Friday
July 25, 2014

Posts by Steve


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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