# 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**

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?