Thursday

May 28, 2015

May 28, 2015

Total # Posts: 31,422

**Math**

Assuming a sinusoidal function, we have the area is (letting x=0 in September) a(x) = 7.5 cos(pi/6 x) + 10.5 we want a(x) > 15. In other words, cos(pi/6 x) > 0.6 -1.77 < x < 1.77 so, using symmetry, in one complete period (a year), there are 3.54 months with more ...
*May 8, 2015*

**maths**

Let v = victor v+24 = lahai so, adding them up, you have v + v+24 = 60
*May 8, 2015*

**STS**

since s=w+3, w=s-3 3/2 = s/(s-3)
*May 8, 2015*

**Math**

correct
*May 8, 2015*

**STS**

.10(40) + 1.00(x) = .20(40+x)
*May 8, 2015*

**STS**

.12x = 69
*May 8, 2015*

**mathematics**

that would be totalpoints/totalstudents: (35*80 + 15*70)/50
*May 8, 2015*

**Geometric Series**

a = 5(-1/6)^5 Note that (-1/6)^(5k) = ((-1/6)^5)^k, so r = (-1/6)^5 S = a/(1-r) = (5(-1/6)^5)/(1-(-1/6)^5) = -5/7777
*May 7, 2015*

**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*