Monday
July 28, 2014

Posts by Steve


Total # Posts: 23,988

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...

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.

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 ...

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

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

not maths
and probably not even homework

maths
24*12*6 = ?

maths
a cloud

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.

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 i...

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>

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

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

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 (...

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)

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

math
-11 + 7 + x = 15 -4 + x = 15 x = 19

science
163/(163+755) = 163/918 = .1776 or 18%

ALGEBRA
8x > 72

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.

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...

Maths
each side is now √425.5969 = 20.63 Reduce by .03 to 20.6

Maths - eh?
no idea what that sentence means. what "same" number?

Math
140mi/14g = 140/14 mi/g = 10 mi/g

physics
current speed is 2.6 sin 28.5° boat velocity across is 2.6 cos 28.5°

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.

math
.02x = .23 x = 11.50

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

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

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 you...

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, ...

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)

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.

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

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

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

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...

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.

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.

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)

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 = ?

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/...

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!

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)

math
45000 * 0.7^5

Math
.06*30 + .04(x-30) = .04x + .6

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

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

pre cal
oops - the real root is at -3.282

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.

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...

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.

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

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

Physics--check answers please
#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

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.

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.

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 ...

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...

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

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

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.

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

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

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 p...

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

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

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.

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

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

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" ...

algebra
-2x-2+7(x+1)=2x -2x-2+7x+7 = 2x 5x+5 = 2x 3x = -5 x = -5/3

Pre-Algebra
oops: tan 30° = 1/√3

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 ...

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 ...

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 ...

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

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

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.

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

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.

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 inductio...

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...

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 (...

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) n...

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

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.

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.

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

math
6 is the same as 5 8/8 So, 5 8/8 - 3 5/8 = 2 3/8

mathematics
can you see how little context you have provided?

algebra
c'mon. You know that 99 = 9*11 So, what might the two consecutive odd integers be? ...

algebra
Note that the terms come in repeating groups of 5. 38 = 7*5 + 3 So, S38 = 7(4+8+2+6+2) +4+8+2 = 168

math
4/7 * 3/8 = 12/56 or 3/14 Good luck finding that measuring cup!

Math 11 - Rational Expressions
the only restrictions are because you cannot divide by zero. So, check the denominator of any rational expression. Wherever it is zero, those values must be omitted from the domain. Otherwise, all real numbers are allowed. So, for #3 above, since 2x^2+5x+2 = (2x+1)(x+2) the va...

math
so, just fix the typo and solve -16t^2-32t+320 = 48 t = 3.24

alegbra
(3x-1)(x+2)

Math
Add up all the numbers: 632 There are 12 numbers, so the mean is 52.666 Now, you want to remove one value so that the remaining 11 have a mean of 56.09. Well, 11*56.09 = 617 So, if you remove one of the 15's, the remaining 11 numbers add up to 617, giving the desired mean.

Pre-Calculus
You show that it is true for n=1. Then you show that if it is true for n=k, then it must also be true for n=k+1. That means that the assertion is true for all values of n, starting with n=1, and thus for n=2,3,4,... For instance, a common proof is that the sum of the first n o...

Math
to lower the mean, remove the highest scores. To raise the mean, remove the lowest scores.

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