Tuesday
August 4, 2015

Posts by Steve


Total # Posts: 32,564

Algebra
|z|^2-2z*+iz = 2i letting z = x+yi, x^2+y^2 - 2(x-yi) + i(x+yi) = 2i x^2+y^2-2x+2yi+ix-y-2i = 0 (x^2+y^2-2x-y)+(x+2y-2)i = 0 so, now just solve x^2+y^2-2x-y=0 x+2y = 2 x = 2-2y (2-2y)^2+y^2-2(2-2y)-y=0 5y^2-5y = 0 y = 0 or 1 so, x = 2 or 0 z = 2, i
June 18, 2015

Calculus
after t seconds, Q(t) = 9*0.996^t Now just solve for what you need.
June 18, 2015

Math
You want x where 3.00(x) + 4.25(8) = 4.00(x+8)
June 17, 2015

math
26 total marbles, so P(red,yellow) = 14/26 * 12/25
June 17, 2015

math
just divide both sides by 19.2L
June 17, 2015

calculus
It might help if you actually supplied the function. Clearly it looks something like -100x^2 --------------------- (x+10)(x-10)
June 17, 2015

logical statements-urgent
We want the truth table to look like this: PQR S TTT F TTF F TFT F TFF F FTT F FTF T FFT F FFF F Looks like it reduces to Q&~(P|R)
June 17, 2015

math
1/3 + 4/9 = 7/9 that help?
June 17, 2015

physics
this is one of the most basic setups. Clearly you need to do some reading. series: R = 1+2+3+5 = 11 parallel: 1/R = 1/1 + 1/2 + 1/3 + 1/4 R = 12/25
June 17, 2015

Calculus
Let side x be parallel to the barn. Then x+2y = 34 a = xy = (34-2y)y = 34y-2y^2 da/dy = 34-4y max area when da/dy=0, or y=17/2 So, the pen is 17 by 17/2 As usual, max area is when the fencing is divided equally among lengths and widths.
June 17, 2015

Finite Math
what do we know? if we let x = # dipped bananas y = # dipped apples z = # dipped strawberries so, to produce such a mix, we need 6x+6y+z = 60 3x+4y+z = 42 equating z, we wind up with 3x+2y = 18 So, let's see what we can do, using only integer values: x y z 0 9 6 2 6 12 4 3...
June 17, 2015

Physics
Recall that the range R = (v^2 sin2θ)/g so, just plug in your numbers.
June 17, 2015

math
the ones digit is 0,2,4,6,8 the 1000's digit is twice the one's, so must be 0,4,8 so far we have xx0xx0 or xx4xx2 or xx8xx4 now add 3 and we have 3x0xx0 7x4xx2 Now fill in the x's with whatever you want
June 17, 2015

Mathematics
r^4 = (1/4)/4 = 1/16 r = 1/2 so, the GP is 4, 2, 1, 1/2, 1/4
June 17, 2015

physics
velocity of ?
June 17, 2015

algebra
not so. Just pick a,b,c so that b^2-4ac is positive. f(x) = -x^2-10x-3 b^2 is positive whether b is positive or negative. It was all good until the last line. That's just rubbish.
June 17, 2015

Calculus
As I recall, you need Newton's law of cooling, which in this case would be T(t) = 2+23e^(-kt) where we try use a positive k. T(10) = 17, so 2+23e^(-10k) = 17 k = 0.0427 and we have T(t) = 2+23e^(-.0427t) So, after 30 minutes, T(30) = 2+23e^(-.0427*30) = 8.388 When T=4, we ...
June 17, 2015

Calculus
well of course if T(t) = 2+23e^kt T(10) will not equal T(30) You sure they're both supposed to be 17? So, what was the original problem?
June 17, 2015

math help please
company paid .80(2300)-250 Carol paid 250+.20(2300)
June 17, 2015

science chemistry
Since 1 dm^3 = 1L, .125 mol/dm^3 = .125M solution So, the 250mL amount needs .125*.250 = 0.03125 moles of KOH multiply that by the molar mass of KOH to get the number of grams.
June 17, 2015

science
Since weight varies directly with mass, Darren's weight would be half as much as on earth, given the same radius of the planet.
June 17, 2015

Chemistry
because each molecule contains 8 atoms. When figuring the mol wt, you need to use the number of molecules, not atoms.
June 17, 2015

Maths
depends on what you consider strengths. I suggest you list the various properties, and then decide what you consider to fit the bill.
June 17, 2015

algebra
try the quadratic formula: x = (-3±√(3^2+4*2*6))/4
June 16, 2015

trig
It occurred to me this might be a physics problem: sin(ωt-π)+sin(ωt+π) = -2sin(ωt)
June 16, 2015

trig
Not sure what the f is doing in there, but recall that sinA + sinB = 2sin((A+B)/2)cos((A-B)/2) I think you got too many π's floating around in there, as well. sin(x+π) = sin(x-π) = -sin(x)
June 16, 2015

Math
3*16 + 1.5*16 + 1*2 + 1 + 3*4 = 87
June 16, 2015

algebra
Sorry. That cannot be reduced. Assuming you mean (2x+1)/(4x^2+8x+5)
June 16, 2015

Algebra 2
draw the graphs as usual. Shade the area above the first. Shade the area below the second. Where the two shaded areas intersect is the solution. Note that the curve is included in the 1st, but excluded from the 2nd. http://www.wolframalpha.com/input/?i=plot++y+%3D+-x^2-8x-12+%...
June 16, 2015

Algebra
20-|7x+1| >= 6 |7x+1| <= 14 |x + 1/7| <= 2 x∊[-15/7,13/7] http://www.wolframalpha.com/input/?i=solve+20-|7x%2B1|+%3E%3D+6
June 16, 2015

Algebra
if |x-h| < n, that means that h-n < x < h+n |7-8x| < 10 | 7/8 - x| < 5/4 so, 7/8-5/4 < x < 7/8+5/4 -3/8 < x < 17/8 or, x∊(-3,8,17/8)
June 16, 2015

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

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