# Posts by Reiny

Total # Posts: 39,952

**math**

btw, point are written in the form (-3,-5) and (-3,-6) your answer is incorrect. As Scott suggested, you have a vertical line. Horizontal lines have zero slope, Vertical lines have .......

**Solids math**

A cube has a column of ?? A cube has a volume of ... ? If so, what is the cube root of 125 ?

**Math (Integrals) (Using given method)**

?sin^2(? x) dx = ?(1/2)(1-cos(2?x) ) dx ---> you had that = ?(1/2 - (1/2)(cos 2x) dx At this point you should be able to put your brain in reverse and ask yourself, "what do I need so that the derivative is 1/2 - (1/2)(cos2?x) remembering that d(sin kx)/dx = k cos kx I...

**Calculus I'm really confused**

dy/dx=y^2/x^3 (1/y^2) dy = (1/x^3) dx ?(1/y^2) dy = ?(1/x^3) dx ? y^-2 dy = ? x^-3 dx - y^-1 = -(1/2)x^-2 + c -1/y = -1/(2x^2) + c at (1,1) -1 = -1/2 + c c = -1/2 -1/y = -1/(2x^2) - 1/2 = (-1 - x^2)/(2x^2) 1/y = (1 + x^2)/(2x^2) y = 2x^2/(1+x^2) f(x) = 2x^2/(1+x^2) check my ...

**Algebra**

Just realized I answered the same question over 2 years ago http://www.jiskha.com/display.cgi?id=1421083338

**Algebra**

or number of children --- c number of adults ---- a a+c = 9 c = 9-a 210c + 315a = 2205 210(9-a) + 315a = 2205 1890 - 210a + 315a = 2205 105a = 315 a = 3 c= 6 3 adult and 6 children check: 1+8 = 9 210(6) + 315(3) = 2205

**Calculus Please Check my answer**

I agree with your first line =.1*4/2+.1*7/2+.3*10/2+.2*13/2+.2(15/2)+.1*18/2 = .1(2) + .1(3.5) + .3(5) + .2(6.5) + .2(7.5) + .1(9) = .1(2+3.5+15+13+15+9) = .1(57.5) = 5.75

**Algebra 2**

no, it is lim x? ? f(x) = 3 your choice would simply be the point (0,3)

**Math**

or the z-score for 71 = (71-64)/35 = 2 going to your tables, or some other suitable source for standard deviation, we find P(z < 2) = .9772 P(z > 2) = .0228 .0228(3000) = 68.4 or appr 68 plants see http://davidmlane.com/normal.html You can enter the data as is, click on ...

**Calculus**

you might have noticed that if we find dy/dx for a circle of the form x^2 + y^2 = r^2 we get 2x + 2y dy/dx = 0 dy/dx = -2x/(2y) = -x/y So we had a circle of the form x^2 + y^2 = r^2 plug in the given point to find r^2 and you are done.

**Calculus**

let the dimensions by x by x by y we know x+x+y ? 138 2x + y ? 138 y ? 138-2x V = x^2 y = x^2(138-2x) = 138x^2 - 2x^3 dV/dx = 276x - 6x^2 = 0 for a max of V 6x^2 = 276x 6x = 276 x = 46 then y = 138-92 = 46 so the box must be a cube of 46 by 46 by 46 as suspected notice 46+46+...

**Geometry**

Volume of first = (1/3)(5^2)(9) = 75 cubic inches 2nd volume = 75 = (1/3)(b^2)(1) = b^2/3 b^2/3 = 75 b^2 = 225 b = ?225 =15

**Statistics**

prob(a 1,2,3, or 4) = 4/6 = 2/3 prob(5 or 6) = 1/3 expectations = (2/3)($1) + (1/3)($3) = $0.67 + $1 = $1.67

**Statistics**

find the prob that he/she will get 8 out of 10, 9 out of 10, or 10 out of 10 correct I will do the 8 out of 10, you do the others prob(exactly 8 out of 10) = C(10,8) (1/2)^8 (1/2)^2 = 45 (1/2)^10 = 45/1024 = appr .0439 Find the other two, and add them up

**math**

No interest ? a deposit of $49.99 ? A rather silly question unless the intent is to see if you can multiply 12 by 49.99 in your head. What would be an easy way to do that ?

**Statistics**

so you want: prob(3 turn up 6) + prob(4 turn up 6) +prob(all 5 turn up 6) = C(5,3) (1/6)^3 (5/6)^2 + C(5,4)(1/6)^4 (5/6) + C(5,5)(1/6)^5 (5/6)^0 = ...

**Math**

your equation h= -16t^2+20t+6 is modelled by a parabola which opens downwards. Find the vertex of this parabola by the means that you learned, and you will have both answers.

**math**

let the smaller be x then the larger is x+33 (x+33) - 3x = 1 easy to solve.

**Calculus**

Make a sketch. Mine has a straight shore line and a lighhouse L and a point A on the shore so that LA is perpendicular to the shore. I let P be a point on the shore so that AP = x Let Ø be the angle between LA and LP given: dØ/dt = 4(2?) radians/min = 8? rads/min...

**Math**

width --- x length ---- 2x+5 x(2x+5) = 42 2x^2 + 5x - 42 = 0 solve for x hint: it factors

**math**

distance = 7(1/6) = 7/6 miles time = 3 1/3 minutes = 10/3 minutes = (10/3)/60 hrs = 1/18 hr speed = distance/time = (7/6) / (1/8) mph =28/3 mph or appr 9.3 mph

**Algebra**

More information needed The way it stands, (1/2)lw = 18 lw = 36 e.g. l = 2, w = 18 l = 4, w= 9 l = 10, w = 3.6 there is an infinite number of possibilities

**Math**

no, (x+3x)(10)/2 = 720 multiply both sides by 2 10(4x) = 1440 40x = 1440 x = 36 so the sides are 36 and 108 check: area = (36+108)(10)/2 = 144(5) = 720 as required. Time to review how to solve simple equations.

**Math**

area of trap = (a+b)(h)/2, where a and b are the two parallel sides and h is the distance between them. you have: (x+3x)(10)/2 = 720 solve for x , then the bases are x and 3x

**Math**

a + c = 134 ---> a = 134 - c 5.4a + 9.3c = 957.6 54a + 93c = 9576 18a + 31c = 3192 sub in a = (134 - c) and solve for a

**Pre calc quick question**

f(x)=?( x^2-16) let's first look at it http://www.wolframalpha.com/input/?i=f(x)%3D%E2%88%9A(+x%5E2-16) consider only the "blue" graph, which is the reals clearly the domain is y ? 0 for the domain, x^2 - 16 ? 0 x^2 ? 16 x ? 4 OR x ? -4 If x ? -4 is part of the ...

**calc**

since they both say y = ... x^3 - 4x= -x - 2 x^3 - 3x + 2 = 0 by inspection x = 1 is a solution are there others? Use your favourite method to find the other factor, I got x^3 - 3x + 2 = (x-1)(x^2 + x - 2) = 0 (x-1)(x+2)(x-1) = 0 if x = 1, y = ... if x = -2, y = ....

**calc**

Find the derivative implicityl 2(x-1) + 2(y-1) dy/dx = 0 plug in (4,-3) , find dy/dx, which is the slope Now that you have the slope and a point, use the method you learned to find the equation of the straight line

**Math**

1. r = 8.4 area = ?(8.4)^2 = 221.67 to the nearest hundredth using a proper value of ? (nobody uses 3.14 anymore, that is so 1960's, if you did it would be 221.56 , quite an error) #2, - incomplete

**Algebra**

Ummh, the amplitude is 5 We also need a vertical shift, as well as a phase shift. I had y = 5cos (?/5(x + 3)) + 9 test: let x =2 , (2:00 am) y = 5cos ? + 9 = 5(-1)+9 = 4 ft, let x = 7, (5 hours later, the max of 14) y = 5cos (2?) + 9 = 5(1) + 9 = 14 ft http://www.wolframalpha....

**maths**

Assuming that the decrease is linear, we could use 2 ordered pairs of the form (t, d) to find the equation , where t is the time, and d is the temperature in ° how about (3,5) ----> at 3:00 the temperature was 5° and (4,3) slope = (3-5)/1 = -2 ---> tells me temp ...

**MATH**

Your choice of Pentagonal pyramid would have 5 vertices at its base plus 1 at the vertex, so 6 vertices, so you are incorrect Make a sketch of a standard rectangular pyramid, (like the common Egyptian pyramid) and count the faces, vertices and edges.

**Math**

Write it this way: (5x - 3)/2 = 4 multiply both sides by 2 add 3 to both sides divide both sides by 5

**Math**

If I wrote it as 3x - 1(5x+2) could you do it?

**Math**

let the shares be 3x, 4x, and 5x 3x + 4x + 5x = 360000 solve for x, sub into my definitions

**Stat**

You are choosing 4 privates from 10, and 2 first class from 5 = C(10,4) * C(5,2) = ....

**Math**

wording is too ambiguous. why are you using the division sign "/" and then "divided by" in the same expression?

**Math**

4m(m-3)+2m^2 = 4m^2 - 12m + 2m^2 = .....

**Math**

1 km = 1000 m 1 hour = 3600 s so, 2 m/ 1s = (2/1000) / (1/3600) km/h = (1/500)(3600) km/h = 7.2 km/h

**math**

You didn't ask a question. Assuming we are factoring: 12x^3 - 26x^2y^2 - 30xy^3 = 2x(6x^2 - 13xy^2 - 15y^3) Much Ado About Nothing

**math**

Direct method: sister ---- x Monica --- (1/3)x or x/3 6 years from now: age of sister = x+6 Monica's age = x/3 + 6 x/3 + 6 = (1/2)(x+6) multiply each term by 6, the LCD 2x + 36 = 3(x+6) 2x+36 = 3x + 18 18 = x The sister is 18, and Monica is 6 or sometimes fractions can be ...

**Math**

What is 2000(.75)^3 ?

**Calculus**

Your question should have been ... "At what point is the function y=csc(2x) NOT continuous?" to make more sense. Remember that csc A = 1/sinA since we cannot divide by zero , the csc(2x) is in trouble whenever sin(2x) = 0 look at y = sin(2x) , when is it zero??? http...

**Math**

prob(yellow) = 1/20 how many chips are left in the bag? how many of those are yellow? What do you think?

**algebra**

#1 and #2 are correct #3 ?(490y^5w^6) = ?49?10 (y^2?y)(w^3) = 7?10 y^2w^3 ?y <--- not one of the choices #4 (?(15y))(3?(81y)) = ?15?y (27?y) = 27y?15 #5 can't tell where the square root ends without brackets #6 1 apple + 6 apples = 7apples 1dollar + 6 dollars = 7 ...

**finance**

first 7 years: i = .05/12 = .004166... n = 7(12) = 84 amount after 7 years = 470(1.041666...^84 - 1)/.004166.. = 47154.47 This will accumulate for another 7 years at 7% pa, compounded monthly i = .07/12 = .0058333... n = 84 amount of first investment = 47154.47(1.0058333..)^84...

**math**

If you meant: g(x)=3/(7x+6) and h(x)=3/(7x-3) the curves look a bit more interesting. http://www.wolframalpha.com/input/?i=plot+y+%3D3%2F(7x%2B6)+,+y+%3D3%2F(7x-3)

**Math**

Hope Clip company complies with Toblerone's copyrights. https://www.google.ca/search?q=toblerone+bar&rlz=1C5CHFA_enCA690CA690&tbm=isch&imgil=QXasLdDaU6pvKM%253A%253B6WE2iIqU9_CjjM%253Bhttp%25253A%25252F%25252Fwww.telegraph.co.uk%25252Fnews%25252F2016%25252F11%25252F08%...

**Geometry**

Cut and paste does not work here, as you can see, but I think I followed your coding. extend both CB and DA to meet at P let FB = 3x, let CF = 4x, let BP= a, let FE = k (we want k) you now have 3 similar triangles PBA, PFE, and PCD a : a+3x : a+7x = 7 : k : 10 a/7 = (a+7x)/10 ...

**algebra equation**

Patience, patience, just did it look back to your previous post 20 minutes ago

**algebra**

correct, good job

**algebra**

"The sum of " --> going to add some stuff, what am I adding? "The sum of the distance, d, divided by 4 and 6" d/4 + 6 " amounts to" , another word for = d/4 + 6 = "2 subtracted from twice the distance, d" d/4 + 6 = 2d - 2 Now do the ...

**Math**

So we are just randomly adding a bunch of numbers that we see ?? I think you knew that the answer was supposed to be 9, so you just "did something" with the 4 numbers given that produced 9. If not, please explain why you added 3+2+4 ? correct way: slope is 5, point ...

**Math**

number over 12 ---- x number under 12 ---- 6-x total weight = 20x + 40(6-x) = 20x + 240 - 40x = 240 - 20x now we know that x is a whole number from 0 to 6 x --- weight 0 240 1 220 2 200 3 180 4 160 5 140 6 120 All the answers they give are possible, so clearly they did not ...

**sir steve reiny plz maths**

and the sum of their cubes is (?5)^3 or 11.18...

**sir steve reiny plz maths**

You don't say what kind of numbers they are , e.g. if they are rationals a=1 b = .5 c= 1.1 d= 1.4 sum of squares of those 4 = 4.42 then the 5th number is ?.58 if they are integers, they must be ±1,±1,±1,±1,±1 or ±2,±1,0,0,0 ...

**Maths**

#2 I don't know brahmagupta's method, but I remembered a method that uses continued fractions. It is a rather easy method compared to some of the other methods that are out there It involves finding the continued fraction terms of ?67 which are 8; 5,2,1,1,7,1,1,2,5,16 ...

**Math**

Assuming we have 7 males and 7 females number of committees = C(7,5)*C(7,1) = ...

**math**

you have to consider the CAST rule using Bosnians answers, we have to eliminate some of the ± cases since sin ? = 12 / 13 ? could be in quadrants I or II in quad I sin?= 12/13 , csc? = 13/12 cos? = 5/13 , sec? = 13/5 tan? = 12/5 , cot? = 5/12 in quad II sin? = 12/13 , ...

**Pre-calculus**

The y = 50000 sure helps, without it it couldn't be done so you want (2*10^(-44))*(e^(0.055x)) = 50000 divide by that extremely small number e^(0.055x) = 2.5*10^48 take ln of both sides and use log rules .055x = ln (2.5*10^48) .055x = 111.44 x = appr 2026.2

**math urgent please**

look at the pattern. Two teams A, B one game: C(2,2) = 1 ---> from 2 choose 2 for a game AB Three teams A,B,C AB, AC, BC --- three games , C(3,2) --> from 3 choose 2 for a game Four teams A,B,C,D AB, AC, AD, BC, BD, CD - 6 games, C(4,2) ---> from 4 choose 2 ... n ...

**Math**

time on bus = distance / rate = 5km/60 km/h = .08333 hrs = 5 minutes (you had distance = rate/distance !) that leaves 20 minutes or 1/3 hour for walking the 2 km rate of walking = 2/(1/3) = 2(3/1) = 6 km/h

**Statistics**

You should have learned that 68% fall between +1 and -1 deviations of the mean. Since 20-25 is one standard deviation below the mean, without any calculation I know it is appr 34% using my favourite stats site http://davidmlane.com/normal.html I got .3413 or 34.13%

**math seriously help me**

I have a suspicion that your equation looked something like an = 2(3^n) - 1 or else , why wouldn't they have written it as an = 6n - 1 , which would indeed be linear, If it is as I suspected, it would be exponential.

**Math PLZ check soon!**

I agree with all of your answers. Good job

**Statistics**

prob(7) = 1/6 prob(11) = 2/36 = 1/18 let X be the event of throwing a 7 or 11 prob(X) = 1/6 + 1/18 = 2/9 prob(notX) = 7/9 odds against X = 7/9 : 2/9 = 7 : 2

**math help. (check answer)**

no idea what your lantern looks like you have given the dimensions of the box. If the lantern has only the 4 sides, it would be 4(12x6) = 144

**Probability**

prob(exactly 3 of 5 will complete) = C(5,3) (2/5)^3 (3/5)^2 = 10(72/3125) = 144/625 or .2304 prob(exactly 4 of 5 will complete) = .... prob(exactly 5 of 5 will complete) = ... add them up

**Math**

let's look a bit further in the pattern 3! = 3*2*1 -----> = 2^1*3 4! = 4*3*2*1 ---> 8*3 = 2^3 * 3 5! = 5*4*3*2*1 --> 8*15 = 2^3 * 15 6! = 6*5*4*3*2*1 = 16*45 = 2^4 * 45 7! = ...... = 16*315 = 2^4 * 45 8! = ..... we are multiplying by 8 which is 2^3, so we have 2^7...

**Math**

1/3 * 2/4 * 3/5 * 4/6 * 5/7 *... ... ... * 98/100 = (1*2*3*4*5*...*98)/(3*4*5*6*...*100) notice all factors in the top from 3*4*..*98 cancel with those at the bottom, leaving you with 1*2/(99*100) = 2/9900 = 1/4950

**maths**

a) What is 152/8 ? b) 60/8 = 7 4/8 line-up of pictures: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 <-- second poster .... 49 50 51 52 53 54 55 56 <--- 6th row 57 58 59 60 61 62 63 64 <-- 7th row 60/8 = 7 4/8 7th poster, 4th picture

**maths**

nope x + x+11 = 9^2 2x + 11 = 81 2x = 70 x = 35 the mother is 35 check: if the mother is 35, then dad is 46 the sum of their ages is 81 which is 9^2 answer of 35 is correct

**maths**

mom ---- x dad ------ x+11 Just translate "The sum of her parents age is the square of Jade's age " into math x + x+11 = 9^2 solve for x

**maths**

number of oranges ---- x number of mangoes ---- 2x solve for x: x+2x = 450 now that you know the number of each, all will fall into place

**math**

Sorry, I posted the wrong link http://www.jiskha.com/display.cgi?id=1423156385

**math**

notice that here https://istrumpatmaralago.org the wording makes sense. Is that what you mean? Then follow the method that Steve used in the question.

**math**

suppose each part was x and then apply changes 1st: x-4 2nd: x+5 3rd: x/2 4th: 3x x-4 + x+5 + x/2 + 3x = 155 5.5x = 154 x = 28 the four parts are 24, 32, 14, and 84 I find it hard to understand what the question really is. Very confusing wording.

**math**

circumference = 7700/14 ft = 550 ft since C = 2?r 2?r = 550 r = 275/? area = ?(275/?)^2 = (275^2)/? = appr 24072.2 ft^2 I waited to do any calculations to the very end, then used ? of my calculator.

**Math**

I did not get that, show me your work to see where you went wrong.

**math**

RS = cot^2 a (1 - csc^2 a) = cot^2 a (-cot^2 a) = - cot^4 a ? LS not true, check your typing

**Math**

no obvious repeat can be seen in the decimal, but the "..." shows an infinite number of decimals, so as it stands I would label it irrational

**Calculus**

I agree with you. I also found the 2nd derivative to be (1/2)t^2 - 3t + 4 and the third derivative to be t - 3 since the 2nd derivative is a quadratic opening upwards, you would have a minimum at t = 3 Could be a misprint

**Math check?**

I read that as f(x) = x^2 - x - 6x^2 - 8x + 15 = -5x^2 -9x + 15 -5x^2 -9x + 15 = 0 5x^2 + 9x - 15 = 0 use the quadratic formula to solve. Both zeros are irrational Somehow I suspect you have a typo in your equation.

**Math**

Notice that is simply a geometric series, where a = 1/5, r = 1/5 since Sum(all terms) = a/(1-r) = (1/5)/(4/5) = 1/4 , it clearly converges What made you think it diverges? What have you studied about diverging and converging series? ( simply adding the first 4 already gives us...

**Algebra 2**

assuming you meant f(x) = 2sin(x^2) - 1 look at the graphs of these two: http://www.wolframalpha.com/input/?i=plot+y%3D2sin(x%5E2)%E2%88%921+,+y%3D2sin(x)%E2%88%925 none of the given answers are correct. The problem is the x ---> x^2 There is compression, but at an ...

**Math help....**

Unusual to have an x in a polar form, was expecting 3r = -6cosØ , will assume that. recall that cosØ = x/r so 3r = -6x/r 3r^2 = -6x x^2 + y^2 = -6x for 3xy = 5 cosØ = x/r ---> x = rcosØ and sinØ = y/r --> y = sinØ 3(rcosØ...

**Math Help ASAP**

All 3 are correct

**Algebra 2 helppppp**

correct

**Math**

Actually, the way you typed the question, you are correct According to the order of operation, each term in the bracket is divided by 2, then multiplied by m^3 multiplication and division is done in the order they occur. What the question probably meant was (-6m^9 - 6m^8-16m^6...

**Math**

after 1 year ---- 950000(.9) = after 2 years ----950000(.9)^2 .. after 5 years ---- 950000(.9)^5 = ....

**Algebra**

amount invested at 4% --- x amount invested at 5% ---- y .04x + .05y = 1000 4x + 5y = 100000 , #1 reversed: .05x + .04y = 1050 5x + 4y = 105000 , #2 solve these two equations.

**Algebra**

unit cost price .... x return = 1.3(8) + .6(92) = 65.6 percentage = 65.6/100 = 65.6% So there is a loss of 34.4% test: suppose he bought them at $1 per egg cost price = $100 return = 8(1.30) + 92(.60) = 10.40 + 55.20 = $65.60 He lost $34.40 out of the $100 he spent. So loss is...

**math question**

You already stated the answer. It is 9/16 of its original area. You probably meant to ask: How do the sides of the reduced triangle compare to the original sides? Remember what I told you in a question similar to this? "The area of similar shapes is proportional to the ...

**Math**

total members ---- x girls ------ (3/8)x or 3x/8 girls that are 6 graders = (2/5)(3x/8) = 6x/40 = 3x/20 so (3/20) of the members are 6 grader girls

**math**

Go with Plumpycat's table, I started mine with the wrong time at 1:00 , DUH here is an easy way 80 false minutes = 60 reals at 6:00 false times , 300 false minutes have passed 80/300 = 60/x 80x = 18000 x = 225 real minutes = 3 hours and 45 minutes add that to 1:00 ---->...

**math**

let's make a chart, RT = real time, FT = false time time expressed as an fraction number since 20 minutes = 1/3 hour .... RT - FT 1.0 1+1/3 = 4/3 --> 1:20 2.0 4/3+4/3 = 8/3 --> 2:40 3.0 12/3 = 4.0 --> 4:00 4.0 16/3 --> 5:20 5.0 20/3 --> 6:40 So the real time...

**math**

let's pretend that a "cog" is a unit of distance so in 160 revs the second wheel went 160(54) or 8640 cogs in that same time the first wheel had to do 8640/32 or 270 revolutions it did that in 45 seconds, so it went 270/45 or 6 revolutions per second ---> so ...

**Statistics**

ok, ok I have answered quite a few for you now. You have shown no ideas or steps of your own. How do you think you should start this one?

**Statistics**

Assuming that he can answer them in any order and that he is not restricted to anwering only 3 of the first 5, that is, he could answer all of the first five. step one: number of ways to answer the obligatory questions = C(5,3) = 10 So now he has to answer 7 more of any of the...

**algebra**

First of all, I would multiply each term by 100 519(y-10) +610 = 300(y - 6.6) + 430 519y - 5190 + 610 = 300y - 1980 + 430 look, no decimals, no fractions, take over