# Posts by Steve

Total # Posts: 51,218

Maths
180,600.00 (1+.0625)^6

calculus
arctan(2x^2y)=x+4xy^2 Using the good old product and chain rules, we get 1/(1+(2x^2y)^2) * (4xy + 2x^2y') = 1 + 4y^2 + 8xyy' Now just collect terms and solve for y': 16x^4y^4 + 4x^4y^2 + 4y^2 - 4xy + 1 - ------------------------------------------- 2x(16x^4y^3 - x...

maths
as with any parallelogram, the area A = bh base * height

maths
Well, the area of the rhombus is half the product of the diagonals. Draw a diagram and see where that takes you.

Last math question of the night plz help quickly!
these are both sloping straight lines. So, they extend forever in all directions. The domain and range are both (-?,?)

algebra
9r^2-30r+21 = -4 9r^2-30r+25 = 0 Note that 9 and 25 are perfect squares, so a good thing to try is (3r-5)^2 = 0 Yep, that's it. So, there is a double root of x = 5/3

Math
Note that y decreases by 5 when x increases by 1. So, start with y = -5x Now note that y(0) = -1, so you need to adjust the function a bit: y = -5x-1

Math
5x = 2x+9 Find x. There are 2x cats.

English
COMplex is a noun comPLEX is an adjective Similar to PROtest: noun proTEST: verb (though you'd never guess it if you listen to the news...)

English
conjunction

Chemistry
4Bi + 3O2 = 2Bi2O3

Math
The slant height is 5!! Don't you know a 3-4-5 right triangle?

Math
Huh? 3^2+4^2 = 9+16 = 25 = 5^2 get a grip, guy!

Math
drop an altitude to the center of the base. Then, looking from the side, you will see that 3^2 + 4^2 = s^2

Mathematics
You know nothing about MN, except that it bisects PQ. It could have a long piece on one side of PQ, and be short on the other.

Math Algebra
recall that for y = ax^2+bx+c the axis and vertex always lie on the line x = -b/2a

Math
If the AP has 1st term=x difference=y a = x+(p-1)y b = x+(q-1)y c = x+(r-1)y Now just plug and chug ... and chug ... and chug

Maths
since the speed (km/hr) is constant, 240/2 = 600/x

calculus
The asymptote is y=0 So, revolving the area around the x-axis, and using symmetry, v = 2?[0,?] ?y^2 dx = 2?[0,?] ?(1/(x^4+1))^2 dx = 3?^2/(4?2) It looks hard, and it is complicated, but you can start off by noting that x^4+1 = (x^2+1)^2 - 2x^2 and then factor that as the ...

Math
x(x-2p)=3(x-p) x^2-2px = 3x-3p x^2-(2p+3) + 3p = 0 for rational roots, the discriminant must be a perfect square. That is, (2p+3)^2-12p = 4p^2+12p+9-12p = 4p^2+9 must be a perfect square. p=2 is one solution check: x(x-4) = 3(x-2) x^2-7x+6 = 0 (x-1)(x-6) = 0 Not only rational...

math
18(2+5) = ?

math
Lat a = 2^(x-2) b = 5^(y-2) Then you have 4a-25b = 3 a+b = 2 Hmmm. I suspect a typo, since the results are strange.

maths
Draw a radius perpendicular to the chord. Draw a radius to the end of the chord. Now you have a right triangle where x^2+6^2 = 8^2

Math
so, divide the annual rate by 12 to get the monthly rate.

Math
well, how many months in a year?

MAth
so, multiply the daily rate by 365 to get the annual rate.

MAth
well, how many days in a year?

Maths
B is the midpoint of AC. So, its coordinates are the average of the endpoints. So, if C=(x,y) we have (x+4)/2 = 1 (y+5)/2 = -1 Now just solve for x and y.

calculus
Just use the product rule y = ?x lnx y' = lnx/(2?x) + 1/?x y" = 1/(2x^(3/2)) + lnx((-1/4)x^(-3/2)) + (-1/2)x^(-3/2) = -lnx/(4x^(3/2))

Maths
P = 2(4+6) A = 4*6

algebra
Just add up the acid content: .45x + .90(120-x) = .60(120)

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

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...

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

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?

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