Friday

July 25, 2014

July 25, 2014

Total # Posts: 23,956

**math**

There are many proofs of this, such as the one here: http://www.wyzant.com/resources/lessons/math/calculus/derivative_proofs/sinx However, it relies on the fact that sinx/x -> 1 as x->0. That is usually proven as given here: http://math.ucsd.edu/~wgarner/math20a/sin%28x%...

**maths**

divide the sum into 5+6+7=18 equal parts of size x. So, 18x = 3600 x = 200 The shares are thus 5*200 = 1000 6*200 = 1200 7*200 = 1400

**physics**

well you know that AxB = -(BxA) So, if they are equal, they are zero. That means the angle is zero or 180. They are parallel.

**maths**

look at what we have: a+b+c+d = 66.5 b = a-2 c = a+1.5 d = c+1.5 Start substituting: a+(a-2)+(a+1.5)+((a+1.5)+1.5) = 66.5 a=16.0 b=14.0 c=17.5 d=19.0

**PHYSICS**

this just algebra I m1*x = m2*3 - m2*x (m1+m2)x = 3m2 x = 3m2/(m1+m2)

**PHYSICS**

think back to your Algebra I. Collect all the vf terms and factor it out.

**PHYSICS**

12t + 1/2 at^2 = 25 12 + at = 0 solve for a. Now you can solve for µ by using the resultant acceleration.

**PHYSICS**

KE = 1/2 mv^2 work is equivalent to energy.

**PHYSICS**

just a note: that's "mu sub-k," not "muse of k" µk Your class must be an oral presentation, if you never saw it written. Anyway, convert mgh=2.0 * 9.8 * 1.5 to KE, 1/2 * 2.0 * v^2 Using that v, and the frictional force of deceleration, figure the ...

**PHYSICS**

mgh + 1/2 mv^2 stays constant, so mgh1 + 1/2 m*2^2 = mg(h1-3) + 1/2 mv2^2 divide out all the m's and you have 9.8*h1 + 2 = 9.8(h1-3) + 1/2 v2^2 2 = -9.8*3 + 1/2 v2^2 v2^2 = 62.8 v2 = 7.92

**PHYSICS**

KE = 1/2 mv^2, so 0.02 = 1/2 * 2 * v^2 ...

**Phyiscs**

that depends on how long it takes.

**science**

How many moles of H2SO4 in 10g? The molarity of the final mix is moles H2SO4 / 0.1 L

**NS 2**

the distance fallen in t seconds is 16t^2. So, when is 16t^2 = 40000? The air speed of 500 mi/hr is irrelevant, since the horizontal speed does not affect the vertical speed.

**Statistics**

The chance that there are no parents is 10/25 * 9/24 * 8/23 * 7/22 * 6/21 = 6/1265 So, the chance that there is at least one parent is 1259/1265

**math**

better review what an integer is...

**College Algebra**

In any case, wolframalpha.com is your friend. It can confirm the results you get through your hard work: http://www.wolframalpha.com/input/?i=%2815x^2-23x-21%29+%2F+%283x-7%29

**area**

w * 2w = 1000 2w^2 = 1000 w^2 = 500 w = 10√5

**math**

y = (x-5)(x^2-2x+1) / (x-7)(x^2+2x+3) = (x-5)(x-1)(x-1) / (x-7)(x^2+2x+3) If 5<x<7, the numerator is positive the denominator is negative So, no real value of x between 5 and 7 satisfies the condition that y > 0 That is, unless I have misinterpreted your somewhat garb...

**math**

the discriminant is negative. That means there are no real roots. That means the graph does not cross the x-axis. That means that the value of y never changes sign. so, your job is to justify why that means that y and a have the same sign.

**Geometry**

tan x = 100/50

**Geometry**

x/20 = sin 65° the height is the side opposite the 65° angle. sine is opposite/hypotenuse

**Another question (math)**

while 2 is 67% of 3, that means that 2 is 33% less than 3. 2 is 1 less than 3. 1 is 33% of 3

**maths**

since the ratio of height to shadow-length is the same, h/22 = 100/55

**math**

2 log base2 (x+15) - log base2 x = 6 log(x+15)^2 - logx = 6 (x+15)^2/x = 2^6 (x+15)^2 = 64x x^2+30x+225 = 64x x^2-34x+225 = 0

**math**

4^y = (2^2)^y = (2^y)^2 so, we have a quadratic in 2^y: (2^y)^2 - 7*2^y - 8 = 0 (2^y-8)(2^y+1) = 0 y=3 2^y is never negative, so 2^y+1=0 has no real solution.

**math**

3 log x = 1 + log (4x+5)/ log 2 That dividing logs stuff is quite unusual for introductory log problems. I will solve 3 log x = 1 + log (4x+5) - log 2 x^3 = 10*(4x+5)/2 2x^3-40x-50 = 0 2(x-5)(x^2+5x+5) = 0 and that's easy If you really did mean to divide the logs, then I c...

**math**

10^(2x+1) -7(10^x) -26 = 0 10*10^2x - 7*10^x - 26 = 0 10*10^(2*2log t) - 7*10^(2log t) - 26 = 0 10*10^(4log t) - 7*10^(2log t) - 26 = 0 10*(10^(log t))^4 - 7*(10^(log t))^2 - 26 = 0 10t^4 - 7t^2 - 26 = 0 (10t^2+13))(t^2-2) = 0 t = ±√2 or ±√(13/10) i

**Physics**

If we let +x be eastward, we have <19.98,13.99> or, approximately <20,14> Add that to <0,-10> and the resultant velocity is <20,4> The (eastward) speed with which the boat is crossing the river is 20m/s. Not sure whether I interpreted your language corr...

**math**

-39 + 78 - 100 = -61

**chemistry**

Ya got me. However, the topic is discussed here: http://en.wikipedia.org/wiki/Magnetic_quantum_number

**math**

review the significance of the equation (x-h)^2 + (y-k)^2 = r^2

**trig**

If cosθ = 7/25 in QI, then sinθ = 24/25 That means tanθ = 24/7, and you (ahem) know that tan2θ = 2tanθ/(1-tan^2 θ)

**math**

35/n

**math**

you need x ml of solution, and 15-x ml of water (0 mg/ml), so 20x + 0 = 10*15 x = 7.5 Since the concentration is being reduced by a factor of 2, the volume needs to be increased by that factor. 2 * 7.5 = 15

**math**

If the two heights are h1, and h2 after n hours, the height is h(t) = h1 - (h1-h2)/n t Just plug in all those missing numbers that were not in your post. The burn rate is the height difference divided by how long it took to burn away.

**math**

The formula is above. Plug in r=3. We will assume a smooth, rather than a dimpled, surface :-)

**math**

4π(2r)^2 / 4πr^2 = 4 the square of the radius ratio

**Algebra II**

p? do you mean √? √(b^2+a^2) = √c^2 clearly the next step is flawed. √(b^2+a^2) ≠ b+a while √(b^2*a^2) = √b^2 * √a^2, √(b^2+a^2) ≠ √b^2 + √a^2 I figure you can take it from there

**Algebra II - Bogus**

I suspect typos. The function is littered with junk. p? +7+8?

**mathematics**

2x^2-y^2+4x+4y-4=0 2x^2+4x - y^2+4y - 4 = 0 2x^2+4x+2 - y^2+4y-4 -4-2+4 = 0 2(x+1)^2 - (y-2)^2 = 2 (x+1)^2 - (y-2)^2/2 = 1 Now just consult the properties of hyperbolas. x = 2cost y = 3cost First off, I think you have a typo, since that is just 3x=2y If you meant x = 2cost y =...

**Math**

so, if you don't want math jargon, what do you mean by parametrically? A simple web search will produce lots of explanations, of varying mathematical sophistication.

**Combinationa and permutation**

There are 3! ways to arrange the three colors. Within each color, there are 5!,3!,4! ways to arrange the different marbles. So, there are 3!5!3!4! = 103680 ways to arrange the marbles as specified.

**algebra**

4x = y+7 x+28 = 2y The numbers are 6 and 17

**physics**

its horizontal velocity is unchanged its vertical velocity is the same speed, but the opposite direction. Play around with that and see what you get.

**Maths- calculus**

They approach at 35 knots. So, when they have gone 55 miles together, they are 45 miles apart. That takes 55/35 hours. How long to consume the whole 100 miles? 100/35 hours. How far has ship A gone by then? How long to cover 130 miles? 130/35 hours. I assume you can convert el...

**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

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