# Posts by Steve

Total # Posts: 54,303

physics
I agree. I used the law of cosines.

m.p.bord maths subject
Not sure what you mean, but I'll guess Ax+By = a-b Bx-Ay = a+b ABX+B^2y = B(a-b) ABX-A^2y = A(a+b) (B^2-A^2)y = B(a-b)-A(a+b) y = (B(a-b)-A(a+b))/(B^2-A^2) Now you can find x. If that's not what you had in mind, you'd better explain it a bit better.

Math
Review your basic trig functions. You will see that the height h can be found using (h-6)/70 = tan 24°

harmonic progression
a useful sum to know is n ?(2k-1)^3 = n^2(2n^2-1) k=1

Physics
Looks right to me.

Physics
did you remember to use °K ? Show what you did, eh?

Physics
1m^3 * 10^6cm^3/m^3 * 8.96g/cm^3 * 1atom/(1.1*10^-22 g) = ? atoms the molar mass does not come into play

geometric progression
since sum(k=0..n) 2^k = 2^n - 1 your series is 1 + 3 + 7 + 15 + ... = (2-1)+(4-1)+(8-1)+... = sum(k=1..n) 2^k - n see where that takes you

Astronomy
B affects the view at different times during the year. Better think again; look at the words "every night"

English
thank you

English
"Know now then thyself, presume not God to scan;/The proper study of mankind is man." Which of these is nearest in meaning to the word presume, as it is used in the passage above? - hasten - invent - cease - attempt My answer is hasten but I thought about attempt

math
Nope. There are 4 variables. Knowing only two make it impossible to pin down the other two.

algebra
are you kidding? It will have to be at least the \$820 you started with, right?

Math can someone help
Where did you get the 0? With the sets A and C you just gave, AUC = {1,2,3,5,7,10} A?C = {2,5,7,10} Note that AUC = A and A?C = C because C is a subset of A You won't get any 0 elements unless you start working with B.

Math can someone help
A?C is the intersection of A and C. That is, all the elements which appear in both A and C. So, what do you think?

math
(12k^-2 (k^-3)^-4)/(6k^5) = (12k^-2 * k^12)/(6k^5) = (12k^10)/(6k^5) = 12/6 * k^10/k^5 = 2k^5 What do you get for the other one?

Algebra
If there are x spots now, then .40x = 24 x = 60 So, there will be 84 after completion.

g.p
If r = 2, Sn = a*(2^(n-1)-1) so, if b = a, it could be a gp a,2a,4a,8a,...2^(n-1)*a Sn = a(1+2+...+2^(n-1)) = a(2^n-1) = a*2^n-a

Chemistry
well, 2.1*10^24 molecules = (2.1*10^24)/(6.02*10^23) = 3.488 moles of O2 4/7 that many moles of NH3 are needed multiply that by the molar mass of NH3.

Physics
so, it took 3 seconds to go up, and 3 to come down. So, with initial velocity v, v-10*3 = 0 v = 30 h = 30t-5t^2 Now plug in t=3

English
"The number of souls in Ireland being usually reckoned one million and a half, of these I calculate there may be about two hundred thousand couples whose wives are breeders, from which number I subtract thirty thousand couples, who are able to maintain their own children...

English
Thank you

English
Read this excerpt from Alexander Pope's The Rape of Lock "No common weapons in their hands are found/ Like gods they fight l, nor dead a mortal wound.../ See, fierce Belinda on the Baron flies/ With more than usual lightning in her eyes..." This account of the ...

Chemistry
note that each molecule (or mole) of O2 produces two molecules (or moles) of H2O

Chemistry
Balance the equation: 2H2+O2 = 2H2O So, you have half as many moles of O2 as of H2 So, 1/2 the volume.

Physics
just plug in your numbers for the formula for a trajectory. The height y = 1.2 + (tan26°)x - 4.9/(40.4 cos26°)^2 x^2 is y(127) >= 3.5?

math
3.25 * (5 5/6) = 13/4 * 35/6 = 455/24 = \$18.96

English
correct (all the others are not even verbs)

pre calculus- math
e^.12t = 3

Algebra I
Huh? There's nothing to solve. Just evaluate the numbers... ½ (900kg)*(20m/s)^2 = ½(900)(20)^2(kg)(m/s)^2 = (450*400) kg-m^2/s^2 = 180000 N-m = 180KJ

Chemistry
Since the force is the same, the height will be inversely proportional to the densities (because the cross-section has the same area) -- think about it: half as dense (half as much mass), twice as high. So, if H is the height of mercury, the height h of iodide obeys h = (13.6/...

math
Looks like 3 to me: HHHHHTTTTT HHHHHHHHTT HHHHHHTTHT HHHHHHHHHH

Math
no idea. what does R have to do with u and r? Is R=r' ? If so, then #1: R = r' = u-r = {2,4,6,...} #2 u-r = {...-4,-2,0,2,4,...}

Algebra 2
huh? Does no one see that "ln" there? ln(x-4) < 6 since e^x is increasing, a<b ==> e^a < e^b x-4 < e^6 x < 4+e^6

Math
You want to get the variable all by itself. So, if you have 2x, you want to divide by 2, since 2/2 = 1, and that leaves you with 1x, or just x. -13x=-65 x = -65/-13 x = 5 multiply by 7, since 7/7=1 r/7=-8 r = -8*7 r = -56 add 10, so b is left alone: b-10=-14 b = -14+10 b = -4 ...

Math
so try posting a few problems you can't solve. Also, google is your friend. Looks for examples of your key topics.

Math - eh?
If this is reverse Polish notation, there are too many operators...

Math
since x = y+9, you want the maximum value of (y+9)y^2 = y^3+9y^2 Not sure what tools you have for finding the maximum, but a quick derivative will show that it is at x = 3 y = -6

Math
just multiply the coordinates by the scale factor!

Math 7a
3a - 4 <= 5 3a <= 9 a <= 3 do the same steps you use to solve an equation

Math 7a
wow - what a lot of text and bad formatting and non-standard font use! n/-3 + 5 > 4 n/-3 > -1 n < 3

Math
draw a dashed line at y=2 shade the region above it

math
4/15 + x + 3/5 = 1 4/15 + x + 9/14 = 15/15 ...

Human Kindness
You cannot. You can only encourage them.

5h - 9 = -16 + 6h subtract 5h from both sides add 16 to both sides now what do you get?

Math
perfect vision!

Math - eh?
you have mismatched brackets what are the spaces supposed to mean? "2f 3 -14 3" makes no sense and there's no "=" sign to make an equation. Geez - check what you write, willya?

physics
PV=kT, so you want (1.02*10^5)(.00661^3) = P(.00650^3) P = 1.07*10^5

Math
so, start with the smallest 3 primes: 2*3*5=30 So, any multiple of 30 can be divided by those three primes. Try using other primes, and see what you think ...

Math
recall the properties of multiplication (-w)(-10w^3) = (-w)(-10)(w^3) = (-1)(w)(-10)(w^3) = (-1)(-10)(w)(w^3) = 10w^4

Calculus
the slope of 3f^2 is 6f f' = 6*5*7=210 So far, so good. 3f^2(3) = 3*5^2 = 75 So, you want the line through (3,75) with slope=210 y-75 = 210(x-3) your surmise is correct

Math
L = F/2 - 5 F = 2(L+5) L + 2(L+5) = 79 Lindsey is 23 and her father is 56

math
2/3 < x/5 < 6/7 10/3 < x < 30/7 3.3 < x < 4.3 Looks like x=4

math
y=m is a horizontal line x=n is a vertical line y=x is a sloping line (a) perpendicular (b) neither

MATH
|x+3| ... shift left 3 -|x+3| ... reflect over x-axis -|x+3|-2 ... shift down 2

PreCalculus
I got my answer from the graphs of the functions: http://www.wolframalpha.com/input/?i=-5e%5E(-4x%2B2)+%2B3%3D+1%2F2+log(1%2Bx%5E2) What I don't understand is how you can evaluate log(sqrt[x^2+1]) without knowing x ... I think when they said to use your calculator, they ...

PreCalculus
Hmmm. I get 0.642538 I'm confused on how you got 1/2 log(1+x^2) = .707486674 in any base, since you don't know x.

Direct Variations
y/x = 10.4/4 = 2.6 y = 2.6x Geez! 3.4*4 = 13.6 Maybe you could show your work, so we can see where you are taking a wrong turn. Or are you just guessing so we'll think you tried?

Algebra
Hmmm (2/3)*3 = 2, not 7 y/x = (7 1/2)/3 = (15/2)/3 = 15/6 = 5/2 y = 5/2 x You need to learn to check your answers. At least do a sanity check. 2/3x < x, so how could y = 2/3 x relate 3 and 7?

Math
(a) just substitute 25 for P (b) solve 50(P-2) = 800

math
Is this a continued fraction? If not, do you mean what you typed? 2?3 + 9÷?3 + 12÷?3 ... = ?3 (2+3+...+10) I'm sure you can add up an arithmetic sequence, right?

Math
Each year she gets 3.5% or 0.035 time the amount invested. So, after 3 years, that's 4500 * 0.035 * 3 Review your formula: I = Prt, right?

Computer
i=0 while (i>=0) { read i,j print i,j } Not sure whether "in order" means in the order given, or smallest first. If you need to sort them, I'm sure you can fill in the missing step. You also say you want 2 numbers, then talk about the "trio." ??? ...

math 7/8 grd
I don't like that subtraction. Subtracting a larger value gives a smaller result. For example, suppose we have small x > 0 d = -7+x > -7 d+s = -7+x+s > -3 x+s > 4 s > 4-x So, suppose x = .1, and thus d = -7+.1 = -6.9 If s > 4-.1 = 3.9, ok, since d+s >...

Pre algebra
Hard to tell just what you meant, but just adding what you wrote (assuming all dimensions are in cm), then p = 8 + 9x + 9 + 9x = 16+18x ...

Mathematics
(a) P(x,y) = 31(20-x)+74(10-y) (b) P(9,4) = 31(20-9)+74(10-4)

geometry
If the 2nd circle's line is a diameter of 14, then its area is done the same way: pi*7^2 = 49pi By the way, if the diameter is 25, the radius is 12.5, not 12. Unless you can tell more about the line and its relation to the 2nd circle, I can't figure out what it is you ...

algebra
|x+3| ... shift left 3 -|x+3| ... reflect over x-axis -|x+3|-2 ... shift down 2

Math helppp
Just use the sum-to-product formulas... sin(a)-sin(b) = 2cos((a+b)/2)sin((a-b)/2) cos(a)-cos(b) = -2sin((a+b)/2)sin((a-b)/2) So, let a=8? b=10? and you have sin(8?)-sin(10?) = 2cos(9?)sin(-?) cos(10?)-cos(8?) = -2sin(9?)sin(?) now it is clear to see that 2cos(9?)sin(-?) = cot(...

physics

calculus for economics
revenue = price * quantity break-even is when revenue = cost

Math
clearly the 4.3m ladder must span the 1.6m distance. Its height is thus h = ?(4.3^2-1.6^2) So, the length of the other ladder must be ?(h^2+5^2) = ?(4.3^2-1.6^2+5^2) = 6.4

physics
3*10^5cm * 1rev/(65? cm) = ? rev

algebra 1
25 times the cost of sending one message ...

Maths
103 12/37 tsp.

Math Unit 3
geez - you have the proof. Just fill in the blanks.

Algebra
since time = distance/speed, if the turtle's speed is x m/min, then since .5 m/hr = 1/120 m/min 21/x = 8 + 21/(x+1/120) + 4 The turtle moves at 7/60 m/min = 7 m/hr The hare moves at 1/8 m/min = 7.5 m/hr you can check the times to verify that they work out.

Math/calculus
use your sun-to-product formulas, and this drops right out.

Math helppp
wolframalpha is your friend. See http://www.wolframalpha.com/input/?i=3cos+(4pix+-pi%2F2)+-2 f(x) = 3cos(4pi(x - 1/8) -2 So, it is just the graph of cos(x) shrunk horizontally by a factor of 4pi shifted right by 1/8 stretched vertically by 3 shifted down 2

Calculus
It appears so. y and z are functions of t, so you need the quotient rule.

Precalc
You want f(±?) = +? This is impossible, since there is a horizontal asymptote at y=0. hole and vertical asymptote: (x-1) / (x-4)(x-1) This also gives y=0 as the vertical asymptote, since the denominator has higher degree than the numerator. not sure what has the ...

math
No, the % increase is the change divided by the original amount: 880/1195 = 0.736 = 73.6% check: 1195 * 1.736 = 2075 and besides, 880/100 = 8.8 = 8800% consider. 6 is 50% more than 4, because 6-4=2 and 2/4 = 0.50 = 50% 4 * 1.50 = 6

Linear Equation
2x + x/2 = 20

Math
x+y-z= 6 2x-y +z=-9 X-2y+3z=1 using substitution, you can do: from #3, x = 2y-3z+1 Using that in #1 and #2, you get (2y-3z+1)+y-z = 6 2(2y-3z+1)-y+z = -9 3y-4z = 5 3y-5z = -11 Now, using 3y=4z+5, (4z+5)-5z = -11 -z = -16 z = 16 3y = 4*16+5 = 69, so y = 23 x = 2*23-3*16+1 = -1 ...

geometry
42

maths
42

math
I assume you mean ?(x+10) + ?(x-17) = 9 ?(x+10) = 9-?(x-17) x+10 = 81-18?(x-17)+x-17 18?(x-17) = 54 ?(x-17) = 3 x-17 = 9 x = 26 check: ?(26+10)+?(26-17) = ?36+?9 = 6+3 = 9 nope

Trigonometry
since sin(?/6) = 1/2 and sine is negative in QII and QIV, 2x = 7?/6 or 11?/6 + 2n? x = 7?/12 + n? or 11?/12 + n?

Math
j = m+4 = 8+d mp = 16+jd clearly, Jack is not a twin with either Mark or David. So, Paul is one of the twins. Either p=j or p=m or p=d See what you can do with that. You now will have three equations in three variables, after getting rid of p.

Maths
know what? Check what you wrote and turn it into something useful ...

Math
(3/10 in) / (7/8 mi) = (3/10) / (7/8) in/mi = 3/10 * 8/7 in/mi = 24/70 = 12/35 in/mi

Math Help
b(ab) = b*a*b = a*b*b = ab^2

Chemistry
how many moles of H2O in 135L (at 18g/mole)? half that many moles of H2SO4 Now use Avogadro's Number to find # molecules.

Maths
suppose you change the numbers to make the method easier? How much do you need to subtract from 12 to make 3? 12-3 = 9 so 12-9 = 3 get it?

John
well, if you meant 2x^4-3x^3-7x^2+12x-4, it is a quartic, but can easily be factored into two quadratic factors. It is (x^2-4)(2x^2-3x+1) which are both easily solved.

John
not a quadratic. A cubic. There are no rational roots, so what techniques do you have for solving polynomials?

Maths
depends on the total distance.

maths
3:1 means 4 parts 12/4 = 3 3*3:3*1 = 9:3 do the other in like wise.

Algebra
50 by 25 As with all such problems, the maximum area is when the fence is divided equally among lengths and widths. x+2y = 100 area = xy = x(100-2x) now just find the vertex of that parabola.