Wednesday
October 1, 2014

# Posts by Steve

Total # Posts: 25,381

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

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

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

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

time n work
1/a + 1/b = 1/16 1/b + 1/c = 1/32 4/a + 12/b + 48/c = 1 a can do the job in 160/7 days b can do the job in 160/3 days c can do the job in 80 days. Check: a can do 7/160 jobs in 1 day, and 28/160 jobs in 4 days b can do 3/160 jobs in 1 day, and 36/160 jobs in 12 days c can do 1...
June 24, 2014

Math
incorrect. The subtraction takes place first, so f(x) = |x-1| Your function is described as take the absolute value and then subtract 1.
June 24, 2014

geometry
as with all solids, the volume changes as the cube of the linear change. So, if it dilated by a factor of 1/5, the volume changes by a factor of (1/5)^3 = 1/125.
June 23, 2014

Math
If there are x trees, the cost is 375(3/5 x) + 500(2/5 x) = 425x Not knowing how many trees were harvested, the cost is unknown, but if there were x trees worth \$80M, then the tax must be 1/20 (\$80M - 425x)
June 23, 2014

math
total tax is 12+5+7 = 24% So, the tax is 24% of 18.75 Add that to the 18.75 price. 18.75 * 1.24 = ?
June 23, 2014

Pre calculus
I see only a cubic, which can have only 3 roots. So, since the complex roots appear in pairs, there are either 1 real and 2 complex, or 3 real roots. Cubics have a discriminant, just like quadratics, but it's not generally known. As shown here: http://www.wolframalpha.com/...
June 23, 2014

Geometry
since all the triangles are equilateral, it must be x=60 How did you arrive at 90? I don't see any right angles in the picture!
June 23, 2014

Geometry
The large square has area 12^2 = 144 The triangle is a 30-60-90 triangle, with legs 6 and 6√3, so its area is 18√3 So, 144-18√3 = (b)
June 23, 2014

math
45000 * 0.7^5
June 23, 2014

Math
.06*30 + .04(x-30) = .04x + .6
June 23, 2014

pre cal
if y = 8/(x^2+2) Then one choice is clearly f(x) = 8/x g(x) = x^2+2 If y = 8/x^2 + 2, then we have f(x) = x+2 g(x) = 8/x^2
June 23, 2014

pre cal
if f(x) = √(9-x) then 9-x cannot be negative. So, 9-x >= 0 x <= 9
June 23, 2014

pre cal
oops - the real root is at -3.282
June 23, 2014

pre cal
I find no rational zeros, but the real zero is very near -1.3, so f(x) = (x+1.3)(2x^2+6.4x-6.12) I assume you have some graphical or numeric tools for solving general polynomials.
June 23, 2014

pre cal
Good grief. How about some math, instead of the noisy words? I'll do one. f(x) = (x^2+x-2)/(x^2-3x-4) All polynomials have domain of all reals. Rationals have a domain of all reals except where the denominator is zero. Since f(x) = (x+2)(x-1) / (x-4)(x+1) The domain is all...
June 23, 2014

Math
the identity must be true for any value of x. That is, for all values of x, whatever you choose. The identity does not say anything about the number x. If there is any value which does not satisfy the equation, then it is not an identity.
June 23, 2014

geometry
since -2/3 * 9 = -6, we want x such that -2/3 x = -10 x = 15
June 23, 2014

physics (motion)
check the units. (a) and (b) are obviously false. So, since (d) means constant velocity, (c) is the only possible choice.
June 23, 2014

#1 ok #2 I get that the player is at (-22.5,-26.8) from the net, so his shot takes the puck to (2.5,-26.8). Making it 26.9 from the net. You can figure the angle. How did you get your solution? #3 ok
June 23, 2014

math
who said anything about coordinates? If you draw the diagram using the given values, you will have two right triangles. Their common leg will be the 20 yards from the sideline to the camera. The length of the field (plus the two end zones) will be 120 yards, divided 50:70.
June 23, 2014

math
Draw a diagram. The camera must pan to one side through an angle x, and to the other side, through an angle y, where tan(x) = 50/20 tan(y) = 70/20 Now just add up x and y.
June 23, 2014

Physics
This is a trick question. If the external load is x ohms, then the fraction of the voltage drop across the load will be x/(x+4), or 20x/(x+4) volts. You can see that if the external load is 0, then the current is 5 amps. But, that would take an infinite number of resistors in ...
June 23, 2014

trigonometry
convert radians to degrees, as usual. Then multiply by 60 and 60 on the decimal parts: 23.461° .461 * 60 = 27.66' .66 * 60 = 40" So, 23°27'40" Do the reverse to go the other way. Divide by 60 and 3600 to convert ' and " to °. Now use that...
June 23, 2014

finite
don't know the formula right off. Why don't you give the formula, and show how you evaluate it?
June 23, 2014

Calculus
I assume you mean (∛x^2)(2x+5)^3 ∛ has domain all reals all polynomials have domain all reals. f' = 2(2x+5)^2(11x+5) / 3∛x Now we see that f' is undefined for x=0 f'=0 for x = -5/2 and -5/11
June 23, 2014

Calculus
If u = 5x^2-3x+1, f(u) = csc^4(u) f'(x) = f'(u)*u' = 4 csc^3(u) (-csc(u)cot(u)) u' u' = 10x-3 Now just do the substitution.
June 23, 2014

Calculus
v = 1/3 pi r^2 h dv/dt = pi/3 (2rh dr/dt + r^2 dh/dt) Now just plug in dv/dt = 300pi dh/dt = -15 r=20 h=30 and solve for dr/dt
June 23, 2014

Calculus
v = 1/3 pi r^2 h From the shape of the cone, you know that r = h/6 so, dr/dt = 1/6 dh/dt dv/dt = pi/3 (2rh dr/dt + r^2 dh/dt) = pi/3(2(h/6)h(1/6 dh/dt) + (h/6)^2 dh/dt) = pi/18 h^2 dh/dt Now just solve for dh/dt when dv/dt = -1/4 h=4
June 23, 2014

mat/117
Not sure just what (9-5 4√6) means. But, let's ignore the 5 for now and pretend you had (9-4√6)(7- 4√8) Just expand like any polynomial: 9*7 - 4√6*7 - 9*4√8 + 4√6*4√8 63 - 28√6 - 36√8 + 16√48 Pulling out all the ...
June 23, 2014

math
Hmm. Obviously I misplaced a decimal point. I expect you can find the flaw in my reasoning.
June 23, 2014

math
look at the amounts of NaF involved: (.6/10^6)*100000 + 1.0*x = (1.75/10^6)(100000+x) x = 0.115 check: .6 ppm in 10^5L = 0.06g add 0.115 g and you have 0.175g, or 1.75ppm
June 23, 2014

physics
well, if it's incompressible, then its volume doesn't change under pressure, right? SO, since the mass also doesn't change, that must mean that the answer is (A), since density = mass/volume, both of which are constant.
June 22, 2014

HELP!!!
If h is the altitude from C to AB, we have 1/2 * ch = 3h = 7.52 So, h = 2.507 Now h/a = sin 40° a = 2.507/0.642 = 3.90
June 22, 2014

Algebra
first, you might fix your typos. Your formulas are bogus. Next, you can easily see that the values get bigger and bigger, so the 1/2 formula can't be right. Your first try is right, but should be written a(1) = 3 a(n) = 2*a(n-1) for n > 1
June 22, 2014

math
For the cost, we know that if there are n items, and each costs c, then the total cost is 330+nc For the revenue, if there are n items selling at price 25, the total revenue is 25n. So, just set things up to total revenue = total cost Not sure what your "break even" ...
June 22, 2014

algebra
-2x-2+7(x+1)=2x -2x-2+7x+7 = 2x 5x+5 = 2x 3x = -5 x = -5/3
June 22, 2014

Pre-Algebra
oops: tan 30° = 1/√3
June 22, 2014

Pre-Algebra
since the sides are in the ratio 1:√3:2 a,b) the sides are 41:41√3:82 c) as we all know (or should, because the come up repeatedly): sin 30° = 1/2 cos 30° = √3/2 tan 30° = √3 And since the co-functions are the functions of the complementary ...
June 22, 2014

math
I assume a typo, and that g(x) = -(x-1)^2 + 3 if -2 < x <= 2 just look at the data: since -2 < 1 <= 2, g(1) = -(1-1)^2 + 3 = 0+3 = 3 since -2 < 2 <= 2, g(2) = -(2-1)^2 + 3 = -1+3 = 2 since 5>2, g(5) = 3 Don't let all the symbols confuse you. Each just ...
June 22, 2014

Math
(8-4x)/(x+5) > 1-x If x+5 > 0, 8-4x > (x+5)(1-x) 8-4x > -x^2-4x+5 x^2+3 > 0 This is true for all x, but the initial condition was that x > -5. So, that is the domain: x > -5 If x+5 < 0, 8-4x < (x+5)(1-x) 8-4x < -x^2-4x+5 x^2 < √3 But, we ...
June 22, 2014

math
look at the amount of tar: 1.0*6 + .05*120 = x(126) x = 0.095, or 9.5% Or, consider that 5% of 120g = 6g So, now you have 12/126 = .095
June 22, 2014

Algebra/Steve
You're not sure about the zero? I'm not sure about the equation!
June 21, 2014

algebra
just do what you did with 13 and 6: wherever you see an x, substitute in p: f(p) = p-7 Not a numeric answer, because you haven't specified what value p has. f(bozo) = bozo-7 f(40) = 40-7 and so forth.
June 21, 2014

math
if the first term is 456, then the 17th term is 456+7*16 Tn = 456 + 7(n-1)
June 21, 2014

programming oop
sum12 = n1 + n2 diffs3 = sum12-n3 prodd4 = diffs3*n4 quotp5 = prodd4/n5 I think you can write the code to gather n1-n5 and display the values calculated above.
June 21, 2014

Algebra
Think of a number between 1 and 10: n Add 1; n+1 double the result; 2(n+1) = 2n+2 add 3; 2n+2+3 = 2n+5 subtract 4; 2n+1 add 5; 2n+6 halve the result; (2n+6)/2 = n+3 add 6; subtract 7; add 8; subtract 9; n+1 subtract the number you first thought of: 1 Don't see any ...
June 21, 2014

geometry
Using only reflections in vertical lines, then horizontal lines, you can get B by reflecting through x = -1/2: (-2,-1) -> (-1,-1) through y = -7/2: (-1,-1) -> (-1,-6) No idea what your operations were. Just move your coordinates an equal distance on the other side of the...
June 21, 2014

calculus - unclear
Man, there's a lot of missing information here. That leads me to conclude that the hammer spins in a counterclockwise direction, then flies in a straight, horizontal line from the circle to the screen. Apparently the screen is a circle of radius 50. Now, your solution of (...
June 21, 2014

math
If the current's speed is x, then 10+x is the downstream speed of the boat 10-x is the upstream speed. the downstream time is 90 minutes (3/2 hours) less than the upstream time. Hence, the given equation. 36/(10+x) = 36/(10-x) - 3/2 36(10-x) = 36(10+x) - 3/2 (10-x)(10+x) ...
June 21, 2014

math
since time = distance/speed, 36/(10+x) = 36/(10-x) - 3/2 x = 2 check: 36/12 = 3 36/8 = 4.5 ok
June 21, 2014

math
if his rowing speed is x and the stream's speed is y, then we have 4/(x+y) = 3/(x-y) 48/(x+y) + 48/(x-y) = 14 x=7 and y=1 check: x-y=6 x+y=8 It is clear these values fit the conditions.
June 21, 2014

Math
assuming you mean integers, 501 - 1499 will both round to 1000 any number can be rounded to the nearest thousand. You will have to be a bit more specific.
June 21, 2014

math
as written, I'd say \$189.95 Now, if you mean that each phone costs \$189.95, then 100 of them cost \$18995.00
June 21, 2014

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