Monday
August 3, 2015

Posts by Steve


Total # Posts: 32,562

Math
27x^3+8y^3 = (3x+2y)(9x^2-6xy+4y^2) (3x+2y)^2 = 144 = 9x^2+12xy+4y^2 . . .
July 2, 2015

Math
well, you have a triangle whose area is half that of the parallelogram. Use Heron's formula on it, since you have all three sides. Then double the result.
July 2, 2015

Math - eh?
evaluate a line that is there with two numbers? Not much to go on. What sort of problems are you studying just now? Are there no similar exercises worked out?
July 1, 2015

calculus
sounds true to me. So, what?
July 1, 2015

Algebra - eh?
there seems to be something missing from the first term. And your notation is inconsistent. log base{3} vs log_{3} Anyway, just recall that log a + log b = log ab regardless of the base.
July 1, 2015

Math
"none" is singular. There are 12 marbles in all, so P(red,red) = 3/12 * 2/11
July 1, 2015

Calculus Derivative - ?
where did you get d/dz e^z = z e^z?
July 1, 2015

Calculus Derivative
if y = u^v then y' = vu^(v-1)u' + lnu u^v v' Note that u^n and a^u are just special cases of this So, what you have is y= e^u y' = e^u u' u = x^x, so u' = x^x (1+lnx) y' = e^(x^x) x^x (1+lnx)
July 1, 2015

math in distress
Why are you adding teachers to students? If there are x teachers, x/1200 = 1/30 x=40
July 1, 2015

math in distress
since time = distance/speed, 480/(x+4) = 480/x - 1/2 x = 60 Why did you divide by 2? It's 480 miles each way. Amazingly, you got the correct answer! 480/60 = 8 480/64 = 7.5 That's like saying 16/64 = 1/4 because you can cancel the sixes!
July 1, 2015

Math
ac = b^(y/x) * b^(y/z) = b^2 That should get you started
July 1, 2015

staTIStics
9 balls in total P(white,red) = 6/9 * 2/8 PS That's color, not collar
July 1, 2015

math in distress
Why, Damon, I'm surprised! You never seem to miss a chance at poking fun at English units. And I (sort of) like all the strange units, just as I miss the old English coinage. That's weird, if the slug is defined in terms of pounds, and not the other way around. Guess ...
July 1, 2015

mechanic
recall that a cylinder of radius r and height h has volume v = πr^2 h so, that would be π*16*8 = 128π = 402 in^3
July 1, 2015

physics
momentum is mass * velocity So, two objects of different masses can have the same momentum if their velocities are different.
July 1, 2015

physics
you need a and b such that 12*15i + 36*5j = 12*6(.866i+.5j) + ai+bj 180i + 180j = 62.35ai+36bj a = 180/62.35 = 2.89 b = 180/36 = 5.00 So, the 36kg ball is moving with speed 5.78 m/s in the direction arctan(5/2.89)=60°
July 1, 2015

Algebra
17+10 = 27 total payment w/o coupon so, how much for each of the 4 people?
July 1, 2015

calculus
Not sure how to apply calculus to this. You can use the Rational Roots Theorem to narrow down your choices. That, and a little synthetic division turns up (5x-1)(x+3)(x^2-6x+13) Now you can find the complex roots.
June 30, 2015

statistics
This is discussed here: http://math.stackexchange.com/questions/353419/what-is-the-probability-that-either-a-or-b-but-not-both-will-occur
June 30, 2015

science
speed changes by 11m/s in 5s = 2.2 m/s^2
June 30, 2015

Algebra 1
Just list the f values for each x value. For example, f(-3) = -(-3)+4 = 7 so, 7 is in the range now do the others as needed. You already know that C and D are out.
June 30, 2015

math
geometric series. a = 1 r = -7/9 sum = 9/16
June 30, 2015

math
this is just a geometric series, with a = 1 r = -3/4 so, the sum is 4/7
June 30, 2015

math
n/(n+3) = 1 - 3/(n+3) The terms clearly converge to 1.
June 30, 2015

Math
I think I like (2/13)(5/12) Dang Siris!
June 29, 2015

calc
y' = x/y you can recognize that as an hyperbola x^2-y^2 = a^2 since (3,1) is on the curve, 9-1 = a^2 x^2-y^2 = 8
June 29, 2015

math
f'(t) = (t^2+11t+24)/(1+cos^2(t)) f'=0 when t^1+11t+24 = 0 That is, when t = -8 or -3 f"(t) = 2t+11 f"(-8) < 0, so the max is there.
June 29, 2015

impoving writting via good speling
I'll let others evaluate the style, but I can say right off that the grammar and spelling need some improvement. My corrections are in bold. There are awkward shifts between viewpoints (first, second, third person). ---------------------------------------- Email is quick; ...
June 29, 2015

Cycle geometry
or, using interior angles, 180(n-2) = 162n 180n-360 = 162n 18n = 360 n = 20
June 29, 2015

math - eh?
what does ^213 x mean? I know that x^2 means x squared I can't figure out what you're trying to express.
June 29, 2015

math
length is 4 less than 3 times the width less than means you're going to be subtracting. 6 is 2 less than 8 50 is 40 less than 90 So, expect to see "-4" because the length is 4 less than something. Less than what? 3 times the width. The "times" indicates...
June 29, 2015

math
kind doesn't really matter. Volume just depends on base and height.
June 29, 2015

math
3x-5y = 2000 2x-3y = 2000 x=4000 y=2000 So, A makes 12000 and spends 10000 B makes 8000 and spends 6000
June 29, 2015

Physics
a(t) = 6.60-2.29t v(t) = 6.60t - 1.145t^2 + c v(0) = 3.20, so c = 3.20, and v(t) = 3.20 + 6.60t - 1.145t^2 s(t) = 3.20t + 3.30t^2 - 0.3817t^3 + c s(0) = 7.30, so c = 7.30 s(t) = 7.30 + 3.20t + 3.30t^2 - 0.3817t^3 max speed occurs when a=0, or at t=2.882 v(2.882) = 12.7109 s(6....
June 29, 2015

Nothern Cape collage
We can assume the rock was thrown from a height of 0. So, now you know that h(t) = vt-5t^2 h(5) = 0, so 5v-125 = 0 v = 25 m/s
June 29, 2015

calc
why all the words? y = arcsin(x/4) using thin horizontal strips, the area is a = ∫[0,π/2] (4-x) dy But x = 4siny, so a = ∫[0,π/2] (4-4siny) dy = 2(π-2) You can check your work using vertical strips: a = ∫[0,4] y dx = ∫[0,4] arcsin(x/4) dx...
June 29, 2015

Algebra
since we want real coefficients, complex roots must come in conjugate pairs. So, f(x) = (x+5)(x-(2+i))(x-(2-i)) = x^3 + x^2 - 15x + 25
June 29, 2015

Algebra
From the first equation, you see that y = 5x+16 so, plug that into the 2nd equation and solve for y. Then you can figure out x.
June 29, 2015

math
The corners of the roughly triangular region are at (1,0),(0,2),(e^2,2) So, using thin washers of thickness dx, v = ∫[0,e^2] π(4^2-(2+lnx)^2) dx = 95.298 Using shells of thickness dy, we have v = ∫[0,2] 2π(2+y)(e^y-1) dy = 95.298
June 29, 2015

Algebra
f+r = 120 10f+13r = 12*120
June 29, 2015

Algebra
you are told that A + B = 50 39.95A + 30.34B = 1747.64 Now go for it.
June 29, 2015

calc
just review your text, and you will see why s(t) = 4 -10t + 15t^2
June 29, 2015

math
3x-4
June 29, 2015

calculus
correct.
June 28, 2015

physics
Looks good to me. except that v^2 = (240m/s)^2, not 240m/s^2, and g=10m/s^2, not ms^2 watch out fer them unit thingees.
June 28, 2015

Math
I'd say 12/15, right?
June 28, 2015

Calculus Partial Fraction
note that x^3-8 = (x-2)(x^2+2x+4) So, your fraction is now x^2 -------------------- (x-2)^2 (x^2+2x+4) As partial fractions, that becomes A/(x-2) + B(x-2)^2 + (Cx+D)/(x^2+2x+4) Placing all that over the common denominator, we have A(x-2)(x^2+2x+4) + B(x^2+2x+4) + (Cx+D)(x-2)^2...
June 28, 2015

math
You need to know how the DJIA is calculated, to figure the effect of any one stock.
June 28, 2015

Math
Using the given formula, your expression is correct, but its value is 3110.50 (D) Expressed correctly, of course, it would be 15,000(0.986975)^(10*12) You must have pushed some buttons wrong if you got (A). Or just guessed...
June 28, 2015

Finance
3000(0.9744^20) = 1785.94
June 28, 2015

Calculus Partial Fraction
well, clearly you can cancel x^2 and you are left with 1 / x(x-2) = A/x + B/(x-2) Now if you place the right side over the common denominator, you have (A(x-2)+Bx)/(x(x-2)) In order for the two numerators to be identical, you need (A+B)x-2A = 0x+1 That is, A+B=0 -2A=1 A = -1/2...
June 28, 2015

Math
could be any of those, depending on the proportion of Microsoft stock in the DJIA.
June 28, 2015

Math
Hmmm. 518400 = (10*9*8)^2 Why did you use that?
June 28, 2015

Math
assuming the order of choice does not matter, 6C4 * 6C4 or, 6C2 * 6C2 = 15*15 = 225
June 28, 2015

Math
P(red,red) = 3/5 * 2/4 You don't really need to record the color, since the bean was not replaced. Unless you have eaten it, you can just look at the two beans drawn.
June 28, 2015

trigonometry
If A is the angle of elevation of the sun, then tanA = height/shadowlength So, height/5 = 5/6 Looks like you need to review the basic trig functions. And always draw a diagram!
June 28, 2015

Math
Looks suspiciously like 30000. Just sayin' ...
June 28, 2015

Maths Problem
Dan finishes in 70 minutes, so Ellen finishes in 75 minutes. If Dan's speed is d m/min Ellen's speed is e m/min So, d = (15/14)e 35e = 35d-300 35e = 35(15e/14)-300 35e = 75e/2-300 5e/2 = 300 e = 120 So, the distance is 120*75 = 9000m You can check to make sure that the...
June 28, 2015

math
16x^2-24x-13=0 16(x^2 - 3/2 x) = 13 16(x^2 - 3/2 x + (3/4)^2 = 13+16(3/4)^2 16(x-3/4)^2 = 22 (x-3/4)^2 = 11/8 x = 3/4 ±√(11/8) or, x = (3±√22)/4 or, eschewing fractions, 16x^2-24x-13 = 0 16x^2-24x+9 = 13+9 (4x-3)^2 = 22 ...
June 28, 2015

maths
I don't believe that one side is only 60cm. Fix that, and just find twice the perimeter, then subtract twice the gate width.
June 28, 2015

Math
recall that 3^4 = 81
June 27, 2015

Finite Math
If there are x Daybrite sets and y Noglare sets, then you want to maximize p=425x+700y subject to x+y <= 400 x >= 70 y >= 160 a good tool is at http://www.zweigmedia.com/RealWorld/LPGrapher/lpg.html it will solve and graph the solution
June 27, 2015

Geometry
the two bases of a parallelogram are equal the two bases of a trapezoid are different Bh vs (b+B)h/2 These can only be the same if b=B.
June 27, 2015

Math
well, did you actually try the values to see which are or are not? (0,-1): -1 = 0^2-1? yes now you try the others and we can check your answers.
June 27, 2015

Math
log3(3) = 1 so, 1+log3(x^2) = log3(3) + log3(x^2) = log3(3 * x^2)
June 27, 2015

Math
I'm not Carnak the Magnificent. What was the question, and how did you arrive at your answer? We're willing to provide help, and even answers, but don't make us come up with the questions, too!!
June 27, 2015

calc
so, what about the root test is causing difficulty?
June 27, 2015

calc
just take the integral from 0 to 2.
June 27, 2015

calc
using discs, we have integral[0,π] π sin^2(sin(x)) dx I don't think that can be evaluated with elementary functions. Do you have numeric methods available?
June 27, 2015

math
#1 600000*.9^4 = 393660 #2 16+32*9 = 304 #3 F12 = 89 #4 8*1/√2^5 = √2 #5 Assuming no one received more than one message 2+4+8+16+32 = 62 I suspect a typo in the problem.
June 27, 2015

algebra
variables are represented by letters: x and y numeric constants stand alone: -9 coefficients are numbers multiplying the variables: 4 and 15
June 27, 2015

Math
since the basic function is y=1, and that's not one of the choices, what do you think? Try the various choices to see which one works.
June 26, 2015

math
Since a = 1 r = 2 S4 = 1(2^4-1)/(2-1) = 15 S15 = 2^15-1 = 32768 So, the sum from S5 to S15 = S15-S4 = 32753
June 26, 2015

math
So far, 70% of your score is allocated as follows: .15*74 + .15*96 + .40*60.5 = 49.7 Since that is only 70% of your score, it's equivalent to 49.7/.70 = 70.1%
June 26, 2015

physics
since the sled is not accelerating, the net force acting on it must be zero. So, since the friction is .15*(30*9.8), that is equal to the force acting on the sled.
June 26, 2015

algebra
If there are x fill-in y multiple-choice z long-answer they have given us the following facts: x+y+z = 24 2x+6y+5z = 100 x+y = z Now you can solve for x,y,z
June 26, 2015

math
400$ * 3tickets/5$ = 1200/5 = 240 tickets
June 26, 2015

math
The curves intersect at (-2,2) and (1,-1) so, the area is the sum of all the little horizontal strips between the line and the parabola: ∫[-1,2] (2-y^2)-(-y) dy = ∫[-1,2] 2+y-y^2 dy = 9/2
June 26, 2015

math
x' = y√(y^2+2) so, the arc length s = ∫[0,1] √(1+x'^2) dy = ∫[0,1] √(1+(y^2)(y^2+2)) dy = ∫[0,1] √(y^4+2y^2+1) dy = ∫[0,1] √(y^2+1)^2 dy = ∫[0,1] y^2+1 dy = 4/3
June 26, 2015

physics
the mass of the rocket does not matter. Given a liftoff speed of v, the height h(t) = vt - 4.9t^2 The max height is reached when t = v/9.8, so we have v(v/9.8) - 4.9(v/9.8)^2 = 100 v = 44.27 m/s Or, you could just use the formula for max height h = v^2/2g and get v^2/19.6 = ...
June 25, 2015

Probability
Assuming a uniform population, the 1st person has a birthday. The 2nd has the same birthday with probability 1/365 same for the 3rd. So, ...
June 25, 2015

DTM
you never have said how many gallons (or liters) of gas (or petrol) have been used. Tough to figure mileage (or kmage) without that.
June 25, 2015

DTM
.50$/km * 100km/day = 50$/day not sure just what it is you want to know.
June 25, 2015

Algebra
If there were x more meets to go, and they won them all, then, since the wins = the losses 2+x = 10-2 take it from there. Note that the value of x is not the answer.
June 25, 2015

Math
I already see one error: gt = ln(v+1)
June 25, 2015

Math
dv/dt = g(1+v) dv/(1+v) = g dt ln(1+v) = gt 1+v = e^(gt) + c v = e^(gt) + c (diferent c) v(0) = 0, so c = -1 v = e^(gt)-1 now, v = ds/dt, so s = 1/g e^(gt) - t + c now, e^(gt) = v-1, so s = 1/g (v-1) - t + c since v = e^(gt)-1, ln(v)+1 = gt t = 1/g (ln(v)+1)) and so s = 1/g (v...
June 25, 2015

Math
.9*77 + .1*67 = 76 Look like it won't hurt too much. 1 point.
June 25, 2015

Algebra
revenue is price * quantity, so R(x) = x*p(x) = x(-.16x+320) = -.16x^2 + 320x Now just find the vertex of that parabola to locate maximum revenue.
June 25, 2015

Algebra
I think you are missing a minus sign on the x^2 term, since g = -32 ft/s^2 h(x) = 1/42 (-16/42 x^2 + 72.7x) = x/42 (-16/42 x + 72.7) h=0 when x=0 (ball is hit), and when x = 190.8 (ball lands) The symmetry of a parabola means that the ball is at its highest midway between the ...
June 25, 2015

math gr. 10
Two good solutions are provided by Reiny and MathMate in the related questions below.
June 25, 2015

maths
well, if y = sum(a_n x^n) y' = sum(n*a_n x^(n-1)) y" = sum(n(n-1)*a_n x^(n-2)) so, from the DE, we have sum(n(n-1)*a_n x^(n-2)) + 3x^2*sum(n*a_n x^(n-1)) - x*sum(a_n x^n) sum(n(n-1)*a_n x^(n-2)) + 3sum(n*a_n x^(n+1)) - sum(a_n x^(n+1)) sum(n(n-1)*a_n x^(n-2)) + sum((...
June 25, 2015

Math
polar can get kind of complicated, but this one's a piece of cake: y = t+4, so t = y-4 x = (y-4)^2 + 4(y-4) + 8 Now expand it out and note that it's just a parabola.
June 25, 2015

Math: Compounded Interest
just use your formula. For quarterly, that is 200(1+.05/4)^(4*1/4) = 202.5
June 25, 2015

Math - thx Reiny
Good catch. I felt vaguely uneasy with the way things worked out, but was in a hurry. No doubt Justine caught the slip on her own...
June 25, 2015

Math
r = 1/(3-4sinθ) (a) see http://www.wolframalpha.com/input/?i=r+%3D+1%2F%283-4sin%CE%B8%29 (b) r = 1/(3-4sinθ) r(3-4sinθ) = 1 3r - 4rsinθ = 1 3√(x^2+y^2) - 4y = 1 3√(x^2+y^2) = 4y+1 3(x^2+y^2) = 16y^2+8y+1 3x^2 - 13y^2 - 8y = 1 3x^2 - 13(y^2 - 8/...
June 25, 2015

math
maybe you should lie on the floor and kick your feet, too. Beats me what would come next. What kind of material are you studying, that they'd drop a sequence like that on you? Or are you just wasting everybody's time with lottery numbers?
June 25, 2015

physics
You know, when you log on here you see all these posts with subjects like math, science, psychology, English, etc. Why do you think that Cowdray Park will be interpreted as a school subject? work = force * distance So, just plug in your numbers.
June 25, 2015

advanced algebra
how about you provide the function, instead of naming a file we cannot see? Is it p(t) = a*e^(kt) with suitable values of a and k?
June 24, 2015

Math
the properties of logs are the same as those of exponents. √2 = 2^1/2 because √2 * √2 = 2 and 2^a * 2^b = 2^(a+b) 2^1/2 * 2^1/2 = 2^1 = 2 And, 2^-n = 1/2^n so, 1/√2 = 2^-1/2
June 24, 2015

Math
4x - e^(-(4x-y+3)) = -e^(-2) e^(-(4x-y+3))= 4x + e^(-2) -(4x-y+3) = ln(4x + e^-2) 4x-y+3 = -ln(4x + e^-2) y = 4x+3 + ln(4x + e^-2)
June 24, 2015

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