Saturday
July 26, 2014

Posts by steve


Total # Posts: 23,963

math - oops
Oops. N=13

math
Since 17 is prime, N=1

math
using the well-known proofs that sinx -> x, we can conclude that tan2x -> 2x so we have the limit as (2x-x)/(3x-x) = 1/2

Grammar
If a shark ate the fish, then, yes, the fish got eaten by a shark. Past tense. However, "gets" can be ok, too. Maybe you are talking about what happens when a fish is near a shark. If the shark is hungry, then what usually happens is that the fish gets eaten by the s...

intermediate Algebra
m = y-7 1/m + 1/y = 1/12 1/(y-7) + 1/y = 1/12 y = 28 so, m = 21 check: working together, in one day they can assemble 1/28 + 1/21 = 1/12 of the whole.

intermediate Algebra
1/2 - 1/4 = 1/x x = 4 Check: water comes in at 1/2 sink/minute water drains out at 1/4 sink/minute net flow: 1/2-1/4 = 1/4 sink/min So, it takes 4 minutes to fill the sink

analytic geometry
AB has slope 2 and length √5 mid(AC) = (-1/2,1/2) mid(BC) = (-1,-1/2) so that segment has slope 2 and length √5/2

geometry
(2,1)+(1,4) = (3,5) (5,2)+(1,4) = (6,6) So, true

geometry
just apply your distance formula. Plot the two points, and join them in a right triangle with legs parallel to the axes; the hypotenuse is the line joining the points.

geometry
pick the pair with (x,y) and (-x,-y)

math
total area = 18*8 = 144 picture area = 14*4 = 56 so, just subtract to get the frame only

calculus
dN/dt = 528e^0.4t / (11+e^0.4t)^2 Now just plug in t=4

calculus
Do you mean to divide? N(t) = 650/(1+649e^-.5t) What's the trouble? Straightforward evaluation of N or solving for t. That's just algebra. If I have the function right, its graphs is http://www.wolframalpha.com/input/?i=650%2F%281%2B649e^%28-.5t%29%29

Math
simple: p(x) = r(x) - c(x)

nau
John's idea is interesting, but leaves you no closer to the solution. 4x+y=21 7x-4y=8 Consider his multiplication idea, and work it this way: 28x+7y = 147 28x-16y = 32 Now subtract to get 23y = 115 y = 5 now you can find x easily. The other set is even simpler. You know wh...

math
and then subtract the 18 minutes already walked. Or, consider that there is 1/4 of the way to go. That is 1/3 as far as he's already gone, so it will take 1/3 as long to walk it. That is, 6 more minutes.

math
yes. care to proofread your posting and rephrase the question?

math
(12*87+18x)/(12+18) = 90 Now just solve for x

statistics
what, you cannot list the samples of size 3? ABC ABD ABE ...

Math - clarify
Hmmm. What does "list price of $100 less 7%, and 6%" mean? Two successive discounts? Also, after all the explanation, I don't see an actual question? What is it you are trying to calculate?

Math
I think it's a divisibility problem, where she meant If a|(b-2c) and a|(2b+3c) the a|b and a|c.

algebra
If there are s students, a adults, and g geezers, then s+a+g = 400 8s+10a+7g = 3535 a = s+g-10 Now just solve for the numbers

calculus
did you check out the hints I gave on your previous post of this problem? If so, where do you get stuck? The ticket problem is similar. How far do you get on that one?

maths
25^2 = 625

Math (Discrete Math)
271 is prime, so N is a multiple of 271 2014 = 2*19*53, If N = 271*2*2014, GCD(N,2014) = 2*271 and GCD(N,271) = 271 So, it appears to me that 271*2*2014 is the smallest N that fits the requirements

math
since the ratio of height-to-shadow is the same for both objects, h/29,2 = 3,5/5,2 Now just solve for h.

Math
well, that would naturally be 0.02 * 5270

mathematics
the figure is really just a sphere of radius r and a cylinder of radius r and height 4r. So, the volume is V = 4/3 π r^3 + πr^2 (4r) = 16/3 π r^3 So, dV/dt = 16πr^2 dr/dt That means that dr dt = dV/dt / (16πr^2) The surface area is A = 4πr^2 + 2&#...

Math Help
just list the digits as given, moving the decimal point 9 places to the right, adding zeroes as needed.

Calculus Help
the domain is 260 <= x <= 410 the price per chair is 88.00 - 0.02(x-260) revenue is price * quantity, so R(x) = x(88.00-.02(x-260)) = 93.2x - .02x^2 For maximum revenue, just find the vertex of the parabola. For minimum, figure the revenue at the two ends of the domain, ...

Calculus Help
revenue is price * quantity, so R(q) = 551q profit is revenue minus cost, so P(q) = 551q - (q^3-60q^2+1200q+760) You should probably graph P(q) to find the max. Take a look here: http://www.wolframalpha.com/input/?i=551q+-+%28q^3-60q^2%2B1200q%2B760%29 If you have calculus as ...

Calculus Help
profit P(q) = R(q)-C(q), so P(q) = 510q - (9400+3q^2) dP/dq = 510 - 6p P is maximized when dP/dq = 0, so ...

maine s
well, 500 is 25% of 2000, so ...

trig
Just review the definitions of the basic trig functions. Check the diagram, and you can see that the height h can be found using h/220 = sin 36°

Lisa
your answer looks correct to me. There must have been a typo in the problem, with a spurious "root" tossed in.

math
assuming that "no students of school A and B would get mixed up" means that each row contains only students from one school, let's find the largest number that divides both 336 and 432. GCF(336,432) = 48 So, school A has 7 rows of 48 and school B has 9 rows of 48

drivers' ed.
Judging from your experience, I would have to say, YES!

Algebra
since your speed is 5 km/hr, all the distances must be multiples of 5, since you start counting at the fountain. Or, if the somewhat vague description means that you want the total distance covered, starting at the fountain, then you have to start with 2, and after that, all t...

math
An equilateral triangle of side s has area √3/2 s^2 You have four triangles of side 8.

math
the slope of the line is (-4-2)/(1+2) = -2 So, use the point-slope form of the line, using either of the given points.

maths
Since time = distance/speed, 1.5/(8-s) + 1.5/(8+s) = 0.4 s = 2

math (help please)
review your "standard angles." sin π/3 = √3/2 sine is negative in QIII and QIV. That means that sin(π+π/3) = sin(2π-π/3) = -√3/2 Now you can add any multiple of 2π to those values, and you get all real numbers as required. If...

math
Recall that if A takes A hours, and B takes B hours, 1/A + 1/B = 1/2 So, if B does the task in x hours, A takes x+3 hours: 1/(x+3) + 1/x = 1/2 Now just solve for x.

math
Assuming you meant √(x-6)=√3-√x, we square both sides and get x-6 = 3-2√(3x)+x -9 = -2√(3x) 9/2 = √(3x) 81/4 = 3x x = 27/4 Check: √(3/4) = √3-√(27/4) √3/2 = √3(1-3/2) √3/2 = -√3/2 Nope. If you meant ...

Algebra
decaying to 10% takes log0.10/log0.5 = 3.32 half-lives So, A's half-life is 33/3.32 = 9.94 days B's half-life is 43/3.32 = 12.95 days Looks like (a) is the answer

math
each line describes the previous line. So, the next line is 311211 BTW, the last entry in your post should have been 111221, making the real next line 312211

Math
Draw the triangle. One leg is 1, and the hypotenuse is 4. So, the other leg is √15 the cosine of the angle is √15/4

Differential Equations
(x^2+1)dx + x^2y^2dy=0 x^2y^2 dy = -(x^2+1) dx y^2 dy = -(x^2+1)/x^2 dx 1/3 y^3 = -x + 1/x + C ...

Algebra
log0.900.6 - log0.850.6 = 1.7 or, since you probably don't have a button for log0.9x, log(0.6)/log(0.9) - log(0.6)/log(0.85) or even log(0.6)(1/log(0.9)-1/log(0.85))

Geometry
I didn't see where the solid was a pyramid. Usually a prism is a right prism, so the v = (area of base)*height

science
Name it analogously with table salt, which is Sodium Chloride. That -ide suffix indicates that there are just the two elements. Ever heard of the ointment Zinc Oxide? Same deal.

math
the x-coordinate is halfway between the two end x-values: (-3 + -8)/2 = -11/2 Do the y-value the same way.

math
after n cuts, the thickness is 0.1 * 2^n mm. so, evaluate when n=30.

algebra
just solve for t when the height is zero: -16t^2 + 112t + 128 = 0 just a normal quadratic equation.

Alegbra
how many times is this going to be posted? Review the point-slope form of a line: a line with slope m, through the point (h,k) has the equation y-k = m(x-h) So, look at the equation above, and read off m and (h,k)

Alegbra
The point is clearly (-5,4) Now since the slope is 3/2, a second point is up 3 and right 2.

Trigonometry
just figure s(5)-s(1)

physics
The tank weighs the same, regardless of its contents. Figure the volume of material, and multiply that by the material's density. :-)

physics
figure the volume: .18 * .78 * .44 m^3 now multiply that by the density, in kg/m^3

Pre algebra
(5*62 + 50)/6

math
let the numbers be x-1,x,x+1 The sum is 3x = 39 so, the middle number is 13

Math
log740353607 = log40353607/log7 = 9 so, 40353607 = 7^9

math
x = 2^(1/2) since log √x = 1/2 log x, log x = -2 x = 10^-2 lnx = ln(e*(x+1)) x = e*(x+1) ...

Physic
1W = 1J/s 1 kwh = 1000 Wh = 1000J/s * 3600s/h

Math
(9+1)/(9+1+6)

physics
750 + 750 + 625

Calculus 2
actually, the integral isn't so bad if you recognize that the integrand is just x^4 + 1/x^4 http://www.wolframalpha.com/input/?i=arc+length+of+x^5%2F10%2B1%2F%286x^3%29+from+3+to+6

Physics
well, you have the mass of 1 liter. So, what is the mass of 2 liters? Now just look up the conversion factor for kg to lb. A handy site is http://www.onlineconversion.com/weight_common.htm On the home page there, you can find many other conversion calculators.

mqr/117
rewrite f(x) as 5(x + 3/10)^2 + 11/20 and then you can just read off the coordinates of the vertex.

Math
you want the set of elements common to your two sets. So, which numbers are in both lists?

Math
The number of people taking something is 23+32-9 So, that leaves how many taking nothing?

Alegbra
They are perpendicular if the product of their slopes is -1. So, is (-7)(-7) = -1 ?

Math
think of the calendar as units of 24 hours So, 5:44 am on day 10 is the same as 29:44 on day 9. So, subtract 14 from 29 and you have 15:44 of the previous day, or 3:44 pm. Or, you could just subtract 24 hours, giving you 5:44 am of the previous day. But you only wanted to subt...

Alegbra
If you mean y = -3/2 (x+5) you can see easily that y=0 when x = -5. So, that's where the graph crosses the x-axis. Now, since the slope -s -3/2, just mark a second point, 3 down and 2 to the right from there. Join those two points with a line, and that's the graph.

math
I'd say that would be 17+3=20 assuming the ladder is laid vertically against the wall -- an unusual placement, to be sure.

math
the grade would be 15/5280 = 0.284%

Math 221
as with most problems involving fractions, work first with the denominators. They cannot be added or subtracted unless they all have the same denominator. 5/12 + 7/9 The GCD(12,9) = 36. So, what you have is 15/36 + 28/36 Now all the "units" are the same. Just as you ...

maths - oops
Err, I mean one leg=2. So half the chord has length √21

maths
Draw a diagram, including the radii to the ends of the chord. Draw the radius perpendicular to the chord. You now have two right triangles with one leg=1 and hypotenuse=5. Half the length of the chord is √24.

Algebra II
no, since 2x^2+x-15 = (2x-5)(x+3) Just multiply both sides by (2x-5)(x+3) The thing to watch out for is to be sure to note that 5/2 and -3 must be excluded from the domain.

mat/117
you want where P < 0 P(x) = 750x(20-x) You know that P=0 when x=0 or 20 Since the graph is a parabola opening downward, P>0 between the roots. So, P<0 if x>20

mat/117
translating upward just means add 11 to g.

mat/117
f(x) = -5(x - 3/10) + 29/20 If that doesn't tell you the answer, review your forms of quadratics.

mat/117
(fg)(x) = f(x)*g(x) = (-6x-1)(4x^2)

mat/117
(f+g)(x) = f(x) + g(x) so, just add the two polynomials together.

phi 208
life is like a simile.

Math
ok. now what?

math
Surely this treated in your text. You want A/(v-1) + B/(v+2) = 1/(v-1)(v+2) A(v+2) + B(v-1) = 1 Av + 2A + Bv - B = 1 (A+B)v + (2A-B) = 0v + 1 For those polynomials to be identical, all of the coefficients must match. So, we have A+B = 0 2A-B = 1 solve those and you get A = 1/3...

math
You use partial fractions. 1/(v+2)(v-1) = 1/3 (1/(v-1) - 1/(v+2))

science
light is reflected from both sides of the glass.

algebra
set x=0 and evaluate y. That's the y-intercept. Ax+By=C has slope -A/B because By = -Ax+C y = -A/B x + c/B In this case, A=9 and B=5

math
look at your functions. They indicate that the ball rises as time goes on, and never comes back down. h1(t) = 156 - 16t^2

MATH
IF UNIT IS 1, HOW ABOUT 9871 ?

Math
oops - I plugged in π/2 instead of π. The solution above is correct if the fan is 1/4 of a circle.

Math
The fan is a sector of a circle. That means that 198 = 1/2 (x+3)^2 θ Unless you know how much of a circle the fan occupies (that is, what is θ, compared to 2π), there's no way to solve for x. If the fan is a half-circle, θ=π, so 198 = 1/2 (x+3)^2 (...

English
They are all four compound sentences, so there should be a comma after "summer" #1 is probably the best. #2 implies that there is a specific group of people under discussion. #3 and #4 suffer from a mismatch between plural and singular.

English
I think #2 is better. The "still" implies that the study is continuing, rather than having been finished in the past. #1 would be ok if it said something like I studied math for ten years, but never really learned it. #1 is still ok as it is, if you are discussing pa...

English
The problem appears to be math, and yes, the sentences seem to mean the same thing. Now it's time to work on your English. That would be Do the three mean the same? Or, Are the three the same?

Alegbra
the slopes are the same, so they are either parallel or the same line. If you multiply the 1st by -3, the constant term is different from 7, so the lines are parallel.

Surds
Hmmm. I get √(4x+1)+√(x+3)=2 4x+1 + 2√(4x^2+13x+3) + x+3 = 4 5x = -2√(4x^2+13x+3) 25x^2 = 4(4x^2+13x+3) 25x^2 = 16x^2 + 52x + 12 9x^2 - 52x - 12 = 0 (9x+2)(x-6) = 0 x = -2/9 , 6 But x=6 does not satisfy the original equation, so -2/9 is the only solution.

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