Wednesday
February 10, 2016

Posts by Steve

Total # Posts: 37,530

maths
well, 6000 is 5/12 std above the mean. Look that up in your Z table. You can play around with this stuff at http://davidmlane.com/hyperstat/z_table.html
December 31, 2015

Math
you want to solve for t in 400t - 16t^2 = 2400 Then find the difference in the two times.
December 31, 2015

probability
well, using brute force, just list the ways you could pair up the socks. How many of those ways fit the requirements?
December 30, 2015

Physics
for inital velocity v, we have h(t) = vt-(g/2)t^2 This reaches a max height at t=v/g, and h(v/g) = v(v/g) - (g/2)(v/g)^2 = v^2/g - v^2/2g = v^2/2g So, we see that max height is directly proportional to v^2 So, double v, and you quadruple the max height. M does not matter, as ...
December 30, 2015

Math
In the first G.P. the numbers are a, ar, ar^2 To form the A.P., the differences are constant, so ar-a = ar^2-4 - ar Then, forming a new G.P. with constant ratio, we have (ar-1)/a = (ar^2-4-1)/(ar-1) Solving for a and r, we have a=1, r=3 or a = 1/9, r=7 The 1st G.P. is 1, 3, 9 ...
December 30, 2015

physics(optics)
nothing.
December 30, 2015

Physics
well, the acceleration is 4 m/s^2, and F=ma.
December 30, 2015

Math advanced function
Since a quadratic can two solutions, and a trig function can two solutions per period, I expect that 4 solutions is as many as you can have. For example, sin^2(x) = 1/4 has 4 solutions in one period. sin^2(x) = 2 has none, sin^2(x) = 1 has two Maybe you can find some with an ...
December 30, 2015

Math
Draw the triangles. Recall that the sides are in the ratio 1:√3:2 Label the longest hypotenuse, and then work down to get the desired leg's size. I get 6. I am assuming there are only two triangles.
December 29, 2015

Physics
check your previous post.
December 29, 2015

maths
In that case, recall that one log is the reciprocal of the other. So, If you let u = log3x, then you have u + 1/u = 5/2 2u^2 - 5u + 2 = 0 (2u-1)(u-2) = 0 u = 1/2 or u=2 Thus, u = √3 or 9
December 29, 2015

maths
Or, did you mean log3x+logx3 = 2.5 ?
December 29, 2015

math
If the lawn has side x meters, then lawn area: x^2 total area: (x+1)^2 path area: (x+1)^2-x^2 = 2x+1 So, we have x^2 = 2x+1 + 23 Now just find x.
December 29, 2015

Physics
original: <0,-398> wind: <-104,0> result: <-104,-398> = 411 at 195° or 411 at S15°W To get back on course, you just need to negate the wind. So, you want <x,y> + <-104,0> = <0,-398> <x,y> = <104,-398> or 411 at S15°E
December 29, 2015

stats
9 dancers total 5 warmed and had no injuries (W & ~I) You want ~W or I = ~(W & ~I) So, your probability is 1 - 5/9 = 4/9
December 29, 2015

maths
well, 3000 is 20 times 150, so it will take 20 times as long, right?
December 29, 2015

Maths
which two factors of 15 differ by 2?
December 29, 2015

Factorize
a^3-b^3 = (a-b)(a^2+ab+b^2) so, x^3 - (x+y)^3 = (x-(x+y))(x^2+x(x+y)+(x+y)^2) Now just simplify that.
December 29, 2015

Maths
well, just substitute: √(1-x^2) = √(1-sin^2 θ) Now, what is your most basic trig identity?
December 29, 2015

chemistry
same as 1 mole of any compound: Avogadro's Number of molecules. Maybe you should review molar mass...
December 29, 2015

Wave
look at the units: f = 1/s speed = m/s So, wavelength (m) = speed/f
December 29, 2015

Math
w+d = 46 (w+4)/(d+4) = 7/2 Now just solve for w and d.
December 29, 2015

St. Francis English medium school.
If the price is each, then we have cost: 110 revenue: 110, with one left over On the other hand, he made a gain of 10% one each clip sold.
December 28, 2015

algebra
If the length is y, then the width w is 1 + y/4. So, 2(1 + y/4 + y) = 62 Now just solve for y, and you can find w.
December 28, 2015

Math
If you mean (2x+7)/(2x^4+21x^3+35x^2-37x+46) then that is approximately (2x+7)/((x+7.966203)(x+3.527066)(2x^2-1.98654x+1.63717)) Now you can just use partial fractions on that mess.
December 28, 2015

mathematics
And assuming the usual sloppiness in the numerator, we have (x²+x+4)/[(1-x)(x²+1)] = (2x+1)/(x²+1) + 3/(1-x) amazing how little difference it made, eh?
December 28, 2015

maths
for x in [0,10000), f(x) = 900 for x in [10000,15000), f(x) = 900+.02(x-10000) for x in [15000,25000] f(x) = 900+.02(x-10000) + 500 I think you can discuss the continuity. If not, draw the graph and it will become clear.
December 28, 2015

mathematics
this cannot be more straightforward, if you have read the relevant section in your text. Namely, the equation for a circle with center at (h,k) and radius r is (x-h)^2 + (y-k)^2 = r^2 Surely you can now see what to do...
December 28, 2015

<b>͡ ͜ʖ ͡</b>
:-)
December 28, 2015

pi -- NOT pie!
grrr
December 28, 2015

PHYSICS
Resolve F1 and F2 into x- and y-components, and then just add them up.
December 28, 2015

physics
conserve momentum: 5(-10) + 6(12) = (5+6)v That will give the final velocity v. Then find KE (1/2 mv^2) for each body before and after the collision.
December 27, 2015

physics
since C=2πr, just multiply the circumference by the revs/min. That will give the speed in cm/min.
December 27, 2015

Math
I suggest that would be 3/5 * 3 = 9/5 mi
December 27, 2015

Calculus
Of course it works. Why don't you show your work and the reason why you rejected it? 2/((2-x)(x+2)^2) = (1/8) (1/(x+2) + 4/(x+2)^2 - 1/(x-2)) So, the integral is just (1/8) (ln(x+2) - 4/(x+2) - ln(x-2)) = (1/8) (ln((x+2)/(x-2)) - 4/(x+2)) + C
December 27, 2015

math
for 2 cm, r=2. So, just figure the circumference of the circle of radius 2... 100/3 rev/min * 2π*2 cm/rev = 400π/3 cm/min similarly for r=15.
December 27, 2015

komenco
Assuming you mean Geometric Sequence, we have For The AP, a=7, so we want d. The ratio between terms of a GP is constant, so we form the ratio between successive given terms of the AP: (7+d)/7 = (7+4d)/(7+d) d=14 or d=0 Now, d=0 is not very interesting: AP = 7,7,7,7,7... GP...
December 27, 2015

mustapha
well, first evaluate 10^(1/3) = 2.1544 Then just multiply as usual.
December 27, 2015

Math
the derivative of sec(u) is sec(u) tan(u) But, if u is a function of x, then we have to apply the chain rule. Since u=tanx, then du/dx = sec^2(x) So, the final damage is sec(tanx) tan(tanx) sec^2(x)
December 27, 2015

math
well, what is half the circumference of the circle? Then just multiply that by the cost per foot.
December 27, 2015

Math
I think you've both gone stray. See http://www.wolframalpha.com/input/?i=derivative+%28sinx%2F%281%2Bcosx%29%29 and http://www.wolframalpha.com/input/?i=derivative+%28sinx%2F%281%2Bcosx%29%29^2
December 27, 2015

math
Because y(0) = 0. It helps if you actually read what I write. Or maybe it has something to do with the mysterious "a".
December 27, 2015

math
well, f'(x) = cos(√2 x) - √2 x sin(√2 x) Not sure what a has to do with things, but if you meant x=0, then f(0) = 0 f'(0) = 1 So, you want the line with slope 1, which passes through (0,0). No too much of a challenge there, eh?
December 27, 2015

math
cancel what out? There are no common factors.
December 27, 2015

math
well, the 1st three terms are 2^2, 3^3, 4^4, so what's your best guess?
December 26, 2015

Maths
42a
December 26, 2015

physics
As I recall, the force grows as the ratio of the areas of the pistons. That means, as the square of the diameter. So, since 6 = 3*2, the force would be 3^2 * 20 Review your text on this subject. I'm sure there are examples. And you can always rely on google for lots of ...
December 26, 2015

Calculus
rearranging things a bit, we have y' = y(t+1) + t+1 y' = (y+1)(t+1) dy/(y+1) = (t+1)/t^2 dt ln(y+1) = ln(t) - 1/t + c y+1 = t e^(-c/t) + c2 or, altering the c values, y = ct e^(-1/t) + c2 y(1) = 0, so 0 = c/e + c2, so c2 = -c/e y = c(t e^(-1/t) - 1) We can ignore the c...
December 25, 2015

Math
how about if we start by saying y-1 = 3sin((1/2)(x+pi)) and y+2 = -1/3 cos(2(x - pi/2)) the shifts and scalings should now be clearer.
December 25, 2015

math
There are infinitely many chords passing through any point within the circle. Two such chords, easy to describe are x=2 and y=3.
December 25, 2015

Statistics
18 rings total, so that would make the probability 10/18 * 9/17
December 25, 2015

math
There are infinitely many chords passing through any point within the circle. Two such chords, easy to describe are x=2 and y=3. ---------------------------------------- Clearly, the vertex of the triangle is at (0,5), so the altitude is 3. The base of the triangle goes ...
December 25, 2015

math
Draw diagonal BD Then triangles ABD and CBD are isosceles. Hence, their altitudes bisect their bases and their vertex angles.
December 25, 2015

physics
54.45 mph = 79.86 ft/s If the rock was thrown with an initial speed k, then k-32*2.75 = -79.6 k = 8.4 ft/s So, the rock was thrown upward at 8.4 ft/s from a height h: h - 32*2.75 - 16*2.75^2 = 0 h = 209 ft
December 25, 2015

mathematics
(x-1)(x-2)(x-k) = x^3 - (k+3)x^2 + (3k+2)x - 2k k+3 = p 3k+2 = 2 q = -2k Looks like k=0, so p=3 q=0 and we have x(x-1)(x-2) = x^3 - 3x^2 + 2x
December 25, 2015

maths
or, using partial fractions, 2 - (5/9)/(x+2) - (13/9)/(x-1) + (1/3)/(x-1)^2
December 25, 2015

Trigonometry- ??????
oh come on. If ab=0, then either a=0 or b=0 So, we have tanx = 0 --> x is a multiple of pi or sin^2(x) = 2 --> no solutions there.
December 24, 2015

Trigonometry- ??????
tan(x) sin^2(x)=2tan(x) tanx(sin^2(x)-2) = 0 How about now?
December 24, 2015

Algebra 1
39.80x + 49.70y <= 150,000
December 24, 2015

Math
looks good to me. or, you could have noted the 41-22 = 19%, and that would be 76.
December 24, 2015

math
the units would be dollars/yd^2 The rate of change is always ∆y/∆x, so the associated units just follow along. y might be the cost (dollars) of some quantity x (yd^2) of carpet.
December 24, 2015

Calculus
u = sinx du = cosx dx so, dx = du/cosx = du/√(1-u^2) sinx(cosx)^2 dx = u(1-u^2)/√(1-u^2) du = u/√(1-u^2) du Now, let v = √(1-u^2) dv = -u/√(1-u^2) du and you have -v dv integrate that to get -1/2 v^2 = -1/2(1-u^2) = -1/2 (1-sin^2(x)) = -1/2 cos^2(...
December 23, 2015

Calculus
because now we are using u, not x. If, after integration on u, you substitute back into terms of x, then you would use the limits [0,2]. When x=0, u=3 and when x=2, u=5.
December 23, 2015

Calculus
∫[0,2] x√(5-√(4-x^2)) dx Let u = 5-√(4-x^2) du = x/√(4-x^2) dx so, x dx = (5-u) du and you now have ∫[3,5] √u (5-u) du and I'm sure you can handle that, eh?
December 23, 2015

Math
n is starting population. t is time period k indicates how fast it grows. To use it, um, just plug in your numbers... Surely, knowing the formula, you have examples of its use. If not, google is your friend.
December 23, 2015

Algebra 2
you have the sum of two cubes, so it factors into (3x+5)((3x)^2-(3x)(5)+5^2) = (3x+5)(9x^2-15x+25) It's easy to check that the quadratic has no real solutions. Just use the quadratic formula, learned long ago in Algebra I...
December 23, 2015

MATH Please help!
if the dimensions increase by a factor of 3, the area increases by a factor of 3^2, so A is correct. 13^2 * 3^2 = (13*3)^2 = 39^2
December 23, 2015

math
domain is positive integers range is (0,N] where N is the maximum time for a single painter. Further restrictions depending on the maximum number of painters, and other information on their required times.
December 22, 2015

math
clearly, the mass depends on the number of candies, which is an easily controlled integer value.
December 22, 2015

Gwu
I think that is supposed to read and spends it takes .75mi * 1hr/2mi = .375hr = 22.5 min to travel between stops. So, assuming we start counting as the train arrives at the 1st intersection, it takes (in minutes) 12*.75 + 11*22.5 = 256.5 minutes before it leaves the final ...
December 22, 2015

SCIENCE
surely it would have taken less time just to look in your text, or google, rather than post here and wait.
December 22, 2015

Algebra
Note that y increases by 4 when x increases by 1. So, the slope is 4. That should help.
December 22, 2015

metreology
just review the wavelengths for the parts of the spectrum.
December 22, 2015

chemistry
google is your friend. Try it. Many discussions.
December 22, 2015

Happy Christmas and Merry New Year!!
Happy RamaHannaKwanzMas!
December 22, 2015

Algebra 2
Since tan(x) has a midline of y=0, and this is shifted down 4 units (due to the -4 at the end), so is the midline: y = -4
December 22, 2015

maths, physics,
Maybe if you show your work, you can learn where you went wrong.
December 22, 2015

maths, physics,
unless otherwise denoted, such as S20°E, headings are indeed clockwise from north. So, the plane (apparently aka helicopter)'s velocity is 400<0.939,0.342> and the wind is 70<-0.707,0.707> <326.11,186.29> = 375.568 at 60.3°
December 22, 2015

Science
this is just the usual 30-60-90 right triangle, with hypotenuse 100. Now just find the sides.
December 22, 2015

victoria university college,Myanmar,mechanical pri
No idea. How many kW does the machine use? Then just multiply by 7 to get kW used and then multiply by $.08 to get cost
December 22, 2015

math
what a deal! Oh - was there a question in there somewhere?
December 21, 2015

statistics
This just like drawing without replacement, so your probability is 8/25 * 7/24 = 7/75
December 21, 2015

pharmacy tech
or just use the 5% solution and add water. Since 3% is 3/5 of 5%, just use 3/5 of the 30mL and fill the rest with water: 18 mL 5% + 12 mL water Or, for a much slower method, pour some 1% solution in a beaker and let it evaporate. Since 1% is 1/3 as much as 3%, start out with 3...
December 21, 2015

geomtery
You know the three angles sum to 180, so 3x+9 + 8x+11 + 5x-8 = 180 16x + 12 = 180 ... Now you can find x, and thus the three angles.
December 21, 2015

Algebra
since the coefficients of x and y are the same, yes they are parallel.
December 21, 2015

statistics
you can play around with Z table stuff at http://davidmlane.com/hyperstat/z_table.html
December 21, 2015

math
since time = distance/speed, time out = d/5 time back: d/3 avg speed = total distance / total time = 2d/(d/5 + d/3) = 2/(1/5 + 1/3) = 2/(8/15) = 15/4 Close to 4, but not quite.
December 21, 2015

maths
4/3 π r^3 = 1/3 π r^2h 4r = h ...
December 21, 2015

maths
the ratios are πr^2h : π/3 r^2h : 2π/3 r^3 = πr^3 : π/3 r^^3 : 2π/3 r^3 I expect you can take it from there. Just factor out the common values and clear the fractions as needed.
December 21, 2015

maths
If the three roots are r,s,t then their product rst = c/a. So, if r = -1, then st = = c/r = c/-1 = -c.
December 21, 2015

math
I have an idea. Why don't you give it a try. To start with, 2 is a factor of any even number...
December 21, 2015

math
I hope -4x-31 is one of the choices. That would be easiest. Of course, there are many many other equivalent expressions...
December 21, 2015

maths
any number whose digits sum to a multiple of 9, is divisible by 9. So, ...
December 21, 2015

our own English school
By an even multiple of 2, do you mean a multiple of 4? As in 6 is an odd (3) multiple of 2, but 24 is an even (12) multiple of 2? In any case, just pick any multiple of 2 or 4, as required, whose digits sum to 9. Such as 72, 234, 69732, etc. Read about "casting out nines&...
December 21, 2015

Math
by now surely you know that |<a,b>| = √(a^2+b^2)
December 21, 2015

Algebra
Eh? I've never seen an or written like that... It's always been in two parts: x < -5 OR x > +5
December 21, 2015

mathamatic
Some of these are simple arithmetic or geometric sequences. Other are easily recognizable powers, such as n^2 or 2^n, or are Fibonacci-like. Why not take a shot at them and let us know what you come up with?
December 21, 2015

mathematics
No idea. You have a mish-mash of notations. Try using the most common online one: ^ for power, as in 12araisedto Power3b = (12a)^(3b) and so on for your others.
December 21, 2015

mathematics
If the son is x, the father is 5x. So, x + 5x = 78 ...
December 21, 2015

vectors
well, you know that you need 2^2+1^2+x^2 = 1 good luck with that, since x^2 is always positive. I suspect there is more to this problem than you posted.
December 21, 2015

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