Monday
July 6, 2015

Posts by steve


Total # Posts: 32,118

math
um, how about 16*3.5 ?
May 7, 2015

Math
If I get past the font gibberish, I sense that you want to prove that 4 sinθ sin(60-θ) sin(60θ) = sin 3θ That isn't so, so try reposting using sin^3 θ for cube of sinθ if that's what you mean.
May 7, 2015

Calculus
the curve is concave down. So, (c)
May 7, 2015

trigonometry
what, forgotten your algebra I, now that you're taking trig? -3sin(t)=15cos(t)sin(t) 15cos(t)sin(t) + 3sin(t) = 0 3sin(t)(5cos(t)+1) = 0 sin(t) = 0 or cos(t) = -1/5 So, find the 4 values of t which do that. 8cos^2(t)=3-2cos(t) 8cos^2(t)+2cos(t)-3 = 0 (4cos(t)+3)(2cos(t)-1...
May 7, 2015

Math
The horizontal parabola y^2 = 4px has directrix p units from the vertex. So, since our directrix is 3 units from the vertex, we start with y^2 = 12x But, that's with a vertex of (0,0). So, our parabola is (y-1)^2 = 12(x+2) But, that opens to the right. Our vertex is to the...
May 7, 2015

Calc/Precalc
just do the same stuff: xy = cot(xy) y + xy' = -csc^2(xy) (y + xy') y'(x + xcsc^2(xy)) = -ycsc^2(xy)-y xy' (1+csc^2(xy)) = -y(1+csc^2(xy)) xy' = -y y' = -y/x The other is just a simple chain rule. y = cos(u), so y' = -sin(u) u'
May 7, 2015

Poly
42
May 7, 2015

math
4 of each length...
May 7, 2015

Math
can't happen. The angles must add up to 360.
May 7, 2015

Math
hint: r = 3
May 7, 2015

Math
That would of course be 6C2 (3x)^4 (-y)^2 = 15(81x^4)(y^2) = 1215x^4y^2
May 7, 2015

Trig
no, no. Draw your triangles: if cos(s) = 1/5, then sin(s) = √24/5 = 2√6/5 if sin(t) = 3/5, then cos(t) = 4/5 sin(s+t) = (2√6/5)(4/5) + (1/5)(3/5) = (8√6+3)/25 and similarly for sin(s-t)
May 7, 2015

maths
you want km/L. So, use what you have: (44km)/(11/4 L) = 44km * 4/11L = 16 km/L
May 7, 2015

Calculus
that would be ∫[0,2] f(x) dx ------------------- 2-0
May 7, 2015

Algebra
15+12x+40 = 127
May 7, 2015

matha
250500 * 1/5 * 2/5 = ?
May 7, 2015

Calculus
V = ∫[-1,1] π(e^x)^2 dx or V = ∫[0,1/e] 2π(1/e)(1-(-1)) dy + ∫[1/e,e] 2π(y)(1-lny) dy
May 7, 2015

maths
3/4 of 4L = 3L 1 - 3/4 = 1/4
May 7, 2015

Calculus
we can check using shells. V = ∫[0,1] 2πrh dy where r = 1-y and h = y-y^3 V = 2π∫[0,1] (1-y)(y-y^3) dy = 2π∫[0,1] y^4-y^3-y^2+y dy = 2π(1/5 y^5 - 1/4 y^4 - 1/3 y^3 + 1/2 y^2) [0,1] = 2π(1/5 - 1/4 - 1/3 + 1/2) = 2π(7/60) = 7π...
May 7, 2015

Calculus
or, using shells, you can do V = ∫[0,9] 2πrh dy where r = y and h = 3-x = 2π∫[0,9] y(3-√y) dy = 2π(3/2 y^2 - 2/5 y^(5/2)) [0,9] = 2π(3/2 * 81 - 2/5 * 243) = 2π(243/10) = 243π/5
May 7, 2015

Math
x + 1/ x - 1 + x^2 -1 / x + 1 x+(1/x)-1+x^2-(1/x)+1 x-1+x^2+1 x+x^2 However, assuming the usual sloppiness with parentheses, I suspect you meant (x+1)/(x-1) + (x^2-1)/(x+1) (x+1)/(x-1) + (x-1)(x+1)/(x+1) (x+1)/(x-1) + (x-1) (x+1)/(x-1) + (x-1)^2/(x-1) (x+1 + (x-1)^2)/(x-1) (x^...
May 7, 2015

Help plz on Calc
Think of the shells as nested cylinders, starting 1 unit away from the y-axis, and extending to the end of the ellipse: V = ∫[1,3] 2πrh dx where r=x and h=y V = 2π∫[1,3] x(2√(1-x^2/9)) dx = 2π/3 ∫[1,3] 2x√(9-x^2) dx = 2π/3 (32/...
May 6, 2015

intermediate algebra
if the radiator already contains pure antifreeze, how would adding more antifreeze change anything?
May 6, 2015

intermediate algebra
better read what you posted . . .
May 6, 2015

Algebra
a = 100 r = -1/20 An = ar^(n-1) Sn = a (1-r^n)/(1-r) A4 = 100(-1/10)^3 = 100(-1/1000) = -1/10 S4 = 100(1-(-1/10)^4)/(1 - (-1/10)) = 100(9999/10000)/(11/10) = 909/10
May 6, 2015

calculus
so, find a table of integrals and look it up. You will probably just find some power reduction formulas, such as ∫ x^n sinx dx = -x^n cosx + n∫ x^(n-1) cosx dx You can see that you will have to use integration by parts 4 times to get rid of all the x^n terms. So, ...
May 6, 2015

precalculus
since the vertices are on the y-axis, we will have y^2/a^2 - x^2/b^2 = 1 the slope of the asymptotes is b/a, so y^2 - x^2/4 = 1 but that has vertices at (0,+/-1) so y^2/4 - x^2/16 = 1 To verify, see http://www.wolframalpha.com/input/?i=hyperbola+y%5E2%2F4+-+x%5E2%2F16+%3D+1
May 6, 2015

geometry
tanθ = 1/11
May 6, 2015

math
all are correct, with the following notes: #1 has a typo. The 3rd y value should be zero Why say "1 over 3" when real mathematical notation (1/3) is so much better?
May 6, 2015

chemisrty
The molar mass of Fe(OH)3 is 106.87 g/mol. How many moles of H2SO4 are needed to react completely with 5.419 g of Fe(OH)3?
May 6, 2015

math
well, on the RS, csc^2 - sec^2 = (cos^2-sin^2)/(sin^2 cos^2) That should help...
May 6, 2015

mathematics - eh?
what does "sin alpha 9" mean?
May 6, 2015

Math
that's cylindrical cup sheesh. the area of the circular base, is just the area of a circle. pi r^2 the curved surface is just the circumference times the height: 2pi r h Now just plug in your values for r and h
May 6, 2015

Math
well, just offhand, I'd say that's 80% of 64. Or, .80 * 64 = ? Hmmm. Since 64 is not a multiple of 5, how could 80% (4/5) do it?
May 6, 2015

GEOMETRY
Oh come on. Do you have a triangle? parallel lines? intersecting lines? Geez, just describe the arrangement of the points and lines, fer cryin out loud! What is the relationship between MO and NA? Perpendicular? Parallel? Pretend I can't see the diagram. Tell me what to do...
May 6, 2015

GEOMETRY
you'd better describe the figure. Some of your copy/paste is garbled, and we have no idea of the relative locations of the points.
May 6, 2015

math
y changes by +1 when x changes by 1. So, the slope is +1/1 = 1.
May 6, 2015

math
total water: (4*.750 + 2*1.5)L at 1L/min, how long is that?
May 5, 2015

science
(5000+750)/(180) servings I'll let you decide how much is left over
May 5, 2015

Calc
h(t) = 200 + 40t - 16t^2 now work your magic on (b) and (c)
May 5, 2015

Math
both wrong. see earlier post.
May 5, 2015

Math
if the roots are a and b, the function is (x-a)(x-b) = 0 So, plug in a=(2+√5)/3 b=(2-√5)/3
May 5, 2015

336
Bzzzt, but thanks for playing! since the number of messages is an integer, it is clearly discrete since time can take on any value, it is continuous
May 5, 2015

math
repeated multiplication x^2 = x * x x^3 = x * x * x and so on
May 5, 2015

Math
reflection in the y-axis takes (x,y) -> (-x,y) Just fold the paper along the y-axis and see what the points do.
May 5, 2015

Math
you have y = (x-a)^2 - b so, (x-a)^2 = b x = a±√b = (k/2)±√((k-2)^2/4) = (k/2)±(k-2)/2 = k/2 + k/2 - 1 = k-1 or k/2 - k/2 + 1 = 1 check x=1: (1-(k/2))^2 - (k-2)^2/4 (2-k)^2/4 - (k-2)^2/4 0
May 5, 2015

math
guess you missed the deadline, eh? 5 kinds, choose 3. Sound familiar?
May 5, 2015

Probability
clearly, based on the 69 draws, P(pink) = 36/69 P(brown) = 33/69
May 5, 2015

Math
That's the same as the number of ways to select 6 items all at once, then read them once a week. 20P6 Unless you are allowed to choose the same book more than once. Then the number is 20^6
May 5, 2015

Math
There are 20 books on a summer reading list. In how many ways can you choose 1 per week for 6 weeks.
May 5, 2015

Math
well, how many perfect squares or odds are there in 1..8?
May 5, 2015

Math
You spin a spinner that has 8 equal sections numbered 1 to 8.Find p(perfect square or odd).
May 5, 2015

math
given your matrix A, we need to solve det(nI-A) = 0 so we need to solve |n-1 -1 0 0| |-1 n-1 0 0| |0 0 n 0| |0 0 0 n| = 0 That is n^3(n-2) = 0 As you can see, n = 0,0,0,2
May 5, 2015

Math
6 6/7 is near 7 4 2/7 is near 4 1 3/5 is near 1 3/4 = 7/4 4 * 7/4 = 7 Sounds good to me as an estimate
May 5, 2015

trigonometry
I AM WRONG >
May 5, 2015

trigonometry
How about some parentheses, so we can tell what's what? As it stands, it means 1 + tan2A = cosA + tanA - sinA which is clearly false
May 5, 2015

functions
you want R where k/R^2 = 10(k/r^2) R^2/r^2 = 1/10 R/r = 1/√10
May 5, 2015

functions
v = x(10-2x)(20-2x)
May 5, 2015

Math
so, now you can figure how many miles the light travels in 7200 seconds, right?
May 4, 2015

Math
well, how many seconds in 2 hours?
May 4, 2015

Math
42
May 4, 2015

math
you need 2/x < x/22 44 < x^2 so, 6 < x Now, you need x/22 < 0.33 x < 7.32 So, we have x = 7 2/7 < 7/22 < .33 Do the other in like wise.
May 4, 2015

Algebra
what's the problem? Just start working out the values: a1 = -2 a2 = 2(a1)^2 = 2(-2)^2 = 8 a3 = 2(a2)^2 = 2(8)^2 = 128 ... a1 = ln(e^2) = 2 a2 = ln(e^4) = 4 ... b0 = 1 b1 = 2 b2 = 2(2)-1 = 3 b3 = 2(3)-1 = 5 ...
May 4, 2015

math
it will be a line sloping upward, passing through (0,-4)
May 4, 2015

Math
the intersection(s) will be where x^2 + (x+k)^2 - 25 has one solution. That is, where the discriminant is zero. x^2 + x^2 + 2kx + k^2-25 = 0 2x^2 + 2kx + (k^2-25) = 0 The discriminant is (2k)^2 - 4(2)(k^2-25) 4k^2 - 8k^2 + 200 = 0 k^2 = 50 k = ±√50 So, check out ...
May 4, 2015

Math
y = 4(x^2+6x)-5 = 4(x^2+6x+9) - 5 - 4*9 = 4(x+3)^2 - 41 The vertex is at (-3,-41), and the parabola opens upward, y cannot be less than -41. Did you actually try plugging in, say, 7=700 to see whether there was a solution there?
May 4, 2015

Math
correct
May 4, 2015

Algebra
do this just like the ellipse in your earlier post. That is, complete the squares, then review your text about hyperbolas. 36x^2-24x - (y^2-6y) = 41 36(x - 1/3)^2 - (y-3)^2 = 41 + 36/9 - 9 (x-1/3)^2 - (y-3)^2/36 = 1
May 4, 2015

Math
Switching dircetion is just a shorthand way of moving stuff from one side to the other: -4k > -36 add 4k to both sides: 0 > 4k-36 add 36 to both sides: 36 > 4k or, as you saw above, 4k < 36 k < 9 multiplying and dividing by a negative value change the direction...
May 4, 2015

Algebra
for this ellipse, the major axis is vertical. a = 3 b = 2 The vertices are at (-3,1±3) The co-vertices are at (-3±2,1) Looks like it's time to review your ellipses.
May 4, 2015

Algebra
rearrange stuff and complete the squares: 9x^2+54x + 4y^2-8y = -49 9(x^2+6x) + 4(y^2-2y) = -49 9(x^2+6x+9) + 4(y^2-2y+1) = -49 + 9*9 + 4*1 9(x+3)^2 + 4(y-1)^2 = 36 (x+3)^2/4 + (y-1)^2/9 = 1 Now answer the questions.
May 4, 2015

geometry - eh?
what is the "lip"? and where is your punctuation?
May 4, 2015

Math
F = ma
May 4, 2015

Math
so, if you have the answer, why are you posting the question? Check out the Pythagorean Theorem. x^2+y^2 = 1600 x+y+40 = 96.22
May 4, 2015

Math
2r+h = 25 a = πr(r+2h) = πr(r+25-2r) = π(25r-3r^2) da/dr = 0 when r = 25/3 d = 2r = 50/3 h = 25 - 50/3 = 25/3
May 4, 2015

Math
x+y = 37 x^2+y^2 = 765.5 x^2+(37-x)^2 = 765.5 2x^2 - 74x + 603.5 x^2 - 37x + 301.75 = 0 x = (37±9√2)/2 x = 12.1, 24.8 Hmmm. I don't get their answers either, but I'm a lot closer than you. What did you do?
May 4, 2015

geometry
the diameters are in the ratio 5:6 the larger is 12, so the smaller is 10 the smaller cone has height h=3, so the larger cone has height 3*(6/5) = 18/5
May 4, 2015

Math
Laid out on the x-y plane, the track's line can be described by y = 400 - 2/3 x So, if the rectangle has one corner on the line and the opposite corner at (0,0), its area is a = xy = x(400 - 2/3 x) = 400x - 800/3 x^2 This is just a parabola. Find its vertex, and that is ...
May 4, 2015

Calculus
all of them? f is concave down with a max at x = -3
May 4, 2015

math
divide the total amount by the amount needed for each batch, giving the number of batches: 6/(2/3) = 6 * 3/2 = 9
May 4, 2015

geometry
Recall your rotation matrix. (x,y) -> (x',y') where x' = xcosθ - ysinθ y' = xsinθ + ycosθ So, plug in your θ. You can easily check your work by noting that the point will rotate down to the x-axis.
May 4, 2015

math
300*1.04^5
May 4, 2015

alg
no ideas? Review your conic sections and show us whatcha got.
May 4, 2015

math
since the dice are independent events P(odd,odd) = 1/2 * 1/2
May 4, 2015

math
$5200 / $6.50/m = 800m of fence maximum area for a given perimeter is a square, so we have an isosceles right triangle with both legs 400m long.
May 4, 2015

math
#1 clearly the circle is of radius 5. So, since x^2+y^2 = 5^2, (0,5) lies on the circle. the center is the midpoint of AC: (0,0) so, the radius is 13. 0^2+13^2 = 13^2 7^2 + (2√30)^2 = 49+120 = 13^2 so, all vertices lie on the circle.
May 4, 2015

critical points
critical values are where f' = 0 or undefined. f'(x) = 18x^2-18 = 18(x^2-1) So, where is f' = 0?
May 4, 2015

math
a = s^2 da = 2s ds
May 4, 2015

trigonometry
You can expand both binomials, and watch things cancel out, or note that 2sin^2(45+A) = 1-cos(90+2A) 2sin^2(45-A) = 1-cos(90-2A) cos(90+x) = -sinx cos(90-x) = sinx Now just add it up.
May 4, 2015

math
v = (12-2x)(16-2x)x dv/dx = 4(3x^2-28x+48) set dv/dx=0 and solve for x.
May 4, 2015

math
it reverses direction when v changes from + to - v(t) = 3t^2-18t+24 = 3(t^2-6t+8) = 3(t-2)(t-4) So, where does v(t) cross the axis and become negative? Now use that value to find s(t) and a(t)
May 4, 2015

Physics
1/48 + 1/di = 1/110 M = 110/(110-48)
May 3, 2015

calc (please help)
I'm assuming that the angle between the planes is situated on the edge of the cylinder, so that the two planes intersect the cylinder in a circle and an ellipse. So, the ellipse has major axis of length 2r secβ, and the far side of the major axis is a distance 2r tan...
May 3, 2015

Math--ONE QUESTION
well, -14 = -9-5 0 = 8-8 So, what do you think?
May 3, 2015

Calculus max/min
If you walk directly to a point x feet from the bus stop, your walking distance is park: √(600^2+(2000-x)^2) sidewalk: x so, your time taken (distance/speed) is t(x,d) = √(600^2+(2000-x)^2)/(3.5+d) + x/(5.5+d) t(x) = √(600^2+(2000-x)^2)/4.267 + x/7.267 so, ...
May 3, 2015

Math Trigonometric Identities
if you set the left side over a common denominator of sinx, you have 1/sinx - sin^2x/sinx (1-sin^2 x)/sinx If that does not get you started, I don't know what will...
May 3, 2015

Math Trigonometric Identities
that is correct, but it would have been simpler when you got the LS expanded, to see that you had LS = sin^2x - 2sinxcosx + cos^2x = sin^2x + cos^2x -2sinxcosx = 1 - 2sinxcosx
May 3, 2015

Earth Science
the magnification of a telescope is changed by changing what? my answer is the eyepiece
May 3, 2015

Math
well, just plug in 180 = pi
May 3, 2015

Math
Since you are actually performing the action, I'd have to go with Experimental. If asked just to calculate the probability, then it would be theoretical. The actual observations might or might not agree with the calculation. In fact, for any finite number of trials, the ...
May 3, 2015

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