(1-b) = 2^(4b-6) = 2^(3-3b) thus 4b-6 = 3-3b 7b = 9 b = 9/7 how did you get -9/7 ??
*March 22, 2016*

**Math please help**

Since she has 100 stamps in total, the number of stamps for each country matches the percentage for that country e.g. she has 24 French stamps and 29 Norwegian stamps Can you now answer the question?
*March 22, 2016*

**Math**

Let the total be x children = (2/5)x women = (5/8)(3/5)x = (3/8)x children + women + men = total (2/5)x + (3/8)x + 90 = x multiply each term by 40 16x + 15x + 3600 = 40x continue ....
*March 22, 2016*

**maths**

I constructed my trap ABCD, so that AB=5, BC=4, CD=8, and DA=6 with BC and AD both having a negative slope, (leaning to the left) I dropped perpendiculars from B and from A to meet CD at M and N respecively. (M is on the extension of DC) I let MC = x, then ND = 3+x Notice that...
*March 22, 2016*

**maths**

ax2+bx+c=0 ax^2 + bx = -c <--- subtracted c from both sides x^2 + (b/a)x = -c/a <--- divide everybody by a x^2 + (b/a)x + b^2/(4a^2) = -c/a + b^2/(4a^2) <--- "completed the square" (x + b/(2a) )^2 = (b^2 - 4ac)/(4a^2) <---simplified x + b/(2a) = ±...
*March 22, 2016*

**math help pls pls pls**

I see an x^5 in A and in C
*March 21, 2016*

**math help pls pls pls**

show powers like this: x^4 now in which expression do you see x^5 as the highest term ??
*March 21, 2016*

**math help pls pls pls**

Would it not be much easier to type : 15x^2 y^6 + 50x^4 y^3 - 20x^2 y ? You appear to have forgotten the divisor
*March 21, 2016*

**Algebra 2**

You need brackets to establish the correct order of operation (x^2-9)/(x^2-5x) (5x-x^2)/(x^2-x-12)(x^2-8x+16)/(x-4) = (x+3)(x-3)/(x(x-5)) (x)(5 - x)/((x-4)(x+3)) (x-4)(x-4)/(x-4) = -(x-3) , x ≠ 0, ±3, 4, 5 or = 3-x , x ≠ 0, ±3, 4, 5 Don't use the ...
*March 21, 2016*

**Algebra**

the -7 + i has a conjugate partner of -7 - i so (-7+i)(-7-i) = 49 - i^2 = 50 -7+i + (-7-i) = -14 so we can form the quadratic as x^2 + 14x + 50 as one of the factors. the other is (x+9) so the polynomial could be f(x) = (x+9)(x^2 + 14x + 50)
*March 21, 2016*

**Algebra**

what about it ? It is in point-slope form. Are you bothered by the decimals and/or the fraction ?
*March 21, 2016*

**Math**

Jerry has been doing these push-ups for quite some time, as you can see in the Related Questions below. Only the numbers keep changing. Change the solution here to fit your problem http://www.jiskha.com/display.cgi?id=1452469132
*March 21, 2016*

**Math**

at least 2 reds ---> 2 reds, or 3 reds, or 4 reds, or 5 reds or exclude 0 red and 1 red There are 20 cards of which 10 are red prob(red) = 10/20 = 1/2 number(no red) = C(10,0) C(10,5) = 252 number (1 red) = C(10,1) C(10,4) = 2100 number of 5-card hands without restriction...
*March 21, 2016*

**Math**

A - correct B - I assume we can now use the 1 ?2?4? , so we can use only 7 other digits number of ways = 7x1x6x1x5 = 210 c - correct D - evens at front and end 4x?x?x?x3 , leaves 7 for the other places= 4x7x6x5x3 = 2520
*March 21, 2016*

**Math**

makes no difference, you can do both ways in your head, since (anything)^0 = 1 you will get 1
*March 21, 2016*