Wednesday
September 24, 2014

Posts by STEVE


Total # Posts: 25,190

math
Actually, the volume of a cone is v = 1/3 π r^2 h
September 10, 2014

math
2(w + 2w-3) = 144
September 10, 2014

Math
1,2,3,4,5,6,7,8,9,10,11,12,13 add up to 91. So, it looks like we have 1,2,3,4,5,6,7,8,9,10,11,12,14
September 10, 2014

math
Not quite sure what you're doing there. If a side of the square is 45, its perimeter is 180. Thus, the perimeter of the triangle is 90. So, each side of the triangle must be 30.
September 10, 2014

algebra 1
If x >= 0, |x| = x If x < 0, |x| = -x So, from what we have above, x >= 0 x-2 < 0, or x < 2 So, 0 <= x < 2
September 10, 2014

Trig
If the nearer observer is at distance x from the obelisk, then we have h/x = tan 65° h/(x+25) = tan 44° so, eliminating x, just solve for h in h/tan65° = h/tan44° - 25 h = 25/(cot44°-cot65°)
September 10, 2014

math
400m / 92s = 4.35 m/s or, 400m / 1.533 min = 260.9 m/min
September 10, 2014

college algebra
If x oz. of 1% are used, then the rest (3-x) are 5%, so .01x + .05(3-x) = .04(3) x = 3/4 So, 3/4 oz of 1% and 9/4 oz of 5% Note that 4% is 3/4 of the way from 1% to 5%, so 3/4 of the total is the 5% strength.
September 10, 2014

college algebra
If x is at 8%, the remainder (22000-x) is at 6% so, .08x + .06(22000-x) = 1680 ...
September 10, 2014

math
just plug in your numbers: h(t) = -16t^2 + 84t + 60 assuming he kicks it straight up. Now just plug in t=2
September 10, 2014

Math
Since A+B+C=180, C=94.24 So, using the law of sines, c/sinC = a/sinA Now just plug and chug.
September 10, 2014

Algebra!!!! HELP
Since F=kx, F/x is constant. So, (a) 120/x = 265/0.15 (b) F/0.3 = 265/0.15 Note that you can answer these questions without even determining the value of k explicitly.
September 10, 2014

math
Just use the quadratic formula: x = (-(c-a)±√((c-a)^2 - 4(b-c)(a-b)))/(2(b-c)) You can play around with that some, but I don't see much in the way of simplification. http://www.wolframalpha.com/input/?i=%28b-c%29x%C2%B2+%2B+%28c-a%29x+%2B+%28a-b%29
September 10, 2014

math
(6x+2)/4 + (2x²-1)/(2x²+2) = (10x-1)/4x Clear fractions by using the common denominator of 4x(x²+1). This requires that x≠0. (6x+2)(x(x²+1)) + (2x²-1)(2x) = (10x-1)(x²+1) (6x^4+2x^3+6x^2+2x) + (4x^3-2x) = (10x^3-x^2+10x-1) 6x^4 - 4x^3 + 7x^2...
September 10, 2014

calc
If you found T(t) = r'/|r'|, then you should be able to get N(t) = T'/|T'| Where do you get stuck?
September 10, 2014

math
(1) 2(x + x-3) = x(x-3) x = 1 or 6 But x=1 isn't viable, so only x=6 (2) 2(x+x) = x^2 x = 4
September 10, 2014

maths-calculus
If you let u = -(x+1), you have u(e^(-1/u) - 1) = (e^(-1/u) - 1) / (1/u) Now using l'Hospital's Rule, that is the same as (e^(-1/u) - 1)(1/u^2) / (1/u^2) = e^(-1/u) - 1 -> 0-1 = -1
September 10, 2014

Math
I'd say -40 + 20 = -20
September 10, 2014

math
sounds like a good deal. Was there a question in there somewhere?
September 10, 2014

math
Since the density is obviously 2 seedlings/hill, I suspect you want the density in terms of seedlings/m^2 or something. Since each hill occupies 400cm^2, the density is 2 seedlings/400cm^2 = 1/200 seedlings/cm^2 Maybe not too useful. In terms of m^2, that will come out 2 ...
September 10, 2014

programming
Can you see what a useless question that is to be asking here? Any exposition you find here will only be what you can find in your text (if any) or in any of the sites turned up by google.
September 10, 2014

math
If Stevie sings x songs, then Christine sings x-6 songs. Add them up: 8 + x-6 + x = 18 x = 8
September 10, 2014

Math!!
yes. good job.
September 9, 2014

Math
You have an arithmetic progression where a = 20 d = 4 T20 = 20+19*4 = 96 S30 = 30/2(2*20+29*4) = 2340
September 9, 2014

math
8+(7) = 8+7 = 15
September 9, 2014

mathematics
In order to guarantee any reds at all, you need to draw 41, since the first 40 might be all green and white. So, 45 draws will guarantee 5 reds.
September 9, 2014

Pre-Calculus
easy. Just -5 to x and -4 to y: (-2,1) -> (-7,-3) and similarly for the other points.
September 9, 2014

Algebra - typo?
You know, we work hard to provide help with the problems. Don't make us read your mind as well. And shoot, why not show some of your own work to help us figure out what is troubling you? If you mean to find the solution to the system of equations -7x+8y=-8 -2x+6y=-6 If you...
September 9, 2014

math
they are approaching at the rate of 18 mi/hr They only had to cover 5 miles, so that took 5/18 hours In that time, Jim ran 10 * 5/18 = 25/9 miles
September 9, 2014

Pre-Calculus/Trigonometry
A is true because the 2nd entry for x is 5, and the 2nd entry for f(x) = 6 Now for the others, the domain is the set of x values. The range is the set of f(x) values. D is just like A. That should help some.
September 9, 2014

Pre-Calculus/Trigonometry
there's nothing to solve. Just evaluate the expression. I tend to think that you meant 3/(x+2) - √(x+3) but it's hard to say due to your carelessness with parentheses. If I got it right, then it just evaluates to 3/(7+2)-√(7-3) = 3/9 - √4 = 1/3 + 2 = ...
September 9, 2014

Pre-Calculus/Trigonometry
well, I'd say that it's 3/7+2-√7-3 Insert parentheses as need for proper evaluation!
September 9, 2014

Physics
the velocity changed by -44 m/s in 4.8s, so the acceleration is -44/4.8 m/s^2
September 9, 2014

Math
the minimum cost is found at the vertex of the parabola. As you recall, that is at x = -b/2a, or in this case x = 10/.5 = 20
September 9, 2014

maths
cos(t) = 1.5/3 = 1/2 t = π/3 or 60° Better review you standard 30-60-90 and 45-45-90 triangles. They pop up often.
September 9, 2014

math- help needed badly
The ship travels 20 miles in the time given. If we label the points S for ship (current position), N and F for Near and Far lighthouses, then if we call the original position O, In triangle SNF, S=25° N=125° F=30° In triangle ONS, n = 20 N=55° O=95° so, NS/...
September 9, 2014

Calculus
You have x,y r^2 = x^2+y^2, so r = √29 Now just plug and chug: sin = y/r cos = x/r tan = y/x and so on
September 8, 2014

Precalculus
75/x = tan 40° I assume you meant 40°, not 40', as that would have (a) been hard to measure (b) put the ship well over the horizon
September 8, 2014

math
Nope. C time to review
September 8, 2014

AP CAlc. AB Please helppp!!
As usual draw the graph. Clearly for r < 0, f(x) = -x + 1, so A(r) = ∫[-2,r] -x+1 dx For r > 0, we have f(x) as -x + 1 for -2 <= x <= 0 x + 1 for 0 < x <= r So, A(x) = ∫[-2,0] -x+1 dx + ∫[0,r] x+1 dx Both of those are easy to evaluate, so ...
September 8, 2014

algebra
width: w length: 2w+5 so, 2(w + 2w+5) = 46 Now you can get w, and then 2w+5.
September 8, 2014

Pre-Calculus/Trigonometry
Uh, look at the table. 1 is the 5th entry in the x row 1.3 is the 5th entry in the f(x) row. So, f(1) = 1.3
September 8, 2014

Math Proof
sure could. But the argument is the same. Might as well work with what you were given, in this case at least.
September 8, 2014

Math Proof
Looks good. This is the method usually used to prove that √2 is irrational, but it works for any integer. You can find lots of proofs for that online. Look some up, and see how they use the same argument.
September 8, 2014

Math
clearly, the deduction will be .062*3260 + .0145*3260 It will be the same for all her paychecks, since her annual earnings will fall well short of the SS cutoff point.
September 8, 2014

MATH HELP
Now: 46 At the end of Day 1: 38 Day 2: 30 Day 3: 22 Day 4: 14 - order more Day 5: 6 Day 6: out of stock unless more has arrived
September 8, 2014

Math Proof
sum: Assume that it is rational. That is, if c = a/b, then a/b + x = m/n for some integers m and n. That means that x = m/n - a/b But m/n-a/b = (bm-an)/(bn), clearly a rational number, and x is irrational. So, if x is irrational, c+x cannot be rational. Clearly, cx must also ...
September 8, 2014

math
Assuming you mean (6x)^2 = (6x)(6x) = 36x^2 or, (6x)^2 = 6^2 * x^2 = 36x^2
September 8, 2014

math
D additive identity = 0 multiplicative identity = 1 a+0 = a a*1 = a for any value of a
September 8, 2014

math
hint. substitute to get 6x + 4(3-3x) = 0
September 8, 2014

math
1/2
September 8, 2014

math
since there are three values of x which satisfy the equation, there are three values for 2x+3.
September 8, 2014

math
(3,4/3)
September 8, 2014

math 1 question
powers first: 25-4/5+2 then multiplication and division, left to right: 25 - 0.8 + 2 then addition and subtraction, left to right: 24.2+2 26.2
September 8, 2014

Math
You have 26*1760+385 = 46145 yards since 1 meter = 1.0936 yards, that means you have 46145/1.0936 = 42195 meters When you get stuck, it's best to post your work -- that way we can help figure out where you went wrong. Just sayin'
September 8, 2014

algerbra
divide the second by 3 and you will see that they are the same line.
September 8, 2014

phycis
since mass * distance is the same, and the heaver mass only rises 1/6 as far, it is 6 times the mass, or 360N
September 8, 2014

Math
what is 1000000/100? It's 10,000 So, 10,000 CDs to each of 100 stores makes 1,000,000. 925,733 The 2nd 3 is just 3 The others are true
September 8, 2014

math
Hmmm. If the sides are in the ratio 4:5:6, then the sines of the angles are in the same ratio (law of sines) So, if sinA = 4x, sinB = 5x sinC = 6x arcsin(4x)+arcsin(5x)+arcsin(6x) = pi x = √7/16 A = arcsin(4√7/16) = 41.41 B = arcsin(5√7/16) = 55.77 C = arcsin...
September 8, 2014

Math
Id say f(x) = x h(x) = 4 f(x)
September 8, 2014

math
since the slope is the same, they are either parallel or the same line. I expect you can decide which. If parallel, no solutions, since they do not intersect. If the same line, there are infinitely many solutions, since any point on one line is also on the other.
September 8, 2014

algerbra
well, did you try any to see whether they are? (0,-1): -1 = 6*0-1? yes and so with the others.
September 8, 2014

calculus
∂u/∂x = 2x/(x^2-y^2) ∂u/∂y = -2y/(x^2-y^2) ∂2u/∂x∂y = ∂2u/∂y∂x = -2(x^2+y^2)/(x^2-y^2)^2
September 8, 2014

math check answers
I like all your answers. On #2, the markup based on cost is indeed 67%. The markup based on salling price is 40%, since the $100 markup is 40% of the $250 selling price. Could be they had a typo in the question or mixed up the answers.
September 8, 2014

Math
24(1.06)^(2013-1626) = $1.49*10^11 you may adjust it depending on whether the final year was an entire year.
September 8, 2014

math - eh?
sounds like a good deal. Is there a question in there somewhere?
September 8, 2014

Algebra
width: w length: w+11 so, 2(w + w+11) = 90 Now just solve for w, and figure the length.
September 7, 2014

Algebra
How approximate? Assuming you meant f(x) = -8x^2 + 2x + 2, f(-1) = -10 f(0) = 2 f(1) = -6 So, f(x)=0 somewhere in (-1,0) and (0,1). You can, of course, use the quadratic formula to get an exact answer and then approximate with as many decimal places as you wish. See http://www...
September 7, 2014

math - eh?
Heck, I can't even figure out what the string of digits and slashes even means! Maybe some parentheses around the terms will help. And two = signs? What's up with that?
September 7, 2014

math
If there are x lbs of 4.40 tea, then the rest (120-x) is 2.30 So, we need 4.40x + 2.30(120-x) = 3.00(120) Now just solve for x.
September 7, 2014

Math
If P(x) = x^2-4x, then since P(x) = x(x-4), it has two x-intercepts. Q(x) = x(x^2-4) = x(x-2)(x+2) so Q has 3 roots. x^2-ax = x(x^2-a) = x(x-√a)(x+√a) so there are 3 roots With 3 roots, there must be 2 extrema. x^2+ax = x(x^2+a) since a>0, x^2+a can never be ...
September 7, 2014

Calculus
x + y − 1 = ln(x^5 + y^5) 1 + y' = 1/(x^5+y^5) (5x^4 + 5y^4 y') y'(1 - 5y^4/(x^5+y^5) = 5x^4/(x^5+y^5) - 1 y' = ((x-5)x^4 - y^5)/(x^5 + (y-5)y^4) At (1,0), y' = (-4)/(-1) = 4 So, the line is y = 4(x-1)
September 7, 2014

math
18s^9 t^3 - 2s^9 t^2 can be factored into 2s^9 t^2 (9t-1) No idea how that can be evaluated to 9. I suspect there is something missing or garbled in the problem statement as shown.
September 7, 2014

math
341-115 = 226 341-120 = 221 So, any value between 221 and 226 will produce a number between 115 and 120. Or, using a compound inequality, we have 115 < 341-x < 120 -226 < -x < -221 226 > x > 221
September 7, 2014

math
You can figure out the mass of silver, then do all the conversions of mass to volume and back, or you can note that density(Al)/density(Ag) = 2.57 So, volume(Al)/volume(Ag) = 2.57 But, the volume of a sphere scales as the cube of the radius, so the radius scales as the cube ...
September 7, 2014

math
(12-2)p^7 = 10p^7
September 7, 2014

algebra
do it just the way to multiply 2-digit numbers: (23)(45) = (20+3)(40+5) = 20*40+3*40+10*5+3*5 = 1035 (7-6y)(7-4y) = 7*7 + 7(-4y) - 6y(7) - 6y(-4y) = 49 - 28y - 42y + 24y^2 = 49 - 70y + 24y^2
September 7, 2014

algebra 2
all polynomials have domain of all real numbers. All polynomials of odd degree have range of all real numbers, y=0 when x = ∛4 x=0 when y = -4
September 7, 2014

Calculus
You know the roots are x = (m±√(m^2-4))/2 So, if m<=2 there are not two real roots, so the total area is the same as the integral. If m>2, then you need to divide the integral into 3 parts, with the roots as the limits of integration. Reiny's solution of...
September 7, 2014

Algebra
You have two points on the line: (2,5) and (6,9). So, the line has slope=1, and its equation is c = m-3
September 7, 2014

Geography
∂2u/∂x∂y
September 7, 2014

physics
8.2m / 3.7m/s = 2.2 s
September 7, 2014

physics
just solve for a in 4100t - 17/2 t^2 = 9400t - a/2 t^2 a/2 t^2 = 5300t + 17/2 t^2 at^2 = 10600t + 17t^2 a = 10600/t + 17
September 7, 2014

Quick question
Just how would you propose we do asl in a text forum?
September 7, 2014

Calculus
clearly, each rectangle with upper-right corner at (x,y) has area a = xy Since y = 9-x^2, the area is just a = x(9-x^2) Not sure what you need to do with that information. The question is a bit vague.
September 7, 2014

Math - Urgent
(a) each term is -1/3 the previous term (b) each term is -4 times the previous term Just take the first two terms and find their ratio. Then check to make sure the same ratio is there for the next two terms, and so on.
September 7, 2014

math
the slope of the given line is -1/2 so, the slope of perpendiculars is +2 So, the line you want is y+12 = 2(x+7)
September 7, 2014

Precalc
try C(x) = 4.00 + 0.40⌈10x⌉ where ⌈z⌉ is the ceiling function (the least integer greater than z) For example, ⌈2.37⌉ = 3
September 7, 2014

science/math (mean)
I get 44.60333333... So, to three decimal places, that would be 44.603 However, since all the values are given to two places, I would have given the same answer you did.
September 7, 2014

math
6*22 + .18 * 2766.50 = 629.97
September 7, 2014

math 8
when multiplying powers, add the exponents. when raising a power to a power, multiply exponents. This is because, for example, (x^2)^3 = (x^2)(x^2)(x^2) = x^(2+2+2) So, you have #5: 8^3 * 8^7 = 8^(3+7) = 8^10 #11: (5/8)^3 = 5^3/8^3 = 125/512 #12: ((-2/9)^3)^5 = (-2/9)^15 = -2^...
September 7, 2014

C programming
Hmm. Looks good to me. Can you produce the results for a few values of x? Do you at least get cosh(0) = 1.0 ?
September 7, 2014

math 12
If C=D, C-D=0 and you cannot divide by zero.
September 7, 2014

Math
graphing what?
September 7, 2014

physics
658.1m / .03m/yr = 21936.7 yr
September 7, 2014

physics
in MKS units, .440kg * 98 mi/hr * 1000m/0.62mi * 1hr/3600s = .440*98*1000 / .62*3600 m/s = 19.32 kg-m/s
September 7, 2014

Algebra
correct. So, plug in either point. Using (-2,-3), you have -3 = (-2/7)(-2) + b b = -25/7 so, y = -2/7 x - 25/7
September 7, 2014

Physics
x(3) = 90m x(2) = 40m total distance: 50m total time: 1s avg speed: 50 m/s
September 7, 2014

Math
going down: 5/2 seconds going up: 5/1 seconds so, down+up = ?
September 7, 2014

Geometry help
Did you draw a diagram? AC = CD AD = AC+CD #1 ok #2. The calculation for x is just as in #1. AD = AC+CD = 7+7 = 14 #3. AD=AC+CD = 2(AC), so 6x-4 = 2(4x-3) x = 1 CD = 1 #4. As in #3, 12-x = 2(3x-1) x = 2 CD = 5
September 7, 2014

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