# Posts by steve

Total # Posts: 52,095

Quantitative methods
If 360 days counts as a year, then you want P such that 0.12*P = 934.20 If a year is counted as 365 days, then 0.12*(360/365)*P = 934.20

Math
if the number is 3xxx with x>5, then the minimum sum is 3633=15 so, that will not work If the number is 4xxx, then there must be 2 4's and 2 2's. That leaves only 4422 as a possibility.

MATHS
I guess if you discount B itself and Ø, then that leaves 254 "proper, non-null" subsets.

maths
5^(2?9) = 125^x 5^(2*3) = 125^x (5^3)^2 = 125^x 125^2 = 125^x 2 = x

Economics(help!)
revenue R = 60q profit P = R-C = 60q-(100+q^2) so find q such that dP/dq = 0

math
a+ar+ar^2 = 35 a*ar*ar^2 = 1000 now just solve for a and r.

maths
3xy^2 -4+2y=29 3y^2 + 6xyy' + 2y' = 0 at (1,3), we have 27+18y'+2y' = 0 y' = -27/20 So, now we have a point and a slope, so the tangent line there is y-3 = (-27/20)(x-1)

Calc
4xy+ln(x^2y)=7 4y + 4xy' + 1/(x^2y)(2xy+x^2y') = 0 4xy' + 1/y y' = -4y - 2/x y' = -2(2y + 1/x)/(4x + 1/y) = -2y(2xy+1) --------------- x(4xy+1) or, note that 4xy+ln(x^2y)=7 4xy + 2lnx + lny = 7 4y + 4xy' + 2/x + 1/y y' = 0 (4x+1/y)y' = -4y - 2/x...

Calc
x=sec(1/y) 1 = sec(1/y)tan(1/y)(-1/y^2) dy/dx so, dy/dx = -y^2 cos(1/y) cot(1/y) or, x=sec(1/y) 1/y = arcsec(x) y = 1/arcsec(x) y' = -1/[x?(x^2-1) arcsec(x)^2] you can see that they are the same, since cos(arcsec(u)) = 1/u tan(arcsec(u)) = ?(u^2-1)

Calc
just the good old chain rule and product rule d/dx e^u = e^u du/dx d/dx uv = u'v + uv' so, with y = x cosx + x^4 e^2x y' = (1)cosx + (x)(-sinx) + (4x^3)(e^2x) + (x^4)(e^2x)(2)

MATHS
arc = r? = 7(?/3) perimeter = 2r + arc

Algebra
h = -16t^2 + 60t = 4t(-4t+15) now work on B and C again.

math
since the y values differ by 0.6, and y(0)=4 y = 0.6x + 4

Math
very possibly, but unknown without further information.

geometry
reflection across what? I guess it doesn't matter, since any set of points PQRS will be transformed to some P'Q'R'S' ...

maths
x(x-3) = 18 Work the algebra, but it should be easy to tell which two factors of 18 differ by 3.

Math
40

Math
0x50=0 1x50=50 2x50=100 so, what do you think?

Math
see related questions below

Maths
w+a+b = 100 50w+10a+b = 500 The equations don't work out too well, so let's play around with some values that add up to Rs500, and see whether we can wind up with 100 fruits: (b,a,w) 90,1,8 = 500 91,1,8 = 501 50,40,1 = 500 50,30,3 = 500 Since the first line shows 99 ...

Math
r^2 = 162/18 = 9 Now you can find the 1st term, and then S8 = a(r^8-1)/(r-1)

Aptitude
draw a diagram. It will show 4 identical rectangular areas that are not paved. Find the area of one of those, multiply by 4, and subtract that from the total 1500m^2 area. That will be the area of the paved parts.

maths
a+ar = 28 ar^2+ar^3 = 252 solve for a and r, and then choose the values which make ar^6 positive

maths
a+7d = 5(a+2d) a+6d = a+3d+9 solve for a and d, and then you can write the sequence.

Math
false

Geometry
Do we assume that there is a single triangle, of fixed size, which we are manipulating? That is, its sides are of fixed length?

Calculus
if we let the base have length 20, then the altitude of the triangle is h = 15sin? so the area is a = 1/2 bh = 75sin? da/dt = 75cos? d?/dt when ? = ?/3, then da/dt = 75(1/2)(?/90) = 5?/12 m^2/s

physics
two postings, still no coherent question.

Algebra
A. factor out a 4t B,C. just plug in the value for t. C should be easy to explain if you think of what H=0 means.

Math
for the perimeters, just find the lengths of the sides and add them up. The areas are a bit trickier, but (a) once you get the sides, you will see that it is a right triangle, so the area is easy. (b) is easy, since it is easy to see that it is isosceles, with base=4 and ...

Trigonometry
1/(sin^2x-cos^2x) = 1/[(sinx-cosx)(sinx+cosx)] so, using a common denominator, 1/(sin^2x-cos^2x) - 2/(cosx-sinx) = 1/[(sinx-cosx)(sinx+cosx)] + 2(sinx+cosx)/[(sinx-cosx)(sinx+cosx)] = (1+2sinx+2cosx)/(sin^2x-cos^2x) I see several typos in your posting. If I have interpreted ...

Math
m/w = 3/7 w = m+12 ...

Physics
(5,?/2) it's right up the y-axis...

science

Math
GCD(20,30) = 10 so, 10 bags, each with 2 blueberries and 3 grapes not much of a snack, eh?

Maths
in real math, that is 14/?6 - ?5 - ?11 to get a rational denominator, multiply top and bottom by ?6, giving 14?6/6 - ?5 - ?11 = (14?6 - 6?5 - 6?11)/6

Physics 1st paper
use the law of cosines: x^2 = 8^2 + 8^2 - 2*8*8*cos(60°)

geometry
I'd say enough to cover 1000 ft^2

Calculus
?dx/(x-2) = ln(x-2) first off, ln(x-2) is not defined for x < 2. So, some like to evaluate it as ?[1,3] dx/(x-2) = ln|x-2| [1,3] = ln|3-2|-ln|1-2| = ln1 - ln1 = 0-0 = 0 That is because the graph is symmetric about (1,0) so the upper and lower areas cancel out.

Algebra
yes

Math
uh, 51 ?

Math
50

Math
well, every digit except the 8 must be 9, right?

Math
After x months they will be equal if 310-15x = 90+15x Now, try to make some effort on the other problems, ok? The idea of this site is not to do your homework assignments. We can help, but expect you to bring something to the table, especially when several problems are similar...

English
#1 not #2,3 are both ok.

English
yes, but I've never heard, nor would I say #3 That phrase is usually reserved for nouns with superlative adjectives, as in your other example. Such as ... far and away the tallest mountain the best student the unluckiest man on earth

Calculus
Because sin^2? = 1-cos^2?, the logical choice is x = 2sin? 4-x^2 = 4-4sin^2? = 4cos^2? ?(4-x^2) = 2cos? dx = 2cos? d? Now your integral becomes ?3x?(4-x^2) dx = ?3*2sin? * 2cos? 2cos? d? = 24?cos^2? sin? d? Now let u = cos? and the integral is just = -24?u^2 du = -24(1/3 u^3...

Math
so, what are the even multiples of 13, less than 100?

geometry
OK - I may have misread it again, assuming that the base of the triangle is parallel to the x-axis. This is much trickier than it looks, unless the size of the triangle is somehow determined.

geometry
Nah - that's just too complicated. Take a look at an equilateral triangle, and slice off the top of it. (That's the piece of the x-axis between the sides of the triangle.) That small cap of the big triangle is also an equilateral triangle, and always has the same base ...

geometry
so, two of its vertices are (-h,-k) and (1+h,-k) Thus, the length of the base is (2h+1) That means the altitude is (1/2 + h)?3, making its coordinates (3/2, k+(1/2 + h)?3) See whether you can work out the relationship between h and k, and thus the equation for the path ...

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

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