Tuesday

July 29, 2014

July 29, 2014

Total # Posts: 24,010

**Math pre-calculus**

you know that sin(pi/4 x)=0 when pi/4 x is a multiple of pi. That is, pi/4 x = k*pi x = k*pi * 4/pi = 4k So, when x is a multiple of 4, sin(pi/4 x) is zero. That is where csc(pi/4 x) has vertical asymptotes.

**Basic Physics**

If the vector is in -y direction, the x-component is zero.

**Algebra**

It will still be a trinomial. Each term is just multiplied by a single value. The degree may change, but no new terms will be added or deleted.

**calculus**

P = 2/√g √L dP = 2/√g * 1/2√L dL = 1/√(gL) dL So, the % error in P is dP/P = 1/√(gL) dL/P = 1/√(gL) * √g/2√L dL = 1/√g * √g/2 dL/L = 1/2 dL/L

**math**

I redid the problem using polar coordinates, where I set the (0,0,0) at the base of the paraboloid section, so that z = 3 - (x^2+y^2) That means that we have only to evaluate S = ∫[0,2π]∫[0,√3] r√(1+4r^2) dr dθ and we get π/6 (13√13...

**math**

so, what headway have you made? See any mistakes in my calculations?

**math**

S = ∫[-13,3] 2πx√(1+x'^2) dy x = √(3-y) x' = -1/2√(3-y) 1+x'^2 = 1 + 1/4(3-y) = (13-4y)/(3-y) So, S = ∫[-13,3] 2π√(3-y)(13-4y)/(3-y) dy = 2π∫[-13,3] (13-4y)/√(3-y) dy = 2π (2/3 (4y-15)√(3-y))...

**math**

3.10*11.3 km/s

**Math**

(i) ok (ii) T = 0.06x (iii) S = 20P

**Geometry**

clearly, 10x-7 = 5x + 4x+6 x = 13 so, take it from there.

**math**

The speed must increase by a factor of 17500/1530 = 11.438 So, we need to find x such that x^610 = 10.438 x = 1.004 So, the speed must increase by 0.4% each second.

**chemistry**

It takes 2 moles of HCl to react with each mole of Mg. 48.6 g of Mg = ? moles 150.0 g of HCl = ? moles If there are less than half as many moles of Mg as HCl, it will be the limiting reagent.

**Precal - eh?**

I don't see any statement; just a hard-to-parse expression. Try using 3^n if you want exponents, and fix the statement.

**maths**

Is ST a line in the interior of PQR? If so, I must be missing something. Just knowing the ratio of two sides of PQR tells me nothing about the areas of either triangle. Better explain the overall figure, not just a couple of lines.

**science**

just watch the units: 9.6 J/s * 3.0s = 28.8 J The height lifted is irrelevant, since that will just be part of the work.

**marh**

a/27 = (1/3)^2

**MATH**

not quite. Multiply, instead of dividing, just as you did for the first line. When you see "of" in a calculation, it means "times". 1/2 of 5000 = 5000 * 1/2 3/5 of 2500 = 2500 * 3/5

**business math**

multiply by (1+.30) or 1.3

**Math**

no, it's the next line. The squares are equal; it's the assumption that the roots are equal which is wrong.

**Math**

There is a + and a - root of each squared term. Just because (-4)^2 = 4^2 does not mean -4 = 4.

**Geometry**

they are regular, and all that that entails.

**Math**

ax^2 + bx + c = 0 a(x^2 + b/a x) = -c a(x^2 + b/a x + (b/2a)^2) = -c + a(b/2a)^2 a(x + b/2a)^2 = b^2/4a - c (x + b/2a)^2 = (b^2-4ac)/4a^2 x + b/2a = ±√(b^2-4ac)/2a x = (-b±√(b^2-4ac))/2a

**Algebra**

yes, after combining terms.

**Algebra**

find how long it takes for the ball to drop 6 feet, starting with no upward velocity: -16t^2 + 6 = 0 Looks like 0.6 to me As that's not a choice, I expect there was some initial upward speed.

**math**

figure how many ml in 4 tbsp. If there are x, then the suspension is 240/(240+x) of the whole.

**calculus**

P = R-C

**math**

n+d+q = 60 d = 2q+1 10d = 5n-5 Now go for it.

**algebra**

you want to find when .09s = 260 + .04s So, just solve for s.

**math**

j+g+h = 20 j = 2g-3 h = g-1 Now just start substituting or eliminating to find the values.

**business math**

Looks like 18520/44568 = 42%

**math**

.70*x + 0(100-x) = .45*100 x = 64.28 so, 64ml of concentrate and 36ml of water

**math**

We assume a≠0, because then it's clear that x=0 is a common root. So, we have x²-11x+a: x = (11±√(121-4a))/2 x²-14x+2a: x = (14±√(196-8a))/2 we need some of those expressions to be equal. Some playing around shows that if a = 24: 1...

**maths**

if the roots of x²+px+q=0 are a and b, and x²+qx+p=0 are a and c, then ab = q ac = p a+b = -p a+c = -q b+p = c+q q/a + p = p/a + q (q-p)/a = q-p a = 1 b=q 1+q = -p 1+p+q = 0 Take a crack at part 2.

**Riddle**

your name

**math**

now: x and 18-x after 6 more whites: x and 24-x (24-x)/24 = x/8 8(24-x) = 24x 192-8x = 24x 32x = 192 x = 6

**Science**

well, what's 12% of 400?

**general chem**

looks like 8/58 to me

**MGF 1106**

There are 4P2 = 12 ways to fill the accounting positions There are 2P1 = 2 ways to fill the economics position There are 3P2 = 6 ways to fill the marketing positions So, there are 12*2*6 = 144 ways to fill the positions.

**Math**

Oops. My bad. 4y + 5(x-y) = 5x-y You can think of the party as having x cars of 5 people each, then subtract one person for each of the y cars, which only hold 4.

**Math**

4y+5x So much for math -- now it's time to ask for help with English.

**math**

it's easy to construct a 45° angle -- construct a 90° angle and bisect it. For the 5-6-7 triangle, draw the side of 7, and then a circle at each end, of radius 5 and 6. Where the circles intersect is the third vertex of the triangle.

**math**

250 = 2 * 5^3 175 = 7 * 5^2 so, what's the largest number which divides both 150 and 175? 5^2 = 25

**Calculus**

v = 2 + 3t when does v=14? now take the integral to get the distance

**Physics**

C'mon. In these days, you are never blind. A simple web search immediately points to http://farside.ph.utexas.edu/teaching/302l/lectures/node47.html where the whole topic is discussed, and formulas are derived. Surely you have a text for the course, where this is treated. ...

**Math 221**

(2/9) / (5/12) = 2/9 * 12/5 = 24/45 = 8/15

**Algebra**

Looks like C to me Note that in the table, y increases by a factor of 49 for each x-increase of 2.

**mat/117**

If you mean 6/x = 7/x + 3 then x = -1/3 If you mean 6/x = 7/(x+3) then x = 18

**calc**

I redid the problem using polar coordinates, where I set the (0,0,0) at the base of the paraboloid section, so that z = 4 - (x^2+y^2)/9 That means that we have only to evaluate S = 1/9 ∫[0,2π]∫[0,6] r√(81+4r^2) dr dθ and we get a nice tidy 49π ...

**calc**

Oops. Oh well. The observation about symmetry still holds. The surface area is just the sum of circumferences of many circles of radius y. So, dS = 2πy ds S = 2π∫[4,8] y√(1+y'^2) dx 9x = y^2+36, so y = 3√(x-4) 18 = 2yy' y' = 9/y = 9/W...

**calc**

9x = y^2 + 36 I assume you just mean the part above the x-axis, since the curve is symmetric about that axis. So, using discs, the volume is v = ∫[4,8] πr^2 dx where r^2 = y^2 = 9x-36 v = π∫[4,8] 9x-36 dx = π(9/2 x^2 - 36x) [4,8] = 72π Using she...

**Math 221**

0.05(0.3m + 35n) – 0.8(-0.09n – 22m) 0.05*0.3m + 0.05*35n + 0.8*0.09n + 0.8*22m (0.05*0.3 + 0.8*22)m + (0.05*35 + 0.8*0.09)n 17.615m + 1.822n

**Math 221**

just apply the distributive property as usual: 2w – 3 + 3(w – 4) – 5(w – 6) 2w - 3 + 3w - 12 - 5w + 30 15

**Math 221**

2a(a-5)+4(a-5) 2a*a - 2a*5 + 4a - 4*5 2a^2 - 10a + 4a - 20 2a^2 - 6a - 20

**Set Theory: Sideways U with a line under it**

As you said, 0 is not in the second set, So, the answer is (a): NOT a subset

**algebra**

look for easy roots first: 1,2,3,5,6 A little synthetic division shows that P(x) = (x-5)(x^2+3x+6) and you can do the quadratic as usual

**College Algebra I**

no, but I think we can assume that he wants the solution to the system of equations. Michael, you really should ask a question, and not just dump problems into the forum. Also, show where you get stuck. If you truly have no clue, then you cannot have read the material; a probl...

**math**

so, what did Table 11-1 say?

**Algebra**

you can see that -2x = 1+4y So, -6x = 3+12y Now substitute that into the 2nd equation and solve for y.

**mat/117**

already simplified

**mat/117**

multiply top and bottom by 8-√7 Then note that (8+√7)(8-√7) = 64-7 = 57

**mat/117**

just do normal expansion of distributed sums: √2(9-√2)+5√2 9√2 - √2√2 + 5√2 14√2 - 2

**math**

x^2 + 2√2 x + 6 = 0 use the good old quadratic formula: x = (-2√2 ± √(8-24))/2 = (-2√2 ± 4i)/2 = -√2 ± 2i

**mechanics**

just set 1/2 mv^2 = 36 and solve for v

**algebra**

I think that would be s slices / 6 plates = s/6 slices/plate 6/s gets ever smaller as the number of slices increases...

**math**

Hmmm. Seems to me that he lost 4/36 = 11.1% If he'd sold 40, and lost 4, that would be 10%

**Set Theory :Complements with Ellipses**

simple: A' = {40,41, ...}

**geometry**

6x5 gives greatest area Just think of the factors of 30, and list them in pairs for the others.

**physics**

The force was applied in the direction <16,-41,-13> - <11,-35,-7> F=ma gives you the magnitude of the acceleration Then just figure t to cover the given distance, and v = v0 + at to get the final velocity.

**math**

if the digits are a,b,c,d,e then we have a+b=c b=2a 2b=d e=a+d what is the answer? no idea. What is the question? Hint: it's already given.

**Algebra**

30c+40t = 270 12c+15t = 105 now, from the 2nd equation we see that 12c = 105 - 15t, so 30c = 5/2 (105-15t) plugging that into the 1st equation, we get 5/2(105-15t) + 40t = 270 5(105-15t) + 80t = 540 105-15t+16t=108 t = 3

**math: set theory**

the set is all integers greater than or equal to 4. Looks like (d) BTW, | means "such that" -- lose the "is"

**physics word problem**

conserve momentum. With everything initially at rest, momentum is zero. So, the raft moves in the opposite direction when she jumps. So, the speed s of the raft is such that 180s = 60*4 I note that you asked for speed, so I ignored the direction of the velocity. I expect you c...

**math**

correct

**math**

2x^2+5x-5 2(x^2 + 5/2 x) - 5 2(x^2 + 5/2 x + (5/4)^2) - 5 - 2(5/4)^2 2(x - 5/4)^2 - 65/8

**Math**

500(1+.08/2)^(2*15) = ?

**math**

well, the primes less than 20 are 2,3,5,7,11,13,17,19 So, pick all the pairs that add up to less than 20.

**Finite Math**

If there are x undergrads, y grads, and z faculty, we have x+y+z <= 20 100x + 150y + 200z <= 3200 x >= y+z maximize 18x+25y+30z Now just apply your favorite optimization tool.

**Math**

x(1+.08/4)^(4*4) = 8000 Now just solve for x

**algebra**

since there are two double roots, the graph is tangent to the x-axis at 0 and -1. It crosses only at x=2. So, since it is a 5th degree polynomial, with leading coefficient negative, it rises at the left end and falls on the right end. So, q > 0 for x < -1 q > 0 for -1...

**Algebra**

domain is all reals for all polynomials. So, C and D are out. since a parabola has a vertex, it has a maximum or a minimum, so the range cannot be all reals. So, A is out. B must be the answer. The only confusion might be whether the vertex is a max or a min. If B is correct, ...

**Algebra**

correct

**Math**

supply the missing width (?) and solve for x, where 2(? + x) = 354

**maths Arthmetic**

well, since 4 is half of 8, 4/3 is half of 8/3 so, what number is 22 half of? 44 you are correct

**physics**

greater than 10+15

**physics**

hmmm... If θ is the angle between p+q and p, cosθ = 4/5 If Ø is the angle between p+q and q, then the angle between p and q is θ+Ø Let's let |q| = a, so |p| = a+1 p•q = a(a+1)cos(θ+Ø) (p+q)•p = |p+q|*|p| cosθ = (4/5)(...

**physics**

The two forces clearly have magnitudes 6 and 10. So, use the law of cosines to get r^2 = 100+36-120(-1/2) = 196 r = 14

**physics**

recall that the electric force F = 9.0*10^9 (q1*q2)/r^2 So, plug in your values, remembering how many electrons are in a Coulomb, and you have only 1 electron at each pole. r must be in meters, of course, not km.

**math**

The supplementary angle is always 90° more than the complementary angle.

**Algebra**

(B) the slope is not a constant. Every value is possible for the slope at some point on the curve. you are correct.

**Algebra**

y = a(x-3)^2 + 1 10 = a(0-3)^2+1, so a = 1 Looks like (C) to me

**physics**

looks like 25 mph West to me

**Algebra**

dang typo: y=40

**Algebra**

write down the data. If there are x footballs and y baseballs, then we have p = 6x + 5.5y 35 <= x <= 45 40 <= y <= 55 x+y <= 80 we want to maximize p. Using your favorite linear optimization calculator, you find that x=40 y=50 profit = 460

**Algebra**

that's the ticket.

**Algebra**

evidently 46.5% per time period

**Algebra**

There's no algebraic way to do it. A numeric method or a graphical analysis will be required. See http://www.wolframalpha.com/input/?i=solve+3x^2%2B4lnx%2B4%3D0

**Chemistry**

When reviewing the procedure the student found that 4.912 x 10-1 M barium nitrate solution had been used instead of that in the following procedure: A student synthesized 6.895 g of barium iodate monohydrate, Ba(IO3)2*H2O by adding 30.00 mL of 5.912 x 10-1 M barium nitrate, Ba...

**arithmetic**

After the first 1/8 died, only 7/8 were left 3/5 of those died, meaning 3/5 * 7/8 of the original number died 1/8 = 5/40 3/5 * 7/8 = 21/40 So, 26/40 = 13/20 of the fish died

**Chemistry**

When reviewing the procedure the student found that 4.912 x 10-1 M barium nitrate solution had been used instead of that in the following procedure: A student synthesized 6.895 g of barium iodate monohydrate, Ba(IO3)2*H2O by adding 30.00 mL of 5.912 x 10-1 M barium nitrate, Ba...

**math**

nope. Just because two numbers multiply together to make 1, you still know nothing about the numbers. If nothing else, try your idea. If x=1, 2x+1=3, and 1*3≠1 However, if two numbers multiply to be zero, then one or the other must be zero. So, let's set things equal...

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