Wednesday
August 20, 2014

Posts by steve


Total # Posts: 24,339

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

not maths
and probably not even homework
June 26, 2014

maths
24*12*6 = ?
June 26, 2014

maths
a cloud
June 26, 2014

maths
assuming you meant 16x^2 + 8x + 7, it's just a parabola, with its vertex at x = -b/2a = -8/32, or -1/4 So, just evaluate f(-1/4) to find the minimum. Since the coefficient of x^2 is positive, there is no maximum. Of course, there may be other typos hiding in there.
June 26, 2014

Algebra
for higher-degree polynomials, try some synthetic division to try and find rational roots. In this case, there are none, so you're stuck with graphical or numeric methods. A check on the graph will show that there is a single real root, near x = 2.7, but that's about ...
June 26, 2014

science
just conserve momentum: 2900<34,0,0> + 4800<-18,0,28> = (2900+4800)v <98600,0,0>+<-86400,0,134400> = 7700v <12200,0,134400> = 7700v v = <1.58,0,17.45>
June 25, 2014

math
Since the curve intersects the line at (-2,1) and (2,1), we can use vertical strips to get a = ∫[-2,2] 1 - (x^2-3) dx = 32/3 Or, we can use horizontal strips to get x = ±√(y+3) a = ∫[-3,1] √(y+3) - (-√(y+3)) dy = 32/3
June 25, 2014

science
conserve momentum: .062*150 + 90*0 = (.062+90)v v = 0.103 m/s
June 25, 2014

Precalculus
the diagonal of the rectangle is a diameter of the circle. Since that is 4, if the rectangle has one side of length x, then the other side has length √(16-x^2) So, the area is x√(16-x^2) Well, that is not a choice, so if the side is 2x, rather than x, the area is (...
June 25, 2014

calculus
use the chain rule. let v = -x^2 u = cot v y = 1/2 u^7 y' = 7/2 u^6 u' u' = -csc^2 v v' v' = -2x So, dy/dx = 7/2 cot^6(-x^2) * -csc^2(-x^2) * -2x = 7x cot^2(-x^2) csc^2(-x^2) or, since cot(-x) = -cotx csc(-x) = -csc(x) 7x cot^2(x^2) csc^2(x^2)
June 25, 2014

ALGEBRA
well, let's see 900 lbs capacity 100 lbs luggage subtract to get ?? lbs for passengers
June 25, 2014

math
-11 + 7 + x = 15 -4 + x = 15 x = 19
June 25, 2014

science
163/(163+755) = 163/918 = .1776 or 18%
June 25, 2014

ALGEBRA
8x > 72
June 25, 2014

math
any number rounded to the nearest hundred is a multiple of 100, and so cannot be odd. I suspect that is not the way the question was worded.
June 25, 2014

Algebra
do things just as you would with numbers: (2+5)(7-3) 2*7 + 5*7 - 2*3 - 5*3 You have (n^3+8)(n-4) n^3*n + 8*n - n^3*4 - 8*4 now simplify each term n^4 + 8n - 4n^3 - 32 and arrange in descending powers n^4 - 4n^3 + 8n - 32 Sometimes you may have several terms with the same power...
June 25, 2014

Maths
each side is now √425.5969 = 20.63 Reduce by .03 to 20.6
June 25, 2014

Maths - eh?
no idea what that sentence means. what "same" number?
June 25, 2014

Math
140mi/14g = 140/14 mi/g = 10 mi/g
June 25, 2014

physics
current speed is 2.6 sin 28.5° boat velocity across is 2.6 cos 28.5°
June 24, 2014

math
I'll answer in mg, since 1/2 pint is more than 1 fl oz. Since 1/2 pint = 8 fl oz, there are 8 * 1.2 = 49.6 mg of otylmethoxycinnamate.
June 24, 2014

math
.02x = .23 x = 11.50
June 24, 2014

:-)
Google is your friend. It gave several hits, and this one was indeed elegant and simple.
June 24, 2014

MathMate Help!!!
oops - make that 1/a + 1/b < 1/c < 1/a - 1/b 1/84 < 1/c < 13/84 84/13 < c < 84 So, 83 is the maximum integer side
June 24, 2014

MathMate Help!!!
We know that given sides A,B,C, with A>=B, A-B < C < A+B With a little algebra (as seen here): http://www.algebra.com/algebra/homework/Triangles/Triangles.faq.question.577996.html we know that if the altitudes are a,b,c then 1/a - 1/b < c < 1/a + 1/b So, for ...
June 24, 2014

pre cal
I see a whole bunch of posts, but no indication of your attempts to solve them. I'll do one of them here: f(g) = g^2-3 = (√(3+x))^2 - 3 = 3+x-3 = x g(f) = √(f+3) = √(x^2-3+3) = √x^2 = x However, note that √x^2 is not necessarily x. If x = -3...
June 24, 2014

pre cal
Ok - do you know what (f+g)(x) means? It is f(x)+g(x) Now just plug in your function definitions, and simplify the result. Just to make things easier, lose all the words. You have f(x) = √(5x+7) g(x) = √(5x-7)
June 24, 2014

math
I guess she gives 24/25 of a chocolate to each kid. Or, she can give 1/2 a chocolate to two of the kids, and a whole one to the others.
June 24, 2014

physics - ? -
This reminds me of the cat that ate a piece of cheese, and then sat by the mouse hole with . . . baited breath!
June 24, 2014

math
Not in any base I can think of. Is there some other facet that is unexplained?
June 24, 2014

math
well, that would be 16/31 * 75 = ?
June 24, 2014

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