Wednesday
August 20, 2014

Posts by STEVE


Total # Posts: 24,330

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.
July 11, 2014

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
July 11, 2014

math
better review what an integer is...
July 10, 2014

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
July 10, 2014

area
w * 2w = 1000 2w^2 = 1000 w^2 = 500 w = 10√5
July 10, 2014

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 ...
July 10, 2014

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.
July 10, 2014

Geometry
tan x = 100/50
July 10, 2014

Geometry
x/20 = sin 65° the height is the side opposite the 65° angle. sine is opposite/hypotenuse
July 10, 2014

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
July 10, 2014

maths
since the ratio of height to shadow-length is the same, h/22 = 100/55
July 10, 2014

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
July 10, 2014

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.
July 10, 2014

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 ...
July 10, 2014

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
July 10, 2014

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 ...
July 10, 2014

math
-39 + 78 - 100 = -61
July 10, 2014

chemistry
Ya got me. However, the topic is discussed here: http://en.wikipedia.org/wiki/Magnetic_quantum_number
July 10, 2014

math
review the significance of the equation (x-h)^2 + (y-k)^2 = r^2
July 10, 2014

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)
July 9, 2014

math
35/n
July 9, 2014

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
July 9, 2014

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.
July 9, 2014

math
The formula is above. Plug in r=3. We will assume a smooth, rather than a dimpled, surface :-)
July 9, 2014

math
4π(2r)^2 / 4πr^2 = 4 the square of the radius ratio
July 9, 2014

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
July 9, 2014

Algebra II - Bogus
I suspect typos. The function is littered with junk. p? +7+8?
July 9, 2014

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...
July 9, 2014

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.
July 9, 2014

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.
July 9, 2014

algebra
4x = y+7 x+28 = 2y The numbers are 6 and 17
July 9, 2014

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.
July 9, 2014

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 ...
July 9, 2014

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.
July 9, 2014

Basic Physics
If the vector is in -y direction, the x-component is zero.
July 9, 2014

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.
July 8, 2014

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
July 8, 2014

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...
July 8, 2014

math
so, what headway have you made? See any mistakes in my calculations?
July 8, 2014

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...
July 8, 2014

math
3.10*11.3 km/s
July 8, 2014

Math
(i) ok (ii) T = 0.06x (iii) S = 20P
July 8, 2014

Geometry
clearly, 10x-7 = 5x + 4x+6 x = 13 so, take it from there.
July 8, 2014

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.
July 8, 2014

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.
July 8, 2014

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.
July 8, 2014

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.
July 8, 2014

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.
July 8, 2014

marh
a/27 = (1/3)^2
July 8, 2014

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
July 8, 2014

business math
multiply by (1+.30) or 1.3
July 8, 2014

Math
no, it's the next line. The squares are equal; it's the assumption that the roots are equal which is wrong.
July 7, 2014

Math
There is a + and a - root of each squared term. Just because (-4)^2 = 4^2 does not mean -4 = 4.
July 7, 2014

Geometry
they are regular, and all that that entails.
July 7, 2014

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
July 7, 2014

Algebra
yes, after combining terms.
July 7, 2014

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.
July 7, 2014

math
figure how many ml in 4 tbsp. If there are x, then the suspension is 240/(240+x) of the whole.
July 7, 2014

calculus
P = R-C
July 7, 2014

math
n+d+q = 60 d = 2q+1 10d = 5n-5 Now go for it.
July 7, 2014

algebra
you want to find when .09s = 260 + .04s So, just solve for s.
July 7, 2014

math
j+g+h = 20 j = 2g-3 h = g-1 Now just start substituting or eliminating to find the values.
July 7, 2014

business math
Looks like 18520/44568 = 42%
July 7, 2014

math
.70*x + 0(100-x) = .45*100 x = 64.28 so, 64ml of concentrate and 36ml of water
July 7, 2014

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: ...
July 7, 2014

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.
July 7, 2014

Riddle
your name
July 7, 2014

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
July 7, 2014

Science
well, what's 12% of 400?
July 7, 2014

general chem
looks like 8/58 to me
July 7, 2014

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.
July 7, 2014

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.
July 7, 2014

Math
4y+5x So much for math -- now it's time to ask for help with English.
July 7, 2014

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.
July 7, 2014

math
250 = 2 * 5^3 175 = 7 * 5^2 so, what's the largest number which divides both 150 and 175? 5^2 = 25
July 6, 2014

Calculus
v = 2 + 3t when does v=14? now take the integral to get the distance
July 6, 2014

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. ...
July 6, 2014

Math 221
(2/9) / (5/12) = 2/9 * 12/5 = 24/45 = 8/15
July 6, 2014

Algebra
Looks like C to me Note that in the table, y increases by a factor of 49 for each x-increase of 2.
July 6, 2014

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
July 6, 2014

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 ...
July 6, 2014

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/&#...
July 6, 2014

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 ...
July 6, 2014

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
July 6, 2014

Math 221
just apply the distributive property as usual: 2w – 3 + 3(w – 4) – 5(w – 6) 2w - 3 + 3w - 12 - 5w + 30 15
July 6, 2014

Math 221
2a(a-5)+4(a-5) 2a*a - 2a*5 + 4a - 4*5 2a^2 - 10a + 4a - 20 2a^2 - 6a - 20
July 6, 2014

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
July 6, 2014

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
July 6, 2014

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 ...
July 6, 2014

math
so, what did Table 11-1 say?
July 6, 2014

Algebra
you can see that -2x = 1+4y So, -6x = 3+12y Now substitute that into the 2nd equation and solve for y.
July 6, 2014

mat/117
already simplified
July 6, 2014

mat/117
multiply top and bottom by 8-√7 Then note that (8+√7)(8-√7) = 64-7 = 57
July 6, 2014

mat/117
just do normal expansion of distributed sums: √2(9-√2)+5√2 9√2 - √2√2 + 5√2 14√2 - 2
July 6, 2014

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
July 6, 2014

mechanics
just set 1/2 mv^2 = 36 and solve for v
July 6, 2014

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...
July 6, 2014

math
Hmmm. Seems to me that he lost 4/36 = 11.1% If he'd sold 40, and lost 4, that would be 10%
July 6, 2014

Set Theory :Complements with Ellipses
simple: A' = {40,41, ...}
July 5, 2014

geometry
6x5 gives greatest area Just think of the factors of 30, and list them in pairs for the others.
July 5, 2014

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