Saturday
October 25, 2014

Posts by STEVE


Total # Posts: 26,089

Algebra
<mumble>
October 9, 2014

Algebra
AAAaaarrgh!
October 9, 2014

Algebra 2
mumble
October 9, 2014

ALGEBRA 2
First, fix the typos!
October 9, 2014

Algebra
First, fix the typos!
October 9, 2014

Physics
well, you know that y(t) = 27t - 4.9t^2 y=0 when 27t-4.9t^2 = 0 t = 27/4.9 = 5.51 You are close, but I wonder how you got what you did... Ah. I see you used g = 10 m/s^2, not 9.8 OK, you are correct.
October 9, 2014

Algebra 2
#1 Since y = 34-x, x-(34-x) = 20 2x = 54 x = 27 y = 7 #2 There's a typo. If you meant to say -5x+9y = 11, do a little multiplying to get rid of y: -21x+18y = 33 -10x+18y = 22 -11x = 11 x = -1 y = 2/3 If it was -5x+9y = -11, then x = -5 y = -4
October 9, 2014

Algebra 2
#1 Since x = 3y-4, -3(3y-4)+4y = -3 now just solve for y and then x #2 Since x = 4+4y, -(4+4y) = 4y=-4 or something Again, solve for y, then x
October 9, 2014

Algebra 2
it would help to know just what it is you are after. All I see is a couple of set definitions.
October 9, 2014

Math
The relative max/min occur at x = -2,2 as you said. Since f"(-2) < 0, f(x) has a max at x = -2 (f is concave down) Since f"(2) > 0, f(x) has a minimum at x=2 (f is concave up) f(-5) = -65, so the absolute minimum of f(x) on [-5,2] is at x = -5, but that is just...
October 9, 2014

Math (please check)
It appears to me that you have a product, not a quotient. If f(x) = (t^2 + t^0.5)(t^0.5 - t^-0.5) f'(x) = (2t+0.5t^-0.5)(0.5t^-0.5 + 0.5t^-1.5) = 2.5t^1.5 - 1.5t^0.5 + 1 This can be checked since if we expand f(x), we get f(x) = t^2.5 - t^1.5 + t - 1 f'(1) = 2.5-1.5+1...
October 9, 2014

Calculus
Since both C and P are monthly amounts, I will assume we are looking for the monthly cost per passenger. That would, of course, be C/P = (100+t^2)/(1000+t^2) As you say, (C/P)' = 1800t/(1000+t^2)^2 So, at t=6, (C/P)' = 0.01006246 Close, but I wonder what happened down ...
October 9, 2014

Math! Please check!
correct
October 9, 2014

Math! Please check!
correct Certainly not B: (where the heck is D?)
October 9, 2014

math
what's 62-43?
October 9, 2014

Pre-Calc/Trig...
correct
October 9, 2014

Pre-Calc/Trig...
that would have to be an even power, with a negative coefficient on the highest power.
October 9, 2014

math-physics
the problem is, 200kg is the mass, not the weight. You forgot to multiply by g=9.81 You did W = ms, not W=fs If you had kept track of the units, you'd have spotted your error. kg * m ≠ work
October 9, 2014

Math
law of sines: smallest angle opposite smallest side. That would be between the sides of 24 and 30. The law of cosines tells us that 20^2 = 24^2 + 30^2 - 2(24)(30) cosθ Now just do the math
October 9, 2014

Maths
reverse the scale. Multiply the lengths by 3:2
October 9, 2014

Math: Differential Equations
Hmmm. I also believe that the domain is all reals except x=1.
October 9, 2014

math
y = (4x-8)/(x+1) y' = 12/(x+1)^2 So, y(0) = -8 y'(0) = 12 Now you have a point (0,-8) and a slope (12), so the tangent line is y = 12x-8 See http://www.wolframalpha.com/input/?i=plot+y%3D%284x-8%29%2F%28x%2B1%29%2Cy%3D12x-8+for+x+%3D+-1+to+3
October 9, 2014

Algebra 2
a+c = 55 25a+20c = 1300 Now just solve for a and c.
October 9, 2014

math
no way. There are lots of triangles with those two sides. If the 3rd side is x, all you know is that 2.5-1.6 < x < 2.5+1.6
October 9, 2014

Math
1/2 = 4/8
October 9, 2014

math
P(chosen) = .75 P(all chosen) is therefore .75^11
October 9, 2014

Math
range is the difference between the least and the greatest values So, look at the data and do the math.
October 9, 2014

Science Physics
Well, you have the formula F = GMm/r^2 So, plug in the numbers. What do you get? Oh, OK. The astronaut's mass is thus m = Fr^2/GM
October 9, 2014

Math
the midpoint is just the average of the two ends. In this case, that is (2500+7000)/2
October 8, 2014

Math! Please check!
Nope. 90-37 = 53, not 63. I suspect you saw the 9 and the 3 and subtracted to get 6, but nnnoooooo...
October 8, 2014

biology
google "scientific method" Pick the explanation you find easiest to understand.
October 8, 2014

Geometry
The equilateral triangle has area 25√3 So, now we have 3 isosceles triangle, each of area 5h, which add up to 25√3. Each concrete triangle thus has area 25/√3, so their height is 5h = 25/√3 h = 5/√3
October 8, 2014

Physics
We have a parabola, with y(0) = 0 y(2.0) = 0.55 is the vertex That means its equation is y = 0.1375(4-(x-2)^2) The slope at x=0 is 0.55 sin 32° = 0.53 So, the given data are not exact, but probably close enough. So, using 32° as our benchmark, with tan32° = 0.625, ...
October 8, 2014

Physics
set the staring point at (0,0) Now, figure the relative displacement of each leg of the trip: (200 cos(180-20)°, 200 sin(180-20)°) (300 cos(90+40)°, 300 sin(90+40)°) (400 cos(90-10)°, 400 sin(90-10)°) Now just add up the x- and y-displacements to get ...
October 8, 2014

Algebra
5.815 = 5 815/1000 6.021 = 6 21/1000 Naturally, the sums are equal. I expect you can reduce the fractions as necessary.
October 8, 2014

Math
The slope of Ax+By=C is -A/B This is because you can rearrange things, as in your case, to 5x+2y = 20 2y = -5x + 20 y = -5/2 x + 10 This is the slope-intercept form, and you can easily see that the slope is -5/2.
October 8, 2014

Math
since x is the horizontal axis, and y is the vertical axis, the rise is obviously the change in y So, the run is the change in x
October 8, 2014

pre calc
well, just plug it in: 33/4 - 9x/2 = (-9x^3-6x^2-x+3)/(2x^2+5x+2) http://www.wolframalpha.com/input/?i=solve+33%2F4+-+9x%2F2+%3D+%28-9x^3-6x^2-x%2B3%29%2F%282x^2%2B5x%2B2%29
October 8, 2014

Homework (Math)
recall that 1/i = -i So, you have (1-2i)/(2i) = (1/2)(1/i) - 1 ...
October 8, 2014

Math! Please check!
We have a winner!!
October 8, 2014

Math! Please check!
So, HI=(I-H) = 14-8 = 6 GM = M-G, so M-1 = 6 or 1-M = 6
October 8, 2014

Math
good work.
October 8, 2014

Math
7(-6) - 5(-14) = -42 + 70 = 28 ok What about the others? You have not found them all yet.
October 8, 2014

Math: ALGEBRA
a+b = a+xy b = xy x = b/y try the others. First get all the w or r terms on one side, then factor it out and divide by what's left.
October 8, 2014

ap calc
2x - (x^2+4)/x = 0 2x^2 - x^2 - 4 = 0 x^2 - 4 = 0 x = -2 or 2 Now, find y at those values, and those are the horizontal tangents.
October 8, 2014

ap calc
you know that y^2 = (x^2+4)/x, so just plug that in and solve for x.
October 8, 2014

ap calc
Assuming you meant y= (ax+b)/((x-1)(x-4)) y' = (ax^2+2bx-(4a+5b))/((x-1)(x-4))^2 Now, y'=0 when ax^2+2bx-(4a+5b) = 0 when x=2, that means 4a+4b-4a-5b=0 b=0 So, y = ax/((x-1)(x-4)) at x=2, y=-1, so 2a/-2 = -1 a = 1 and so y = x/((x-1)(x-4))
October 8, 2014

ap calc
So far, so good. We know that for a horizontal tangent, y'=0, so 2x-y^2 = 0 But, we already know that y^2 = (x^2+4)/x, so 2x - (x^2+4)/x = 0 2x^2 - x^2-4 = 0 x^2 = 4 x = 2 or -2 At x = 2, y = 4 At x = -2, y = -4 Those are the horizontal tangents
October 8, 2014

geometry
2(x+y) = 22 x+y=11 So, just list the pairs of numbers which add up to 11.
October 8, 2014

Math @Reiny
Recall that since i^2 = -1, 1/i = -i (1-2i)/(2i) = 1/(2i) - (2i)/(2i) = 1/2 (-i) - 1 = -1 - 1/2 i
October 8, 2014

math help
well, just multiply it out: 12*11*10*9*8
October 8, 2014

Pre-calc/Trig...
correct.
October 8, 2014

Pre-calc/Trig...
a polynomial of degree 2 is a quadratic.
October 8, 2014

Calculus I
since sin^2 = 1-cos^2 and cos(2x) = 2cos^2 - 1, 2cos^2 - 1 - cos = -1+cos^2 - 1/4 cos^2 - cos + 1/4 = 0 (cos - 1/2)^2 = 0 cos = 1/2 x = pi/3 or 5pi/3
October 8, 2014

CALCULUS HELP NEEDED ASAP!
Oops. Do you see my mistake? Hint: C is wrong.
October 8, 2014

CALCULUS HELP NEEDED ASAP!
period of sin(kx) or cos(kx) is 2π/k. SO, for a period of 2 seconds, k = π. V(t) = A cos(πt)+C residual volume is 1150, so V(t) = A cos(πt) + 1150 Tidal volume is 3200, so V(t) = 1600 cos(πt) + 1150 Since cos has max at t=0, we are done.
October 8, 2014

Math-trigonometry
(a) max: d^2 = 192^2 + 71.6^2 min: d^2 = 192^2 + 8.1^2 (a) max: tanθ = 192/8.1 min: tanθ = 192/71.6 Didja forget your Pythagorean Theorem and the definitions of the basic trig functions?
October 8, 2014

Algebra 2
can you say "google?" It took me about 10 seconds to find a site that can generate nice printable number lines.
October 8, 2014

math (need check answer)
Ty I am not sure what you mean by swapping. Q1 asked for the algebraic expression which is x + y Q2 has actual amounts of balloons so now these should be added to the original formula 14x + 8y where x = $3 and y = $4 Therefore 14*3 + 8*4 = $74
October 8, 2014

Not Me, Wrong Answer
The curse of not having used a less common name.
October 8, 2014

math (need check answer)
I think the answer to Q1 is simply x + y
October 8, 2014

caculus
Using similar triangles, if the shadow's length is s and the woman is x away from the light, s/1.5 = (x+s)/6 That should help, eh?
October 8, 2014

caculus
a woman 1.5 tall walks at a rate of 1.2m/s directly away from the street light that is 6m above the street. At what rate is her shadow changing?
October 8, 2014

Math
well, r = -3/6 = (3/2)/-3 = (-3/4)/(3/2) ... 6/2 = ? (-1/2)/1 = ?
October 8, 2014

Math
have you a calculator? Just do the math...
October 8, 2014

Sociology (Stats) Std. Dev
600 is 1 std above the mean. 300 is 3 std below the mean. Just look up the tails in your table. Or, play around some at http://davidmlane.com/hyperstat/z_table.html
October 8, 2014

help
h(t) = 5 + 70t - 16t^2
October 8, 2014

math
5% up, or 5% down? In any case, what's 5% of 85000?
October 8, 2014

math
It's roughly 55000/50 = 1100 the estimate will be low, because we lowered the divided and raised the divisor.
October 7, 2014

Math
#1 clearly, r = -1/2 T11 = ar^10 #2 a(-2)^9 = -1024 #3 Just recall that S = a/(1-r) then plug in the numbers
October 7, 2014

pre-calculus
well, 9 is half of 18, so ...
October 7, 2014

Math
#1 think 8^n #2 .123 123 123 = 123/999 same for the others
October 7, 2014

calculus
The math looks good to me, but the negative answer is strange because the question was, how fast is the angle increasing? That is because dx/dt = -600; the plane is approaching the kangaroo. Hailey, did you do as Reiny asked, and check his math?
October 7, 2014

math
20 kg * 2.2 lb/kg * 50 mg/lb * 1mL/100mg = 22 mL
October 7, 2014

Math
well, what's the mean? 86.2 The deviations from the mean are thus 8.2, 4.2, ... Now just take the mean of those values. That's the mean deviation.
October 7, 2014

Pre-Calc/Trig..
I think I prefer y = 2(x-3)^2
October 7, 2014

Calculus question
simple, but tedious. See http://en.wikibooks.org/wiki/Trigonometry/Simplifying_a_sin%28x%29_%2B_b_cos%28x%29
October 7, 2014

math/physics
conserve momentum: 0.600(+4.00) + 1.00(-5.00) = 1.00(-7.25) + 0.600v v = +7.75 Now, what's wrong with this picture?
October 7, 2014

Calculus
of course -- where y=0
October 7, 2014

Algebra
I get 2.9 how did you get your answer?
October 7, 2014

math
if the angle is x, 12/22 = tan(x)
October 7, 2014

Math
apparently the formula is d = v√(h/4.9) multiply that by √4.9/√4.9 and you have d = v√(4.9h)/4.9 Now just plug in the numbers.
October 7, 2014

physics
PE at top: mgh = 35.9*9.8*20.3 = 7142 J She loses half that on the way down. KE = 1/2 mv^2 = 3571 So, v^2 = 3571/35.9 = 99.47 Call it 100 So, v = 10
October 7, 2014

calculus
√(2x+4y) + √(2xy) = 13.4 (x+2y) / 2√(2x+4y) * (2+4y') + 1/(2√xy) * (2y + 2xy') = 0 (x+2y)/√(2x+4y) + 2(x+2y)y'/√(2x+4y) + √(y/x) + √(x/y) y' = 0 y' = -[(x+2y)/√(2x+4y)+√(y/x)]/[2/√(2x+4y...
October 7, 2014

Calculus
The distance traveled after t hours is: If boat N is at (0,y) boat E is at (x,0), then the distance z from N to E is z^2 = x^2+y^2 At the given moment, z=√(56^2+20^2) = √3536 = 4√221 2z dz/dt = 2x dx/dt + 2y dy/dt Now plug in the numbers (after canceling out ...
October 7, 2014

math
I'd say 2x where x is the cost of one book
October 7, 2014

AP Calculus
f(x+h) = 1/√(x+h) + x+h f(x) = 1/√x + x f(x+h)-f(x) = 1/√(x+h) - 1/√x + h = (x+h)^(-1/2) - x^(-1/2) + h From the binomial theorem, (a+b)^n = a^n + n a^n-1 b + ... (x+h)^(-1/2) = x^(-1/2) - 1/2 x^(-3/2)h + 3/8 x^(-5/2)h^2 + ... where ... is stuff with ...
October 7, 2014

Algebra
Woah! Where did the 15# bags come from? Clearly, there will be more bags if the hold less.
October 7, 2014

math
ever heard of a calculator? Why would you post such a trivial problem? It takes much less time just to punch it in on your calculator, and you don't have to wait for and endure snide replies. Do you not trust your calculator? Is there something else about multiplication ...
October 7, 2014

Math
assuming you want trim all around, and plan to use miter cuts at the corners, then you need 2(10 3/4 + 129/10 3/4) = 45 1/2 ft see how much was left unsaid?
October 7, 2014

Grammar
No ideas on any of them? Nominative case: I,he,she,we,they Objective case: me,him,her,us,them So, #3 she #6 them #7 our -- why? "our" is an adjective can you get the others?
October 7, 2014

math
if the area is 42 m^2, the side is √42 m So, the perimeter is 4√42 m. Now just do the math...
October 7, 2014

Physics
no calculus needed. Just plug in your formulas: h(x) = tanθ x - g/(2 (v cosθ)^2) x^2 = 0.75x - .0000547 x^2 That is just a parabola with vertex at (6855.6,2570.8) I expect you can find x when h=0.
October 6, 2014

math
clearly that would be 6*18 - 4*6 = ?
October 6, 2014

ap calc
lim (x->3) 4-(√(25-x2))/(3-x) Use l'Hospital's Rule to get = lim (x->3) (x/√(25-x^2)]/(-1) = (3/4)/(-1) = -3/4 Recall that dy/dx at any point on the circle is -x/y
October 6, 2014

Physics
yes. Friction is just another force; nothing special about it.
October 6, 2014

College Physics
a = (-284.4 m/s)/1.4s = -203.1 m/s^2 s = Vo t + 1/2 at^2 = 284.4*1.4 - 1/2 (203.1)(1.4^2) = 199.1 m
October 6, 2014

Math
If each member makes x candles, then 40x = 39(x+3) x = 117 So now you can find the total.
October 6, 2014

MATH
d/dx (x^5 + y^8) is indeed 5x^4 + 8y^7 y' Usually this is done in conjunction with implicit derivatives, where you have some equation like x^5 + y^8 = 7 and you wind up with y' = -5x^4/8y^7 which you then have to evaluate at some point. ------------------------------ h...
October 6, 2014

AP Calc
y^2 = x^2 + 4/x 2y y' = 2x - 4/x^2 y' = (2x^3-4)/x^2 * 1/2y = (x^3-2) / x^2y Now as long as y≠0, y'=0 when x=∛2 y(∛2) = ±√(∛4+4/∛2) = ±√(6/∛2) so that's ok. It looks like the only place with ...
October 6, 2014

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