# 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

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

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

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!

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

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