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Posts by Steve

Total # Posts: 50,492

Series
clearly, 1,3,5 are an AP 2,4,8 are a GP Now just plug in your formulas for partial sums.

algebra
0.95x = 4.75

@Elsa
I like your 25 stones.

Mathematics
I like Elsa's proof, using Heron's formula. Works for me.

Mathematics
The line containing (a,0),(0,b) has equation x/a + y/b = 1 This is called the intercept form of a line. Clearly, (1,1) lies on that line if 1/a + 1/b = 1

Math, Series
well, just plug and chug 1/(2y) - 1/(y-x) = 1/(y-z) - 1/(2y) (x+y)/(2xy-2y^2) = (y+z)/(2y^2-2yz) (x+y)/(x-y) = (y+z)/(y-z) (x+y)(y-z) = (y+z)(x-y) xy+y^2-xz-yz = xy+xz-y^2-yz y^2-xz = xz-y^2 y^2 = xz y/x = z/y Thus x,y,z form a geometric progression

Math, Series
Do you mean 1/(y-x), 1/(2y), and 1/(y-z) or 1/(y-x), (1/2)y, and (1/y)-z ??

Math
Again, the curve is unbounded. If you mean y=(x^3/3)+x^2+x+1/(4x)+4 then here is the graph: http://www.wolframalpha.com/input/?i=(x%5E3%2F3)%2Bx%5E2%2Bx%2B1%2F(4x)%2B4 So, which part of the curve do you want?

Calculus
Consider the interior of the bowl as a stack of thin circles. At height h, the circle has area ?r^2 = ?(16(h+1)) So integrate that from 0 to 2

Math
If there are no correct answers, then the possible scores are 0,2,4,...,24 If 1, then 5,7,9,...,27 If 2, then 10,12,14,...,30 I think you can see the pattern here. Just make a 12x12 table and fill in the scores. Then cross them off a list of values from 1-60. Those remaining ...

math
If she travels x minutes at 70m/min, then the distance is 70x meters. It takes her 2 minutes longer at 60m/min. 70x = 60(x+2) x = 12 So, the distance is 840 meters. Her normal speed takes her 22 minutes, so she leaves at 7:38

maths
http://formulas.tutorvista.com/math/orthocenter-formula.html This will give you the orthocenter, if you have the vertices of a triangle. If you set up your right triangle with the right angle at C=(0,0) then let the other two vertices be at A=(a,0) and B=(0,b). Then the right-...

math
I think that the ? is just a way of giving us the slope of the ladder. If the firefighter has climbed a distance z to a height h, then we have x^2+y^2 = 29^2 w^2+(y-h)^2 = (29-z)^2 when ?=?/3, x = 29/2 and y=29?3/2 w = (29-z)/2 and h = z?3/2 when z=6, then, w = 23/2 and h=3?3 ...

math
they are the same. 10/10, 5000/5000, ...

Math
any plane intersection with a sphere is a circle.

Algebra
What were you expecting it to "add up" to? -4b * (1-b)/b = -4b(1-b)/b = -4(1-b) = 4b-4

algebra, series
The n'th term is ar^(n-1) Sn = a(1-r^n)/(1-r) = 1/4 4a(1-r^n) = 1-r 4a - 4ar^n = 1-r 4a - 4ar^(n-1)*r = 1-r ar^(n-1) = (1-r-4a)/(4r) I can't see how you can solve for r and a. There are many possible solutions. n=1: a=1/4 n=2: a(1+r) = 1/4 a = 1, r = -3/4 a = -1/3, r...

Pre-Algebra
12 is 3/7, so 4 is 1/7 Now how much would you pay?

sir damon steve damon damon help maths
That is correct. The average value of a function over an interval if ?[a,b] f(t) dt ------------------ b-a

Algebra
You know the factors will be (3n-?)(n+?) or (3n+?)(n-?) where the ?? pairs are 1,4 or 2,2 So, just poke around a bit and you will soon find that (3n-4)(n+1) works

Math
12/28 as much time, so 28/12 as many workers. 28/12 * 3 = 7

Math
distance = speed * time Since their distances are the same, if Jim's speed is x, then x(1/4) = (12)(1/3) x = 16 mi/hr Or, you can consider it like this. Jim takes 3/4 as long, so his speed must be 4/3 as great. 4/3 * 12 = 16

english
8 - 10 paragraphs on The Odyssey part 1. PLEASE, I WONT TAKE THIS FOR GRANTED. god bless. i tried but i cant read it very well

Math
The curve is unbounded. Also, there appears to be a typo. Why the +x+14x? As with any curve, its length over a given interval [a,b] is s = ?[a,b] ?(1+y'^2) dx

Math1
(a) do not know the formula (b) your text formatting sucks. try writing fractions as 3/4 and sequence terms as t7 or t20

Math! Help Hurry!
each small block has a volume of (1/4)^3 so the whole lot has a volume of 576 * (1/4)^3 = 9 ft^3

Math! Help Hurry!
I thought you said these problems were all different. They look exactly the same to me. Figure the volume of one of the small blocks, and use that to divide into the whole volume. 3 1/4 = 13/4 so the box has a volume of 13/4 * 3 * 1 = 39/4 ft^3 each small block has a volume of...

Math and Hurry Please!
2304 * (1/4)^3 = 36 cm^3

Math
the new mix of 32+8=40 oz contains 4+8=12 oz of cream 12/40 = 30%

Caclulus
#1 I assume that x,y,z are integers, or there is no maximum sum. The minimum sum would be 3?500 ? 23.811 500 = 2^2 5^3 so its factors are 1,2,250 1,4,125 1,5,100 1,10,50 1,20,25 2,2,125 2,5,50 2,10,25 5,5,20 5,10,10 5,25,4 Now pick the largest and smallest sums. #2 v = ?r^2h...

Mathematics
Take a look at the distances for each stone, numbering them outward. I'm assuming that we only include the distances actually carrying stones. The actual distance walked would be twice that. # d 1 10 2 20 3 30 ... n 10n So, after collecting n stones on each side, the ...

Mathematics
In that case, you must have forgotten your Algebra I. Look at what you know: a+7d = 2(a+2d) 8/2 (2a+7d) = 39 or, massaged a bit, a = 3d 8a+28d = 39

intermediate algebra
-2x - 5 < -2 -5 < 2x-2 -3 < 2x -3/2 < x or, x > -3/2 do the others similarly.

intermediate algebra
add 3 to each part

mat222
your copy/paste skills are severely lacking. What's so hard about this? You have the function pieces and their domains. Just plug in your numbers for the proper part.

Algebra
since ?WED ? ?FRI, ?R ? ?E So, solve for x.

Mathematics
consider the top of a large cone which has been cut off to leave the frustrum. Draw a side view. Using similar triangles, we know that the top of the bucket is 3/4 as high as the uncut cone. So, the piece that was cut off has an altitude of 15 cm. Subtract the small top of the...

maths
This should help a lot. You can construct the vectors u and v for the two orthocenters, and then just get the magnitude of |u-v| http://mathforum.org/library/drmath/view/70440.html

maths sir damon reiny or steve help!steve see
surely you know about the chain rule. ?u/?r = ?u/?x ?x/?r + ?u/?y ?y/?r = 2x sin(t) + 2*0 = 2x sin(t) similarly for ?u/?t

calculus
f = (6-x)e^-x f' = (x-7)e^-x f" = (8-x)e^-x f"=0 at x=8 f(8) = -2e^-8 so (x,y) = (8,-0.00067) See http://www.wolframalpha.com/input/?i=(6-x)e%5E-x+for+6+%3C%3D+x+%3C%3D+11

calculus
(a) [?[0,?] (10 sin(x)-5sin(2x)) dx]/(?-0) = 20/? (b) 10sin(c)-5sin(2c) = 20/? c ? 1.238 or 2.808

calculus
well, the weight is 44-0.2t now integrate that over the required distance.

maths
AC = AB+BC = a+b and so on. Of course they sum to zero, since that is a closed path.

Trig
so, think back to your Algebra II days and finish it up. What you have is correct, but make it look good: x^2-4x + y^2+4y = 0 x^2-4x+4 + y^2+4y+4 = 8 (x-2)^2 + (y+2)^2 = 8 http://www.wolframalpha.com/input/?i=r%3D4cos%CE%B8+-+4sin%CE%B8

math
unchanged

physics newton
F = ma

Math
log2(2?3/5)) = log2(2) + 1/2 log2(3/5) = 1 + 1/2 (log2(3)-log2(5))

math
try n=5 1+4*5 < 2^5 -- true So, what about n+1? 1+4(n+1) = 1+4n + 4 Now just show that it is less than 2^(n+1)

MATH AGAIN
surely by now you could have figured this out. Since ?ABC is isosceles, ?A = ?B = 30° Therefore, ?BMC is a 30-60-90 right triangle, with ?MCB = 90° So, BC = 12?3 Now drop an altitude from C to AB and use BC to find AB.

physical science
work = PE = mgh

Math
$80

math
Cool. Now where the heck is PR? Get with it, ok?

help
force is N = kg-m/s^2 work is J or N-m

Math
I hope you are not the one who has already posted this several times, receiving an answer each time. It is (11+9)/2 * 6 * 16/12

algebra
multiplying by 10, we have -2x+25 = 22 ...

Math
17000*1.03^5

algebra 2
x = (6+y)/(2y) 2xy = 6+y y = 6/(2x-1)

math
Note that ?MQP = ?MPQ so ?QMP is isosceles. MQ = MP = 18 ?MRQ is 30-60-90, with a hypotenuse of 18 RQ = 9?3

math
and PR is where?

math
where is M?

Math
well, the area is (11+9)/2 * 6 = 60 m^2 How many boxes is that? So, how much cost?

Math
you cannot simplify the log of a sum. Since there are no common factors to remove, this is as simple as it gets. Unless you mean log 6(7m+3q) = log 6 + log (7m+3q)

Math
Since 100 = 10^2 take the square root of both sides, and you have 10 = 100^(1/2) x = 1/2

science
PE is measured in J or N-m PE = mgh

algebra
V=kT/P so PV/T = k, a constant. You want T such that 10*74/T = 8*42/84 also, "cm to the 3" is written cm^3

algebra
3x+10 >= 4 3x >= -6 ...

Algebra 2
(x+2)(x-3) --------------- (x+2) This is equal to (x-3) for every value of x except -2, where it is undefined.

Math
recall that (a+b)^2 = a^2+2ab+b^2 so, take 1/2 of the middle coefficient and square it.

Math
since the center is at y=5, and it is tangent to the x-axis, the radius is 5. Now, what is the standard equation for a circle?

Math
well v increased by 3 m/s in 8 seconds. now, what is the definition of acceleration?

Math
figure the lengths of the sides. Then use the law of cosines. c^2 = a^2 + b^2 - 2ab cosC

Math
x^2?6x+9+y^2+2y+1 = 25 (x-3)^2 + (y+1)^2 = 5^2 Look familiar?

math
Draw a diagram, where a radius bisects the chord. You will see that the arc is subtended by the angle ?, where sin(?/2) = 9/14 The arc length is then s = r?

Rox
yes

math
top is 14 left is 12 right is 10 bottom is 20 If the figure is a trapezoid, then 144-x^2 = 100-(6-x)^2 x = 20/3 The height h is h^2 = 144-(20/3)^2 h = 8/3 ?14 So, the area is a = (14+20)/2 * 8/3 ?14 = 136/3 ?14

Maths
what is the shape of the rope? straight lines? parabola? catenary?

Science
1 and 2 are ok. On #3 you confuse frequency and wavelength. (and that's "greater")

Physics
conserve momentum: 5v = (8000+5)*0.50

Maths
(15 km/hr * 10^5 cm/km) * (49? cm^2) * x hr = (50m * 44m)(100cm/m)^2 * 21cm x = 2 hr

algebra
you don't say whether the values given are opposite or adjacent angles. So, you have one of two cases: x+40 = 3x-20 x+40 + 3x-20 = 180 Pick the one you want, solve for x, and then you can answer the questions.

math
pair them up 2,2n 4,2n-2 6,2n-4 ... What is the average of each pair? Or, consider their sum: 2+4+...+2n = 2(1+2+...+n) = 2*n(n+1)/2 = n(n+1) So, what is the average of that sum?

math
(a + b+10)/2 = (a+b)/2 + 5

maths
N arctan(8/5)° E

mathematics
remember the point-slope form of a line. The line with gradient m through (h,k) is y-k = m(x-h) Now just plug in your numbers.

calculus
y = -(x-3)(x-4) So, using discs of thickness dx, v = ?[3,4] ?r^2 dx where r=y v = ?[3,4] ?(x^2-7x+12)^2 dx = ?/30 Using shells of thickness dy, and taking advantage of the symmetry, v = 2?[0,1/4] 2?rh dy where r=y and h=?(1/4 - y) v = 2?[0,1/4] 2?y?(1/4 - y) dy = ?/30

Math
well, there are 10 choices for each digit, so ...

math
first step: what is the probability of rolling a 7?

Math
x^2-x-6 = (x-3)(x+2) x^2-5x+6 = (x-3)(x-2)

calculus
each shell has thickness dx, so v = ?[1,3] 2?rh dx where r=x-1 and h=y-3 v = ?[1,3] 2?(x-1)(4x-x^2-3) dx = 8?/3 as a check, using discs of thickness dy, v = ?[3,4] ?(R^2-r^2) dy where R=(2+?(4-y)-1) and r=(2-?(4-y)-1) v = ?[3,4] ?((1+?(4-y))^2-(1-?(4-y))^2) dy = 8?/3

calculus
Each shell has thickness dx, so v = ?[0,2] 2?rh dx where r = 9-x and h = 8-y v = ?[0,2] 2?(9-x)(8-x^3) dx = 984?/5 as a check, using discs (washers) of thickness dy, v = ?[0,8] ?(R^2-r^2) dy where R=9 and r = 9-x v = ?[0,8] ?(9^2-(9-?y)^2) dy = 984?/5

Math
x/4 + 2 = -2 x/4 = -4 x = -16

General Math
Presumably, the same percentage of seals was tagged as was found in the later sample. So, 6982/x = 245/700

8th grade math asp help
as you can see, no pictures here.

Crimal Justice
thank you

Crimal Justice
Julia has served one year of her 10-year sentence in prison. She has behaved herself, work at the library, and has not acted out in any way. She is hoping that at her next hearing judge will reduce her sentence. What type of sentence is julia hoping that at her next hearing ...

Math
well, a common right triangle is 5-12-13

calculus
because y is a function of x. You must use the chain rule. d/dx (3y^2) = d/dy (3y^2) * dy/dx

calculus
ln(x+y+3) = xy + y^3 (1+y')/(y+x+3) = y + xy' + 3y^2 y' Collect terms and solve for y': y' =      1-y(x+y+3) -------------------------- (x+y+3)(x+3y^2)-1 so, at (-4,2), y' = -1/7 So, now you have a point and a slope, and the ...

maths extrema need hlp
for extrema, you need ?f/?x and ?f/?y = 0 ?f/?x = cosx + cos(x+y) = 0 ?f/?y = cosy + cos(x+y) = 0 recall that cos ?/3 = -cos(2?/3) So that should get you started.

mathematics plz need help sir steve
Do you mean the Jacobian? F1x = 4x^3y^3 F1y = 3x^4y^2 F2x = 35x^6 F2y = 3cos(3y) So, the determinant of J(f1,f2,x,y) is (4x^3y^3)(3cos(3y))-(35x^6)(3x^4y^2) = 12x^3y^3 cos(3y) - 105x^10y^2 See http://www.wolframalpha.com/input/?i=jacobian+of+(x%5E4y%5E3,+5x%5E7%2Bsin(3y))

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