Tuesday
September 23, 2014

Posts by steve


Total # Posts: 25,164

math
If there are t tourists and r rooms, t = 6r-9 t = 3(r+4) 6r-9 = 3r+12 3r = 21 r = 7 so, t=33
July 2, 2014

math
(ab)^2 = abab If abab = aabb then the middle ba = ab
July 2, 2014

math
y" + 9y = cos2x+sin2x You know that y"+9y=0 has solutions y = a cos3x + b sin3x so the solution here is y = a cos 3x + b sin 3x + (cos2x+sin2x)/5
July 2, 2014

Algebra
first step: expand the polynomial. You will see that x^3 goes away, leaving you with just 3x^2+2x = 85 Now just solve as you normally would: 3x^2 + 2x - 85 = 0 (3x+17)(x-5) = 0
July 2, 2014

104B
500*2.5*r = 40 r = 0.032
July 1, 2014

math
19/3x - 20
July 1, 2014

Math
if x at 7%, then .07x + .08(x+6000) = 7.80 Fix the interest amount and solve for x. And pay more attention to what you type.
July 1, 2014

Math
4c + 5m = 25.50 2m = c+1.75 Now just solve the two equations, using your favorite method. I get (A) assuming a missing decimal point.
July 1, 2014

Math - incomplete
some data missing here. Read what got posted and fill in what got omitted.
July 1, 2014

physics 1
if the initial velocity was v, v - 3.55*2.13 = 4.90 v = 12.46 m/s the displacement s is thus s = 12.46*2.13 - 3.55/2 * 2.13^2 s = 18.49 m
July 1, 2014

math
we want to approximate ∫[0,4] e^(3√t) sin 3t dt So, divide the interval[0,4] into 8 pieces, each of width 0.5 Now apply each Rule named above, calculating f(x) for each value from 0 to 4, and add up the areas of all the rectangles or trapezoids. There are online ...
July 1, 2014

Heron's formula
anything to do with the area of triangles. Just look around your home and see what triangles you might be interested in. Painting gables, carpeting a corner of a room, etc.
July 1, 2014

Math - bzzzt
Sorry. If PQ joins the midpoints of AB and AC, then it is parallel to BC and half its length. You cannot have PQ=2 and BC=3.
July 1, 2014

Chem
You have: .0286*.169 = 0.004833 moles of Na3PO4 .0397*.255 = 0.010124 moles of Ca(NO3)2 If the reaction is 2Na3PO4 + Ca(NO3)2 = 2NaNO3 + Ca(PO4)2 then you need 2 moles of Na for each mole of Ca. Since there is extra Ca, you will wind up with .09666 moles of Ca(PO4)2 Just ...
July 1, 2014

algebra 1
well, the triangle obviously has area = 12 So, the whole outfit has area 6x+12. So, 6x+12 = 150 6x = 138 x = 23
July 1, 2014

math
surely you can count days on a calendar...
July 1, 2014

Math
If you subtract the 2nd equation from the first, you get 4x-3y-4 = 0 4x+2y+5 = 0 ---------------- -5y-9 = 0 now add 9 to both sides: -5y = 9 now divide by -5: y = -9/5 Knowing that y = -9/5, just plug it into either of the original equations and then solve for x. The work is ...
July 1, 2014

algebra
20m
July 1, 2014

math
Just think about it. Every second it travels 1 meter. So, 5 seconds ago it was down 5 meters. now think forward in time for 120 meters above.
July 1, 2014

math
if now is time t=0, then the temperature at any time t is -2t. So, we want -2(-3) and -2(5)
July 1, 2014

Math
that would be 420/12 = ?
July 1, 2014

math
If they were laid out flat, they'd each be 4.8 units long. So, they must be more than that, and since 4.8 is not an acceptable answer, 4.9 is what we have to go with.
July 1, 2014

math
The midpoint of two points is (6,2). One of the points is (3,5). Since the two ends must be equidistant from the midpoint, 3 = 6-3, 9 = 6+3 5 = 2+3, -1 = 2-3 So, (9,-1) is at the other end.
July 1, 2014

Physics
it gained (18-12)=6 m/s in (4-2)=2 seconds, so that is 6/2 = 3 m/s^2 In the first 2 seconds, then, it gained 6 m/s, so it started at 6 m/s.
July 1, 2014

geometry
hmmm. you have the formula. What's the trouble? The same formula applies for ym: (y1+y2)/2 A value midway between two others is just their average: the sum/2.
June 30, 2014

10 gr math
ok. plug in the data and evaluate: the distance between (1,3) and (7,2) is √((7-1)^2 + (2-3)^2)
June 30, 2014

Chemistry
When reviewing the procedure the student found that 4.912 x 10-1 M barium nitrate solution had been used instead of that in the following procedure: A student synthesized 6.895 g of barium iodate monohydrate, Ba(IO3)2*H2O by adding 30.00 mL of 5.912 x 10-1 M barium nitrate, Ba...
June 30, 2014

algebra
A. No - the decrease in intensity is not a constant, but depends on the previous intensity. The intensity I of x meters of cable is I = 1500 * 0.964^x C yes you can probably write that one on your own.
June 30, 2014

Math
if there are 8x tools, then there are 3x shovels and 5x rakes. So, 5x = 3x+10 x=5 so, there are 15 shovels and 25 rakes
June 30, 2014

Math
If you can find the midpoint of a line segment know that the slope of the perpendicular is -1/(slope of line segment) remember the point-slope form of a line then all of these problems are straighforward. Review those topics, give it a try, show where you get stuck, if you do.
June 30, 2014

Non
just a note: that's mu sub-k, not "muse of k" µk
June 30, 2014

Volume
Just figure the tank's volume (66.75*132*10) and divide it by 231 in^3, the volume of a gallon.
June 30, 2014

algebra
x^2+8x = x(x+8) Pick any positive value for x and you get a rectangle.
June 30, 2014

math
take a look at the graph of (1+.10/n)^(n) It shows the effective yield of 10% compounded n times per year. It approaches continuous compounding, e^.1 http://www.wolframalpha.com/input/?i=plot+y%3D%281%2B.1%2Fn%29^n+for+n+%3D+1..40%2C+y%3De^.1
June 30, 2014

algebra
solve it just as you would an equation: 42 = -6d -7 = d However, multiplying and dividing by negative values changes the direction of the inequality. So, you have 42 < -6d 7 < -d -7 > d or d < -7 Since you can always add and subtract without changing the direction...
June 30, 2014

science
I may have messed up the sign change, so double check my math.
June 30, 2014

science
the position falling from a height of h feet is y = h - 16t^2 After t seconds, y=0, so h=16t^2 So, we have (h-16t^2) - (h-16(t-1)^2) = 11h/36 0 - (16t^2 - 16(t-1)^2) = 11(16t^2)/36 32t-16 = 44/9 t^2 11t^2 - 72t - 36 = 0 t = 7.01 So, h = 16t^2 = 786.24 ft
June 30, 2014

calc
first off, I'd use partial fractions: (x^3 -3x^2 -9)/(x^3 -3x^2) = 1 + 1/x + 3/x^2 - 1/(x-3) There are no discontinuities on [4,5], so it's straightforward. The integral is just x + logx - 3/x - log(x-3) so we get (5 + log5 - 3/5 - log2)-(4 + log4 - 3/4 - log1) = 23/20...
June 30, 2014

Math
54° is 3/20 of a full circle. SO, the whole circumference 3/20 c = 9 c = 60
June 30, 2014

ALGEBRA - eh?
cannot parse the "8n 12" part
June 30, 2014

math
The solution of this equation is so complex, I have to assume you're doing numerical methods or something. Take a peek at http://www.wolframalpha.com/input/?i=sin^6x+-sin^2+4x+%3D+sin2x+sin10x for further insight.
June 30, 2014

trigonometry
well, we have h/120 = tan 10°18' h = 21.8 ft
June 30, 2014

Maths
y = 1/x y' = -1/x^2 y'(1/4) = -1/(1/16) = -16 I think you lost a minus sign. And, of course, you have displayed the usual sloppiness with parentheses.
June 30, 2014

math
I don't see any way. Each odd number is of the form 2k+1 Add up 7 of those, and you have a sum of the form 2n+7 = 20 But 2n cannot be 13. The sum of an odd number of odd numbers cannot be even.
June 30, 2014

Math
well, ∫ lnx/x^2 dx = -(lnx + 1)/x recall that ln √x = 1/2 lnx let u = 3-5x^2 and du=-10x dx That gives you ∫ -1/10 2^u du which is just 2^u / ln u Now it's pretty straightforward
June 29, 2014

Math
well, we know that d/dx arccosh u = 1/√(u^2-1) du So just use the chain rule, and note that (2x-1)^2-1 = 4x^2-4x
June 29, 2014

physics
(i) the range for angle θ is R = v^2/g sin2θ (ii) Naturally max height is reached at θ = 45° (iii) given the range, and that horizontal velocity is constant, getting t is easy. So, what do you get?
June 29, 2014

Algebra
y(x) = 3*2^x y(x+1) = 3*2^(x+1) = 3*2*2^x = 2y(x) So, each year y doubles.
June 29, 2014

Wood working
Of course, if each stripe is that wide, there will be no space between them, so the board will just be solid white. Now you have to decide how much blank space to allocate between the stripes, and whether the end stripes will reach to the very ends of the board, or whether ...
June 29, 2014

Math-Parabolas
If you mean y = x^2+9 you can see that since x^2 can never be less than zero, the vertex is at x=0. Since y=9 there, the vertex is at (0,9) Or, recalling that the vertex of y = (x-h)^2 + k is at (h,k), note that we have h=0 and k=9.
June 29, 2014

pre cal
since complex roots come in pairs, we have (x-3)(x+13)(x-(5+4i))(x-(5-4i)) (x-3)(x+13)((x-5)-4i)((x-5)+4i) (x-3)(x+13)((x-5)^2+4^2) (x^2+10x-39)(x^2-10x+41) x^4 - 98x^2 + 800x - 1599
June 29, 2014

Science
Some of the CO2 was lost as a gas. Also, depending on how hot the mixture became, maybe some of the water was lost as steam.
June 29, 2014

pre-cal
However, assuming the chopper starts at (0,h) and the vehicle starts at (0,0), after t minutes the chopper and vehicle are at (2640t,h - 5/33 t) and (4224t,0) So, the line between them has slope (h-5/33 t)/(1584t) Now you have the angle tanθ = (h-5/33 t)/(1584t) so you ...
June 29, 2014

pre-cal - incomplete
So the helicopter drops 400 feet. How high was it when it started its descent? what is "the vehicle"? Is it a car driving directly underneath the chopper? Did we start at t=0 when the chopper was directly above "the vehicle"? Which angle of depression? ...
June 29, 2014

maths (exponents
Well, just using brute force, we have b/(b+ab+1) + c/(c+bc+1) + a/(a+ac+1) expand all that over a common denominator, and you get (a^2b^2c + a^bc^2 + 2a^2bc + a^2b + ab^2c^2 + 2ab^2c + 2abc^2 + 6abc + 2ab + ac^2 + 2ac + a + b^2c + 2bc + b + c) / (a^2b^2c^2 + a^2b^2c + a^2bc^2...
June 29, 2014

Trigonometry
the angle is x, where cos x = 15/20 the area is 15√(20^2-15^2)
June 29, 2014

Algebra
1.2^-t = 1 / 1.2^t That is clearly not the same as 1 / 2^t recall that x^-a = 1/x^a
June 28, 2014

Maths
Since the diagonals of a rhombus are perpendicular, and all four sides are the same length, the rhombus can be divided into four right triangles with one leg of 5 and an hypotenuse of 8. So, the other leg is √39 So, the area of all four triangles is 10√39 m^2 ...
June 28, 2014

maths
I see a lot of perfect cubes there 8x^3 - 27y^3 = (2x-3y)(4x^2+6xy+9y^2) Hmmm. No joy there. wolframalpha.com factors it, but I can see no motivation for trying (2x-3y+5) as a factor.
June 28, 2014

math
area of ABCD = ab area of ABCD+path = (a+2c)(b+2c) area of path = (a+2c)(b+2c)-ab
June 27, 2014

Calculus help
for multiple periods per year, just divide the interest rate and multiply the number of years. (b) P = 2000(1+.057/12)^(12*10) and similarly for other divisions of the year into multiple parts.
June 27, 2014

Algebra
C is correct
June 27, 2014

calc
Note that since (x-3)^2 = x^2-6x+9, what you have is ∫√(25-(x-3)^2) dx If u = x-3, du = dx, and it's just ∫√(25-u^2) du which you should know. If not, just use the trig substitution u = 5sinθ The answer can be seen at http://www.wolframalpha....
June 27, 2014

Algebra
continuously: A(t) = 1000*e^.08t daily: A(t) = 1100(1+.08/365)^(365t) so, when are they equal? When 1000 e^.08t = 1100(1+.08/365)^(365t) t = 10,873 years. continuous compounding is so close to daily compounding (1.08328% vs 1.08327%) that it takes a long time to overcome the ...
June 27, 2014

MATH
look at the differences: 2,3,5,7 My guess is that the next difference will be 11, the next prime. If not for the 2, I'd have said odd numbers were the differences.
June 27, 2014

maths
The formula must have a typo. If not, you are saying that r(x) = 600x, or $600 per person. I suspect that the problem is incorrectly stated. It appears that the $20 discount is only being applied to those people in excess of the 25-passenger price break. That explains the -20x...
June 27, 2014

maths
40m north and 40m south cancel out, leaving only the 30m east.
June 27, 2014

maths
draw a diagram, and you will see a 3-4-5 right triangle. So, the final displacement is 5, the hypotenuse. The direction (measured from due east) is x, where tan(x) = 40/30
June 27, 2014

maths
-j x i = k
June 27, 2014

maths
zero
June 27, 2014

maths
|A+B|^2 = 2^2 + 2^2 - 2(2)(2)cos 120°
June 27, 2014

math
.327... = 327/999 = 109/333 1000x = 327.327327... x = 0.327327... 999x = 327
June 27, 2014

Maths
(i) 3*b = 2*3+b = 6+b b*5 = 2*b + 5 = 2b+5 so, 6+b = 2b+5 b = 1 (ii) 3*d = 6+d d*(3*d) = 2d+(6+d) = 3d+6 d*3 = 2d+3 (d*3)*d = 2(2d+3)+d = 5d+6 so, 3d+6 = 5d+6 d = 0
June 27, 2014

math
first, note that if u = 6x, you have 1/6 ∫ sin^5 u du = 1/6 ∫sin^4(u) sinu du = -1/6 ∫(1-cos^2 u)^2 (-sinu du) If v = cos u, then dv = -sinu du, and you have -1/6 ∫(1-v^2)^2 dv just expand that and it's a regular old polynomial.
June 27, 2014

Physics . pls help me :)
we need to find where the cars have gone the same distance. So, 0 + 0t + (1/2)(2)t^2 = 30 + 4t that is, t^2 - 4t - 30 = 0 t = 7.83 Just plug that value in for t to see where they met.
June 27, 2014

math - eh? eh? eh?
that cannot possibly be how the question was presented. why not post it as it was given?
June 27, 2014

mathematics
well, just plug and chug: u = ln(x^2+y^2) - ln(x+y) ∂u/∂x = 2x/(x^2+y^2) - 1/(x+y) ∂u/∂y = 2y/(x^2+y^2) - 1/(x+y) x ∂u/∂x + y ∂u/∂y = 2x^2/(x^2+y^2) - x/(x+y) + 2y^2/(x^2+y^2) - y/(x+y) = 2(x^2+y^2)/(x^2+y^2) - (x+y)/(x+y) = 3 so...
June 27, 2014

mathematics
the volume is just |u•v×w| That's pretty straightforward. What do you get?
June 27, 2014

mathematics
assuming you meant t=π/6 The unit tangent vector T(t) = r'/|r'| = cot(t) i - tan(t) j ------------------------- tan^2(t) + cot^2(t) The unit normal is T'/|T'| = -(csc^2(t) i + sec^2(t) j) ---------------------------------- csc^4(t) + sec^4(t) which at t...
June 27, 2014

mathematics
find a line in each plane the cross product of those two vectors is perpendicular to them both. Then translate the vector so it passes through P.
June 27, 2014

mathematics
for all x ≠ -3, (x^2-9)/(x+3) = x-3 So, the limit as x->0 is just -3. How did you get -6?
June 27, 2014

shizo homework dump
if you're going to just dump your homework, at least use a consistent name... Lots of problems, no evident effort displayed on your part.
June 27, 2014

maths
R(x) = 120x if x <= 25 100x is 25 < x <= 40
June 27, 2014

Algebra
B = 2A-8 B = C+32 A+B+C = 152 C = B-32 = 2A-8-32 A + 2A-8 + 2A-40 = 152 5A - 48 = 152 5A = 200 A=40 B=72 C=40
June 26, 2014

Algebra
(3+√18) / 4√12 = (3+3√2) / 8√3 = 3√3 (1+√2) / 24 = (1+√2)√3 / 8 = (√3+√6)/8 or several other ways to express it
June 26, 2014

Calculus I
f = ax e^(bx^2) f' = (a + ax(2bx)) e^(bx^2) = a(1+2bx^2) e^(bx^2) So, f achieves a max/min where f'=0 That is, where a(1+2bx^2) = 0 Or, where x^2 = -1/2b So, it looks like we need b < 0, since x^2 is always positive Not surprisingly, the value of a does not affect ...
June 26, 2014

algebra
I will assume the usual carelessness with parentheses, and that you mean (7y+5)/3 = -8/(y-3) Clear fractions (assuming y≠3) and we have (7y+5)(y-3) = -8(3) 7y^2 - 16y - 15 = -24 7y^2 - 16y + 9 = 0 (7y-9)(y-1) = 0 y = 1 or 9/7
June 26, 2014

Integral question
for ∫x^3/(x^4+1) dx let u = x^4+1, and so du = 4x^3 dx. So, your integral becomes ∫ 1/4 du/u which should look familiar
June 26, 2014

Integral question
∫[-1,1] 5sinx - 2tanx + 3x^5 dx If you look carefully, all three terms are odd functions, so the whole integrand is odd. So, the integral from -1 to 1 is zero. However, if you want to do the integration, note that since tanx = sinx/cosx = -d(cosx)/cosx, we have -5cosx + ...
June 26, 2014

Derivatives
x secy + y^5 = 5x^3 - 7 secy + x secy tany y' + 5y^4 y' = 15x^2 (x secy tany + 5y^4)y' = 15x^2 - secy So, y' = 15x^2 - secy ---------------------------- x secy tany + 5y^4
June 26, 2014

math
The 6.02 looks good, but you should have added exponents 6.02 * 10^(5 + -13) = 6.02 * 10^-8
June 26, 2014

Calc please help
just use the chain rule: f = u^4 u = csc(v) v = 2x^2+1 f' = 4u^3 u' u' = -csc(v) cot(v) v' v' = 4x So, f' = 4 (csc(2x^2+1)^3 * (-csc(2x^2+1)*cot(2x^2+1)) * (4x) = -16x csc^4(2x^2+1) cot(2x^2+1)
June 26, 2014

Calc please help
Oops. A typo. Should be (x*cosx-sinx)/(x*sinx) just take derivatives, top and bottom. The limit is the same as for (-x*sinx+cosx-cosx)/(sinx + xcosx) = (-x sinx)/(sinx + x cosx) still -> 0/0, so do it again: (-sinx - x*cosx)/(cosx + cosx - x*sinx) -> 0/2 = 0
June 26, 2014

Calc please help
massage the form to 1/x - cosx/sinx = (cosx-x)/(x*sinx) and apply l'Hospital's Rule
June 26, 2014

Math
(1.9/9.5) * 10^(-6-4) = 0.2 * 10^-10 = 2.0 * 10^-11 How did you get 1.6?
June 26, 2014

Algebra
so, write it clearly: limit as x->1 of (x-1)/(√x - 2x) I see no problem here, since √x - 2x -> -1, which is not zero. (x-1)/(√x-2x) -> 0 Apparently I have it wrong, but cannot see an easy way to massage it into something which -> 0/0 Anyway, try l...
June 26, 2014

math
millions could be 5,7,9 in any order No idea what "all the other digits are 21" means, but surely you can work it out now.
June 26, 2014

math
the beads recur in cycles of 5 colors. 85 is the largest multiple of 5 which is less than 90. So bead #85 is red. After that is yellow,blue, making 87 beads in all. I have no idea what "the first bead is yellow, and the last bead is blue for each color" means, since ...
June 26, 2014

math
in tiles, the pool is 50*10 x 20*10, or 500 x 200. So, how many tiles is that? Or, you can do it by dividing the areas: 50mx20m / .1mx.1m = 1000/.01 tiles
June 26, 2014

math
just multiply the two numbers. I assume you want the dollar value. 7.25kg is always the same, regardless of its price...
June 26, 2014

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