math - oops
Since 17 is prime, N=1
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
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...
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.
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
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
(2,1)+(1,4) = (3,5) (5,2)+(1,4) = (6,6) So, true
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.
pick the pair with (x,y) and (-x,-y)
total area = 18*8 = 144 picture area = 14*4 = 56 so, just subtract to get the frame only
dN/dt = 528e^0.4t / (11+e^0.4t)^2 Now just plug in t=4
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
simple: p(x) = r(x) - c(x)
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...
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.
yes. care to proofread your posting and rephrase the question?
(12*87+18x)/(12+18) = 90 Now just solve for x
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?
I think it's a divisibility problem, where she meant If a|(b-2c) and a|(2b+3c) the a|b and a|c.
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
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?
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
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.
well, that would naturally be 0.02 * 5270
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...
just list the digits as given, moving the decimal point 9 places to the right, adding zeroes as needed.
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, ...
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 ...
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 ...
well, 500 is 25% of 2000, so ...
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°
your answer looks correct to me. There must have been a typo in the problem, with a spurious "root" tossed in.
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
Judging from your experience, I would have to say, YES!
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...
An equilateral triangle of side s has area √3/2 s^2 You have four triangles of side 8.
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.
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...
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.
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 ...
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
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
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
(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 ...
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))
I didn't see where the solid was a pyramid. Usually a prism is a right prism, so the v = (area of base)*height
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.
the x-coordinate is halfway between the two end x-values: (-3 + -8)/2 = -11/2 Do the y-value the same way.
after n cuts, the thickness is 0.1 * 2^n mm. so, evaluate when n=30.
just solve for t when the height is zero: -16t^2 + 112t + 128 = 0 just a normal quadratic equation.
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)
The point is clearly (-5,4) Now since the slope is 3/2, a second point is up 3 and right 2.
just figure s(5)-s(1)
The tank weighs the same, regardless of its contents. Figure the volume of material, and multiply that by the material's density. :-)
figure the volume: .18 * .78 * .44 m^3 now multiply that by the density, in kg/m^3
(5*62 + 50)/6
let the numbers be x-1,x,x+1 The sum is 3x = 39 so, the middle number is 13
log740353607 = log40353607/log7 = 9 so, 40353607 = 7^9
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) ...
1W = 1J/s 1 kwh = 1000 Wh = 1000J/s * 3600s/h
750 + 750 + 625
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
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.
rewrite f(x) as 5(x + 3/10)^2 + 11/20 and then you can just read off the coordinates of the vertex.
you want the set of elements common to your two sets. So, which numbers are in both lists?
The number of people taking something is 23+32-9 So, that leaves how many taking nothing?
They are perpendicular if the product of their slopes is -1. So, is (-7)(-7) = -1 ?
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...
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.
I'd say that would be 17+3=20 assuming the ladder is laid vertically against the wall -- an unusual placement, to be sure.
the grade would be 15/5280 = 0.284%
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
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.
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.
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
translating upward just means add 11 to g.
f(x) = -5(x - 3/10) + 29/20 If that doesn't tell you the answer, review your forms of quadratics.
(fg)(x) = f(x)*g(x) = (-6x-1)(4x^2)
(f+g)(x) = f(x) + g(x) so, just add the two polynomials together.
life is like a simile.
ok. now what?
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...
You use partial fractions. 1/(v+2)(v-1) = 1/3 (1/(v-1) - 1/(v+2))
light is reflected from both sides of the glass.
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
look at your functions. They indicate that the ball rises as time goes on, and never comes back down. h1(t) = 156 - 16t^2
IF UNIT IS 1, HOW ABOUT 9871 ?
oops - I plugged in π/2 instead of π. The solution above is correct if the fan is 1/4 of a circle.
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 (...
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.
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...
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?
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.
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.