Wednesday
September 2, 2015

Posts by Steve


Total # Posts: 33,233

Maths
using the common difference of the AP, you know that x-2 = y-x Using the common ratio of the GP, you know that (x-1)/2 = y/(x-1) So, solve those two equations to get x and y.
June 16, 2015

Algebra
Read what I wrote. I guarantee that you will find the answer.
June 16, 2015

Algebra
well, you have 2m(n-8) - 7n So, if you want a common factor of n-8, you would need 56 That would give you 2m(n-8) - 7n + 56 = 2m(n-8) - 7(n-8) = (2m-7)(n-8)
June 16, 2015

pre-calculus 11
that is correct, except that you seem to be a bit fuzzy on how apostrophes are used. . .
June 16, 2015

Algebra
well, geez. You cant solve 3k+50 = 0? k = -50/3 (25 - 50/3 i)*(3+2i) = 325/3 which is a real number
June 16, 2015

Algebra
(25 + ki)*(3+2i) = 75+3ki+50i-2k = 75-2k + (3k+50)i So, you need 3k+50 = 0, since real numbers have zero imaginary part.
June 16, 2015

pre-calculus 11
Looks good to me.
June 16, 2015

Algebra
Hint: slope-intercept: y = mx+b point-slope: (y-k) = m(x-h) standard: Ax+By = C rise-run: ? never heard of it.
June 16, 2015

Math
If the area of the deck is 3 times the pool, then the total area of pool+deck is 4 times just the pool. If the width of the deck is w, you need (3+2w)(4+2w) = 4(3)(4)
June 16, 2015

pre-calculus 11
The round trip is 5400, so each half is only 2700 km. So, I get 2700/x + 2700/(95+x) = 7.6 x = 666 km/hr
June 16, 2015

math
I get the b and h for the triangular bases, but cannot figure out how the length can be both 7 and 15. Maybe you can clear that up.
June 16, 2015

Maths
If the depth is x cm, then since 1L = 1000cm^3, you have 100*140*x = 275*1000 x = 10.64 cm
June 16, 2015

pre-calculus 11
If you use some parentheses to properly specify the numerators and denominators, I think you have a typo and meant -x/(x-3) + 2x/((x+2)(x-1)) * ((x-2)(x+2))/((x-3)(x+3)) As usual, do multiplication before addition. In effect you have -x + y * z Do the y*z first, giving you -x...
June 16, 2015

pre-calculus 11
no, that would mean 8 <= t <= 16 That is an 8-hr window centered at 12:00 You want |10-t| <= 2
June 16, 2015

sgmic
I think you have it wrong: tan 3θ = tan(θ+2θ) tan 3θ = (tanθ+tan2θ)/(1-tanθtan2θ) tan3θ(1-tanθtan2θ) = tanθ+tan2θ tan3θ - tanθtan2θtan3θ = tanθ+tan2θ tan3θ - tan2θ - tan&#...
June 16, 2015

math
well, geez. Just list the even digits which sum to 12: 048 246 in whatever order you want to use them. Then sprinkle the 8's everywhere else.
June 16, 2015

Math
as you say, y = 70-2x, and the area a = xy = x(70-2x) You found the roots of that function which is where the area is zero! The vertex of a parabola is midway between the roots, at x = 17.5 So, y=35 and the maximum area is indeed 612.5
June 16, 2015

Math
If the digits, reading left to right, are abcde, then we are told b = a-2 b = c+2 So, abc are consecutive descending odd numbers. d = e+2 e = c-4 Looks like all 5 digits are in order: 97531
June 16, 2015

math
1/(2/7) = 7/2 So, there are 5/2 hours left to go.
June 16, 2015

Geometry
I must be missing something here. If AB and CD are diameters, then AD = BC, since the diameters must intersect in the center of the circle. No idea where E is.
June 16, 2015

Mathematics
see the related question below.
June 16, 2015

cubic function
That is clearly so. From the Rational Roots Theorem, you know that the only possible rational roots are ±1. So, the only way to find the roots are to graph it and try to read off the roots, or use some numerical method, such as bisection or Newton's method, or ...
June 16, 2015

science
Since you are given very little information, expect the math involved to be simple. How about you start with that most basic equation of motion: F = ma
June 16, 2015

trig
The 6 feet at the top is just noise, placed there to see whether you know how to subtract. The wire is attached 465 feet from the ground. So, you have a right triangle with an angle of 23.1° opposite the pole. (assuming the pole is vertical) Checking your basic trig ...
June 16, 2015

Math
Assuming you meant 131/10 = 20/x that would give you 131x = 20*10 x = 1.5 What can that mean? The ratios do not seem intuitive to me. I would have reasoned this way: Of the sample caught, 10/20 were tagged. We can expect that the same fraction of the total population was ...
June 15, 2015

Physics
Draw the two vectors. The resultant speed is the hypotenuse of the triangle. That is, √(2.4^2 + 1.7^2) = 2.94 m/s The direction is arctan(1.7/2.4) = E35.3°S
June 15, 2015

Differential equation
sorry - had to run off - also had a typo above d((x+4)^5 y) = 16(x+4)^3 (x+4)^5 y = c + 4(x+4)^4 y = c/(x+4)^5 + 4/(x+4) Now you can solve the initial value problem.
June 15, 2015

Differential equation
we have (x+4)^2y′+5(x+4)y=16 y' + 5/(x+4) y = 16/(x+4)^2 The integrating factor is e^(∫5/(x+4) dx) = (x+4)^5 So, multiplying through by that we have (x+4)^5 y' + 5(x+4)^4 y = 16(x+4)^3 d((x+4)^5 y = 16(x+4)^3 x+4)^5 y = 4(x+4)^3 + C ...
June 15, 2015

Differential equation
since e^lnu = u and (e^a)^b = e^(ab) e^(5ln(x+4)) = (e^ln(x+4))^5 = (x+4)^5 That help?
June 15, 2015

Maths
w(w+3)*16 = 364 now just solve for w.
June 15, 2015

algebra
the two functions are 40+8m 25+12.5m Now go for it...
June 15, 2015

math
Assuming you meant 16 passed math, Draw your Venn diagram and start filling in the missing pieces. 3 passed all three subjects 7 passed E and M 1 passed M only So, 33 passed something. I expect you can take it from there.
June 15, 2015

MATH
Hmm. I get a negative value for q. Is there maybe a typo?
June 15, 2015

math - eh?
beats me. you want to explain in words what you are trying to solve? Like, how long does it take to administer 1000ml at 15 drops per hour, or something like that? Your units are all mixed up. On the left, you have ml*gtt*hr On the right you have ml*gtt*hr*min I think you need...
June 15, 2015

math 4
since the events are independent, p = (1/2)(1/2)(1/2)
June 15, 2015

math
gee, does not the name of the function tell you how to fill in the blank?
June 15, 2015

Math
Looks like about 8% to me
June 15, 2015

Math-NPV
You want NPV, using NPV(.11,11) = -110000 + sum(t=1 to 11) 17000/(1+.11)^t = -110000 + 105510.76 = -4489.24 NPV(.17,11) = -110000 + 82219.03 = -27780.97 the IRR is r where sum(t=1 to 11) 17000/(1+r) = 110000 r = 10.08%
June 15, 2015

algebra
so, did you get out your graph paper and plot the points? They are (0,3), (-9,0), and (-3,0) The vertex is at (-6,-3) You know the graph will be V-shaped. Since you know that there will be a minimum at x = -6, the V opens upward. You know that the point of the V is at x = -6. ...
June 15, 2015

calculus
s(t) = ∫ v(t) dt = ∫ 4-t^2 dt = 4t - 1/3 t^3 + C Since s(0) = 0, C=0, and s(t) = 4t - 1/3 t^3
June 15, 2015

calculus
h(t) = 64t-16t^2 so, at max height, dh/dt=0. So, find t for that.
June 15, 2015

algebra
well, why not just plug in the values for x? f(3)-f(2) = 3|3-1| - 3|2-1| = 3*2-3*1 = 3 Now divide that by 3.
June 15, 2015

Calculus
You need to read the question more carefully. They gave you dy/dt, and you need to find dx/dt. 2x dx/dt + 2y dy/dt = 0 when x=18, y=24 The ladder is being pulled up the wall at 1.5 ft/min. That means dy/dt = 3/2 Plugging all that into the equation gives 2(18) dx/dt + 2(24)(3/2...
June 15, 2015

Calculus
we have x^2+y^2 = 30 so, 2x dx/dt + 2y dy/dt = 0 when x=18, y=24 2*18 dx/dt + 2*24 dy/dt = 0 . . .
June 15, 2015

math
yes, because neither event affects the other. Unless maybe you toss the coin and it lands on the cube . . .
June 15, 2015

math
f◦g = (g-1)^5 = (-6x)^5 = -7776x^5 g◦f = 1-6f = 1-6(x-1)^5 = ... f(f(x)) = f◦f = (f-1)^5 = ((x-1)^5-1)^5 That will expand to a long 10th-degree polynomial f^2(x) = (f(x))^2 = ((x-1)^5)^2 = (x-1)^10 f is squared, not x.
June 15, 2015

calc
the diameter of each semicircle is y. So, adding up all the discs of thickness dx, we have v = ∫[0,1] 1/2 πr^2 dx = π/8 ∫[0,1] e^(-2x) dx and now it's a cinch, right?
June 15, 2015

Math
you need length+width=6, so 1x5 2x4 3x3 If you were angling for the more complex scenario proposed by PsyDAG, then things do get a bit trickier.
June 15, 2015

pre-calculus 11
numerator zero is no problem. 0/x = 0 for any nonzero x. The only restrictions you need worry about are where the denominator is zero.
June 15, 2015

Physics
did you try drawing the figure? You just wind up with a right triangle, where one angle is 40° and the hypotenuse is 10. x = 10 cos40° y = -10 sin40° Looks like time to review your trigonometry.
June 15, 2015

Area/volume of hollow figure
It occurs to me that I gave you the volume of the box's material. The interior volume is just (10-2)(10-2)(100-2)
June 15, 2015

Area/volume of hollow figure
the volume is the volume outside the box, less the volume inside the box. Assuming you are given the outside dimensions, and the box has no open sides, then the interior volume would be (10)(10)(500) - (10-2)(10-2)(100-2) You do the same for the area. Each interior face has ...
June 15, 2015

Math
That's what I get. x/31 = 60/50 x = 37.2 Looks closer to 37 than 38, even using your rounded-off figures.
June 15, 2015

physic
v changed by -1.5m/s in 1.2s a = -1.5/1.2 = -1.25 m/s^2
June 15, 2015

E.s groly
5(a+4d) = 10(a+9d) 5a+20d = 10a+90d a = -14d So, there is no unique solution. Some examples are a = 14 d = -1 14,13,12,11,10,9,8,7,6,5 5*10 = 10*5 a = -7 d = 0.5 -7,-6.6,-6,-5.5,-5,-4.5,-4,-3.5,-3.-2.5 5(-5) = 10(-2.5)
June 15, 2015

Math
first, find the length of a $50 note.
June 14, 2015

Math
depends on the weight of the people. It might also depend on the size of the people, since the elevator car might not hold enough bodies to max out the weight.
June 14, 2015

pre-calculus 11
Not only are the signs backwards, but the intervals are incorrect as well. Take a look at the graph and see whether you can fix it. http://www.wolframalpha.com/input/?i=-|x^2-9|+for+-5+%3C%3D+x+%3C%3D+5 The trick to getting signs right is remembering that |x| = x if x >= 0...
June 14, 2015

pre-calculus 11
wolframalpha is your friend. Just type in your request, as shown below: http://www.wolframalpha.com/input/?i=|1%2F2x+%2B1|+%3Dx%2B1
June 14, 2015

geometry
a = pi(8^2 - 5^2) = 122.52 You were correct, if they are asking about the area of the top or bottom surface of the cylinder. However, maybe they are asking about the area of the curved surface. In that case, it would be 2pi(8-5)h and you'd need to know the height of the ring.
June 14, 2015

math
since the x-coordinate is the same for all of the points, they lie on a vertical line. So, just pick any three values for y and plot the points. For example, (-2.8,0) (-2.8,-5) (-2.8,1.73)
June 14, 2015

Math
Your algebra is correct. Your logic is wrong, however. x=0,8 are roots of the function. That is, where the area is zero. If you rewrite it as 20x - 5/2 x^2 you see it is a parabola with its vertex at x = -b/2a = 20/5 = 4 So, y=10 and the largest area is 4*10 = 40 http://www....
June 14, 2015

math
since the period of sin and cos is 2pi, the function clearly satisfies Rolle's Theorem. So, we want to find c (possibly more than one value) where f'(c) = 0 f'(x) = cosx - sinx so, f'(c) = 0 if cosx = sinx That is when x = pi/4 or 5pi/4 See the graph at http://...
June 14, 2015

physics
start with F = ma
June 14, 2015

Algebra2
or, look at it like this: 2|3x-5|-8=8 2|3x-5| = 16 |3x-5| = 8 |x - 5/3| = 8/3 so, x = 5/3 ± 8/3 x = 13/3 or -1 or, you can use the "extraneous root" introduced by squaring both sides. |3x-5| = 8 (3x-5)^2 = 64 3x-5 = ±8 3x = 5±8 x = 5/3 ± 8/3
June 14, 2015

Algebra
1 < y < 6 why?
June 14, 2015

queen's science Academy
Since the height of the falling stone is the same as that of the projected stone after 2 seconds, h-4.9t^2 = 20t-4.9t^2 h = 20t = 40
June 14, 2015

math
Still a typo. Is that 180+x or 180-x? 180x makes no sense. And where do the A's fit in?
June 14, 2015

math
so. what have you got so far? How can a digit have no value?
June 14, 2015

math trigonometry
sin(360-x) = -sin(x) tan(-x) = -tan(x) cos(180-x) = -cos(x) so, you have sin(x)tan(x)/cos(x) = sin^2(x)/cos^2(x) = tan^2(x) Not sure where the A comes from, but you get the idea. Just reduce everything to simple trig functions and then combine them. If you need further help, ...
June 14, 2015

math trigonometry
Simplify the following expression to a single trigonometric term sin(360-x)*tan(-x)/cos(180 x)*(sin^2A cos^2A) answer= -sinx*-tanx/cosx*(1) after that how do i continue?
June 14, 2015

Math
the volume of water hitting the roof is just the area of the roof's horizontal projection, times the depth of the rainfall. That is just 12√48 * .30 m^3 = 24.94m^3 1 m^3 = 1000L, so the barrel needs to hold 24900L. v = πr^2h, so π(3/2)^2h = 24.94 h = 3.53m ...
June 14, 2015

maths
as long as you multiply top and bottom by the same thing, the value is unchanged. So, 2/3 * 3/3 = 6/9 2/3 * 9/9 = 18/27 2/3 * 1.2/1.2 = 2.4/3.6 2/3 * 100/100 = 200/200 and so on
June 14, 2015

Matsogella
Is there a question somewhere in there? Heck, or even a subject?
June 14, 2015

math
There are 36 possible outcomes. List the ones you want. For example, sum < 6: 1 4 2 3 3 2 4 1 There are 4 ways to get that, so P(sum<6) = 4/36 Same for the other one.
June 14, 2015

calc
I see several similar questions in the Related Problems below. I expect they will help out.
June 13, 2015

statistics
it is the correlation coefficient. Better read your text, or google some articles.
June 13, 2015

Calculus
If he lands x miles from the nearest point on the shore to P (call it O), and O is m miles from Q, then the distance traveled is z = √(x^2+1) + m-x The time taken is thus t = 1/3 √(x^2+1) + (m-x)/5 You want to minimize t, so dt/dx = x/3√(x^2+1) - 1/5 dt/dx = ...
June 13, 2015

Calculus
There are several similar related questions below. I'm sure you can adapt one of those solutions to your specific numbers.
June 13, 2015

Algebra
I'm assuming you meant "starting with n=1". If so, just start substituting in values for n: a1 = 2^(1-1) = 2^0 = 1 a2 = 2^(2-1) = 2^1 = 2 and so on.
June 13, 2015

math
the raise increases the mean from 34600 to 34600+3900/5 = 35380. The median will not change, since only the highest salary has increased. The number of salaries above and below the median has not changed. Same for the mode, since the wording of the question implies that there ...
June 13, 2015

Math
clearly, since 0 <= |sin x| <= 1, the extrema are where sin^2(2x) = 1 or 0 That is, sin(2x) = ±1 or sin(2x) = 0 In the indicated domain, that leaves 2x = π/2 or 3π/2 or 0 or π or 2π x = π/4 or 3π/4 or 0 or π/2 or π See the ...
June 13, 2015

Alg 2 HELP!!
#1 since y=ab^x, just plug in the two points you are given: ab^2 = 48 ab^5 = 3072 Divide the 2nd by the first and you have b^3 = 64 b = 4 a*4^2 = 48, so a = 3 and y = 3*4^x #2 inverse variation means xy = k, a constant. Plug in your values and you have (6)(-1) = (3)(y) y = -2...
June 13, 2015

Alg 2
8^log(8)x = x I stated it clearly as one of the examples. Similarly, log(8) 8^x = x
June 13, 2015

Alg 2
^ and log are inverse operations x+8 - 8 = x x/8 * 8 = x (√x)^2 = x log88x = x 8log8x = x The thing that makes logs initially so confusing is the notation. If we had a cute symbol like + or / or √ things would be a lot easier. The definition of log8x is that power ...
June 13, 2015

trigonometry
Of course the answer is complete. I have evaluated every trig function given. What else can there be? What makes you think that there might be something missing?
June 13, 2015

trigonometry
sin 150 = sin 30 = 1/2 cos 315 = cos 45 = 1/√2 cos(90-x) = sin x sin (360-x) = -sin x cos -240 = cos 240 = -cos 60 = -1/2 sin 135 = 1/√2 So you have 2(1/2)(1/√2)(sin x) ------------------------- (-sin x)(-1/2)(1/√2) Think you can handle it now? As I ...
June 13, 2015

trigonometry math help
Reduce things to reference angles in Quadrant I: sin 250 = sin(270-20) = -cos 20 = -m since sin^2+cos^2 = 1, sin 20 = √(1-m^2)
June 13, 2015

university
it will take 0.69 seconds for the water to fall 2.35 meters. At 1.70 m/s, the water will be 1.177 m from the wall when it hits. So, how wide is your walk? More important, how tall do you expect the pedestrians to be? The water must be far enough from the wall not to hit the ...
June 13, 2015

math
well, 150*48 = 7200 150*43 = 6450 what do you think?
June 13, 2015

algebra
You want 200((1.06^71 - 1)/(1.06-1) - 1) Better study your annuity formula and how it arises.
June 13, 2015

Algebra 1
Well, I doubt that -5.26 is a solution, but you can easily check that 7.58 works just fine. Don't you check your answers when you get them?
June 13, 2015

chemistry
Oxalic acid is H2C2O4 with a mol wt of 126.07 grams I expect you can take it from there . . .
June 13, 2015

Math
You must surely have discussed this topic, for otherwise there would be no need to ask such a question. The brief discussion in wikipedia sheds some light on the topic. http://www.geneseo.edu/~bearden/socl211/chisquareweb/chisquare.html google is your friend on questions of ...
June 12, 2015

physics
x/2.5 = 48/5.0 and do the same for the other question.
June 12, 2015

Differential equation
oops typo that should be √(1+x^4) everywhere. I seem to have slipped in some 1+x^2...
June 12, 2015

Differential equation
y′=12x^3 √(1+x^4)(1+y^2) Man, after the last one, this should not have caused you any headaches. It's basically the same thing dy = 12x^3 √(1+x^4)(1+y^2) dx dy/(1+y^2) = 12x^3 √(1+x^4) arctan(y) = 2(1+x^2)^(3/2) + c y = tan(2(1+x^2)^(3/2) + c) y(0)=...
June 12, 2015

Physics
y = a(x-h)^2 + k y'(0) = tan 50° = 1.1917 k = 0.0674 a(1.06-h)^2 + k = 0 2a(-h) = 1.1917 y = -0.7782(x-0.7657)^2+0.0674 y = -0.7782x^2 + 1.1917x - 0.3887 Let the height y be given by y = ax^2+bx+c y(-b/2a) = 0.0674 y(1.06) = 0 y'(0) = 2ax+b = tan 50° = 1.1917 ...
June 12, 2015

Differential equation
dy = 8e^(4x)(1+y^2) dx dy/(1+y^2) = 8e^(4x) dx arctan(y) = 2e^(4x)+c y = tan(2e^(4x)+c) at x=0 you have tan(2+c) = -2 c+2 = arctan(-2) = -1.107 c = -3.107 y = tan(2e^(4x)-3.107)
June 12, 2015

math
(3a)^2 = 9a^2 ((3a)^1/2)^-1/2 = (3a)^-1/4 There's just no valid way to come up with what you got.
June 12, 2015

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