# Posts by Steve

Total # Posts: 51,744

math
those sure look like primes to me

Algebra 2
A: you have the starting value, and the decay factor, so v(t) = 250 * 0.98^t where t is the years since 2000 B: just plug in t=11 C: all pure exponentials look just the same, up to scaling.

Calculus
well, you are still vague. I assume you mean to revolve the triangle around the y-axis. So, revolve the small triangle. The volume is v = ?[1,2] 2?rh dx where r = x and h = y-1 = 2x-2 v = ?[1,2] 2?x(2x-2) dx = 10?/3 to verify, do it again with discs of thickness dy, where v...

Calculus
revolve around what? And why reflect it as well? I will say that the line from (1,1) to (2,3) is y = 2x-1 You can use that when doing the volume of a shell, which is v = 2?rh dx

Mathematics-Integration
Hmmm. That's a possibility. You might also try doing integration by parts twice to yield the recursive sequence derived here: https://math.stackexchange.com/questions/416162/a-recursive-formula-for-a-n-int-0-pi-2-sin2nxdx-namely-a-n

maths
Hmmm. That's not what I get. (1+(1/2.7176022)) = 1.36797 1.36797^3.7176022 = 2.20537 (2000/1999)^1999 = 2.7176022 close, but not nearly correct. (1+1/e)^(e+1) = 3.20527 I get a solution at x = -2000 (1+(1/-2000))^(-2000+1) = 2.7176022

Algebra 1B
enter your polynomials here and see all the details http://calc101.com/webMathematica/long-divide.jsp

Maths
or, doubling the first equation, 2x+4y = 18 2x-4y = 2 now just add the two equations, and y goes away...

physics
(200-11.6)/14.9 = ?

Mathematics-Integration
how about this: x = sin? ?(1-x^2) = cos? dx = cos? d? so, d? = dx/cos? = dx/?(1-x^2) Then the integrand is ln((2sin?+3)cos?) d? Unfortunately, that doesn't integrate any better. We can't use the same trick from before, since we don't have a definite integral. If we...

Math
well 10 is 5 times 2, so the distance will also be 5 times as big x/25 = 10/2

MATHS
see related questions below

Geometry
fast!

math
This is clearly an exercise in completing the square. 3x^2 - 6x - 2 3(x^2-2x) - 2 now add and subtract 3, leaving the value unchanged: 3(x^2-2x+1) - 2 - 3 3(x-1)^2 - 5

what you need to do is recognize the special angles with known trig values. ?/6 is one of those angles. sin(5?/6) = sin(?/6) = 1/2 the real question is: why did you calculate (5-pi)/6 instead of just doing 5pi/6 ? If your function is f(x)=15.3sin(?x6)+44.1 propagating your ...

Algebra 2
stuck how? Just replace x with 5 and evaluate! too bad you could not be bothered to show us what you did. f(x) = 15.3sin(?x/6)+44.1 f(5) = 15.3sin(5?/6)+44.1 = 15.3(1/2)+44.1 ...

Maths
well, distance = speed * time, so 70x + 80*0.5(x+3) = 460 ...

maths
w*4w = 1024 w^2 = 256 ...

Maths
naturally the number of steps will not be measured in meters. Each 3 steps, she advances 0.5 meters (0.5+0.5-0.5) So, after 2*3*19 = 114 steps, she has advanced 19 meters. On the 116th step she has gone the last meter, and does not need to step back again.

math
well, surely that is 0.125 * 13650 = ?

math
even if you fix the mismatched parentheses, I don't see an easy algebraic way to solve this. You'd better use a graphical or numeric method. What tools do you have?

Math
I'd say it depends on the set. Do you have some further context?

math
c = ks/?m plugging your numbers, c = 55k/4 If you have an actual value for c, then you can find k.

math- ouch!
I got that wrong. The angles are not in the same ratio as the sides. The sines of the angles are. So, you can still draw the triangle, but then you need to circumscribe it. You can easily find online the relationship between the radius and the sides. In this case, with sides ...

Math
so, draw the circle. The central angles subtended by the sides will be 100,120,140 degrees. It is easy to construct a 120° angle, so you can draw the side of length 6x first. Then from its ends draw arcs of radius 5x and 7x. They will intersect at the third vertex.

physics
draw the velocity vectors. The resultant speed has magnitude v=?(2^2+8^2) It drifts downstream by an angle ? such that tan? = 2/8 without knowing the distance across the river, it's hard to say how far downstream it will have drifted. Also, you don't define exactly ...

Science
mass(g) = density(g/cm^3) * volume(cm^3)

Algebra
(x + 1/x)^2 = x^2 + 2 + 1/x^2 so, x^2 + 1/x^2 = a^2-2 (x + 1/x)^3 = x^3 + 3x + 3/x + 1/x^3 so, x^3 + 1/x^3 = a^3 - 3(x + 1/x) = a^3-3a

Algebra
ah! that makes all the difference! Since the center line is at y = -1, the distance to the extremes is the amplitude. So, the amplitude is 4 and the vertical shift is -1. That means y = 4sin(b(x-c))-1 since sin(0) = 0, that means y+1=0 at x=6, so the horizontal shift is 6 the ...

Algebra
What do you mean by a "zero" value? You do not include a vertical shift term. The minimum of -5 indicates to me that y = 5sin(b(x-c)) I assume your zero value is supposed to help define the period...

Algebra
let u = 3^x Then your equation becomes 3^(2x+1) = 5*3^x + 2 3*3^(2x) = 5*3^x + 2 3u^2-5u-2 = 0 ...

Multivariable calculus
dw/dv = (dw/dx) / (dv/dx) dw/dx = ?w/?x + ?w/?y dy/dx + ?w/?z dz/dx and similarly for u,v See where you get with that.

? = 15 rev/min * 1min/60s * 2?rad/rev = ? rad/s s = r? = 12cm * ? rad/s * rs = ? cm

these are standard angles - learn the trig function values they will pop up over and over.

Maths
i) ?(9/16) = 3/4 ii) since C?r, the same ratio.

Math
You can see all the details here: http://www.gregthatcher.com/Mathematics/GaussJordan.aspx

@Bosnian got it
I neglected the fact that there were two parents... Always read the problem carefully!

math-ed 16
(90-72)/2 = 9

math 5
so, start off with the millions place: 5,xxx,xxx The rest is pretty vague. One possibility is 5,040,100 The 4,1 can be replaced with any other two values that add to 5.

Maths
if dropping 2°/hr, then 9 hours ago, it was 2*9 = 18° higher than it is now.

Math
just plug your numbers into the formula, which I'm sure you have. We can check your work . . .

Physics
recall that s(t) = 1/2 at^2 so, solve s(2) = 20 for a, and then use that a to find s(6). Your final answer is s(6)-s(2)

Math
You got x = -3,2 correct, but your final answer is wrong.

Math
correct, since the discriminant b^2-4ac is positive

steve reiny proportion help maths reiny!!!
If y is the illumination c is the candlepower d is the distance, then y = kc/d^2 so, if y is constant, c/d^2 = y/k, which is constant So, you want d such that 8/150^2 = 5/d^2 d^2 = 5*150^2/8 d = 118.56 cm or, using a proportion, you use c2/c1 = d2^2/d1^2 d2/d1 = ?(c2/c1)

math
well, just 1 section out of the 10, so ...

Math
there are 4/5 as many boys as girls, so ...

math
assuming you want an integer value, then 349

Math
counting in seconds, 1/45 - 1/60 = 1/x x = 180 so, it will take 3 minutes

Math
since cos(x) = sin(90-x) sin(x+24) = sin(90-x) x+24 = 90-x 2x = 66 x = 33 check: sin(57) = cos(33) yep

physics
v = at

math
he just multiplied length,width and depth of water added

Trigonometry
this diagram is no trick. Draw a horizontal line: the water draw a vertical line: the lighthouse. Where the vertical line hits the water, call that point B: bottom of tower At the top, label it T. The height of the vertical line is 25 Now somewhere out on the water, label a ...

Algebra
first off, you have no equation -- just an expression (as you might expect, an equation needs an equal sign: =) The only commutative parts I can see here are (3+a+b)3 = 3(3+a+b) now, if you want to talk about commutative addition, or distributive properties, then we can go on ...

Math
correct. a rectangle is rotated about one of its sides.

math-probability
If you want permutations of elements, that implies no duplications, unless there are duplicate elements. If you just wall all possible 4-letter strings of ABCD, then there are 4 choices for each position in the string: 4^4 = 256 If you want all strings of length up to 4, then ...

Math
P(white) = (#whites)/(#marbles) so, how many marbles are white? how many total marbles are there?

Math
what - you can't replace x with 5 and evaluate the result?

Math
8(2 - 1/2) = 12 I suspect a typo.

Math
well, f(x) = 3x +4 so f(-1) = 3(-1)+4 ...

physics
draw the velocity vectors. They form a 3-4-5 right triangle, with the straight-across side of length 3. So, scale it up by a factor of 5/3 to get an equivalent distance triangle. He will have to row 25/3 km along his path, while drifting downstream 20/3 km, landing exactly 5 ...

math
right. So, 1/100 chance of getting it.

math
so, in the numbers from 00-99 how many are 44?

math
20C5 = (20*19*18*17)/(1*2*3*4*5)

Math
(3/4)/9 = 3/4 * 1/9 = 3/36 = ?

math
15/16 as many men, so 16/15 as much time 5/4 as many tables, so 5/4 as much time 9 * 16/15 * 5/4 = 12 days or, using the man-days of labor, there are 16*9/800 man-days/table 1000 tables * 144/800 m-d/table = (1000*144/800 m-d)/(15 men) = 12 days

Math: Probability
P(some hearts) = 1-P(no hearts) = 1 - (39/52)(38/51)(37/50) = 0.58647

Mathematics
You had me with 2*1+1^2 = 3 since A was the only sequence starting with 3.

Mathematics -Integration : to Steve
actually, a bit more examination of your attempt is in order. We have ?[0,?/4] ln(sinx+cosx) - ln(cosx) dx recall from your cosine subtraction formula, that this becomes ?[0,?/4] ln(?2(cos(?/4-x)) - ln(cosx) dx = ?[0,?/4] ln(?2)+ln(cos(?/4-x)) - ln(cosx) dx and with the little...

Mathematics -Integration : to Steve
your idea of splitting the log is wrong, since ln(1+tanx) = ln((cosx+sinx)/cosx) = ln(cosx+sinx) - ln(cosx) but ln(cosx+sinx) ? ln(cosx)+ln(sinx) and you can't integrate those either.

Mathematics -Integration : to Steve
You may not have come across the trick that says that ?[0,a] f(x) dx = ?[0,a] f(a-x) dx It's kind of like integrating from right to left, instead of left to right, but the area is the same. Now you have to include the limits of integration as part of the substitution. x = ...

Mathematics-Integration
try using x = tan? dx = sec^2? d? see where that takes you!

math
well, the discriminant b^2-4ac is negative, so what does that tell you?

math
(g?f)(-5) = g(f(-5)) = g((-5)^2+7) = g(32) = (32+3)/32 = 35/32 or, g(f) = (f+3)/f = (x^2+7+3)/(x^2+7) = (x^2+10)/(x^2+7) so, (g?f)(-5) = (25+10)/(25+7) = 35/32

Algebra
if no duplicates, then 5P2 = 20 if duplicates allowed, then 5^2 = 25

Math
median=10, 6 numbers, so median is between 3rd and 4th .. 9 11 . . mode=11 .. 9 11 11 . range=4 7 8 9 11 11 11

math
(x+y)^2 + (x-y)^2 = x^2+2xy+y^2 + x^2-2xy+y^2 = 2(x^2+y^2) ...

Math
apparently white is + and black is - big black square: -x^3 small black square: -x rectangles: x^2 or 1 See what you can do with that...

math
xa-xb = x(a-b) = 12 a-b = 2*3 = 6 x = x(a-b)/(a-b) = 12/6 = 2

math
a/x = (b/x)(a/b) so, 36/x = 36*6 1/x = 6

math
your copy/paste mangled the 2nd expression, but if it is (a-b)^2 = 64, then (a+b)^2 + (a-b)^2 = a^2+2ab+b^2 + a^2-2ab+b^2 = 2(a^2+b^2) so, 2(a^2+b^2) = 100+64 a^2+b^2 = 82

math
x^2-y^2 = (x-y)(x+y) = ab

maths
if you don't like the law of sines, just study the tan/cot functions. You can easily see that the height h can be found from h cot25° - h cot37° = 57

Calculus
the line from (1,1) to (3,2) is just y-1 = 1/2 (x-1) y = 1/2 x + 1/2

math-limit
some parentheses would also help. Since (?5 + x - ?5)/x = 1, that's probably not what you had in mind. (?(5+x)-?5)/x -> 0/0 so, multiply top and bottom by (?(5+x)+?5) and you end up with ((5+x)-5)/(x(?(5+x)+?5)) see where that takes you...

math
sorry - still not much use...

math
solve for r in (1+r)^15 = 426/258

math
the "mid" or "bi" or "med" indicates the middle, so ...

Science(maths)
(# moles)*(H atoms per molecule)*6.023*10^23

science
when: 100-4.9t^2 = 25t-4.9t^2 where: evaluate either expression at the found value of t.

math
25cm/3m = 25cm/300cm = 25/300 = ?

Science
almost, but no.

Mathematics
nope. It's just that the series converges iff |t| < 1 If you look at the formula, it's the same whether t<1 or t>1. The signs of the numerator and denominator both change, but the result is the same.

Mathematics
If t = (5x+6)/(3x-2) then |t| < 1 if -4 < x < -1/2

Pre-Calculus 12
well, you have to know the basic steps to finding intercepts and asymptotes. Review the examples in your text, and then it's just a matter of figuring out the relevant features of the graph. The intercepts and stuff are just handy landmarks to pinpoint specific places.

Pre-Calculus 12
y = (x-5)(x+2)/(x-2) a fraction is zero when its numerator is zero, right? Damon was just trying to give you the x-intercepts as an aid to graphing the curve. With Damon's input, you have the x-intercepts, the asymptote, and the y-intercept. Unfortunately, the asymptote is...

math
is that 1/z + 3 or 1/(z+3) ? Take a look at https://math.stackexchange.com/questions/1792628/complex-variable-limit-at-infinity

Physics