Thursday
September 3, 2015

# Posts by STEVE

Total # Posts: 33,290

math
Since a = 1 r = 2 S4 = 1(2^4-1)/(2-1) = 15 S15 = 2^15-1 = 32768 So, the sum from S5 to S15 = S15-S4 = 32753
June 26, 2015

math
So far, 70% of your score is allocated as follows: .15*74 + .15*96 + .40*60.5 = 49.7 Since that is only 70% of your score, it's equivalent to 49.7/.70 = 70.1%
June 26, 2015

physics
since the sled is not accelerating, the net force acting on it must be zero. So, since the friction is .15*(30*9.8), that is equal to the force acting on the sled.
June 26, 2015

algebra
If there are x fill-in y multiple-choice z long-answer they have given us the following facts: x+y+z = 24 2x+6y+5z = 100 x+y = z Now you can solve for x,y,z
June 26, 2015

math
400\$ * 3tickets/5\$ = 1200/5 = 240 tickets
June 26, 2015

math
The curves intersect at (-2,2) and (1,-1) so, the area is the sum of all the little horizontal strips between the line and the parabola: ∫[-1,2] (2-y^2)-(-y) dy = ∫[-1,2] 2+y-y^2 dy = 9/2
June 26, 2015

math
x' = y√(y^2+2) so, the arc length s = ∫[0,1] √(1+x'^2) dy = ∫[0,1] √(1+(y^2)(y^2+2)) dy = ∫[0,1] √(y^4+2y^2+1) dy = ∫[0,1] √(y^2+1)^2 dy = ∫[0,1] y^2+1 dy = 4/3
June 26, 2015

physics
the mass of the rocket does not matter. Given a liftoff speed of v, the height h(t) = vt - 4.9t^2 The max height is reached when t = v/9.8, so we have v(v/9.8) - 4.9(v/9.8)^2 = 100 v = 44.27 m/s Or, you could just use the formula for max height h = v^2/2g and get v^2/19.6 = ...
June 25, 2015

Probability
Assuming a uniform population, the 1st person has a birthday. The 2nd has the same birthday with probability 1/365 same for the 3rd. So, ...
June 25, 2015

DTM
you never have said how many gallons (or liters) of gas (or petrol) have been used. Tough to figure mileage (or kmage) without that.
June 25, 2015

DTM
.50\$/km * 100km/day = 50\$/day not sure just what it is you want to know.
June 25, 2015

Algebra
If there were x more meets to go, and they won them all, then, since the wins = the losses 2+x = 10-2 take it from there. Note that the value of x is not the answer.
June 25, 2015

Math
I already see one error: gt = ln(v+1)
June 25, 2015

Math
dv/dt = g(1+v) dv/(1+v) = g dt ln(1+v) = gt 1+v = e^(gt) + c v = e^(gt) + c (diferent c) v(0) = 0, so c = -1 v = e^(gt)-1 now, v = ds/dt, so s = 1/g e^(gt) - t + c now, e^(gt) = v-1, so s = 1/g (v-1) - t + c since v = e^(gt)-1, ln(v)+1 = gt t = 1/g (ln(v)+1)) and so s = 1/g (v...
June 25, 2015

Math
.9*77 + .1*67 = 76 Look like it won't hurt too much. 1 point.
June 25, 2015

Algebra
revenue is price * quantity, so R(x) = x*p(x) = x(-.16x+320) = -.16x^2 + 320x Now just find the vertex of that parabola to locate maximum revenue.
June 25, 2015

Algebra
I think you are missing a minus sign on the x^2 term, since g = -32 ft/s^2 h(x) = 1/42 (-16/42 x^2 + 72.7x) = x/42 (-16/42 x + 72.7) h=0 when x=0 (ball is hit), and when x = 190.8 (ball lands) The symmetry of a parabola means that the ball is at its highest midway between the ...
June 25, 2015

math gr. 10
Two good solutions are provided by Reiny and MathMate in the related questions below.
June 25, 2015

maths
well, if y = sum(a_n x^n) y' = sum(n*a_n x^(n-1)) y" = sum(n(n-1)*a_n x^(n-2)) so, from the DE, we have sum(n(n-1)*a_n x^(n-2)) + 3x^2*sum(n*a_n x^(n-1)) - x*sum(a_n x^n) sum(n(n-1)*a_n x^(n-2)) + 3sum(n*a_n x^(n+1)) - sum(a_n x^(n+1)) sum(n(n-1)*a_n x^(n-2)) + sum((...
June 25, 2015

Math
polar can get kind of complicated, but this one's a piece of cake: y = t+4, so t = y-4 x = (y-4)^2 + 4(y-4) + 8 Now expand it out and note that it's just a parabola.
June 25, 2015

Math: Compounded Interest
just use your formula. For quarterly, that is 200(1+.05/4)^(4*1/4) = 202.5
June 25, 2015

Math - thx Reiny
Good catch. I felt vaguely uneasy with the way things worked out, but was in a hurry. No doubt Justine caught the slip on her own...
June 25, 2015

Math
r = 1/(3-4sinθ) (a) see http://www.wolframalpha.com/input/?i=r+%3D+1%2F%283-4sin%CE%B8%29 (b) r = 1/(3-4sinθ) r(3-4sinθ) = 1 3r - 4rsinθ = 1 3√(x^2+y^2) - 4y = 1 3√(x^2+y^2) = 4y+1 3(x^2+y^2) = 16y^2+8y+1 3x^2 - 13y^2 - 8y = 1 3x^2 - 13(y^2 - 8/...
June 25, 2015

math
maybe you should lie on the floor and kick your feet, too. Beats me what would come next. What kind of material are you studying, that they'd drop a sequence like that on you? Or are you just wasting everybody's time with lottery numbers?
June 25, 2015

physics
You know, when you log on here you see all these posts with subjects like math, science, psychology, English, etc. Why do you think that Cowdray Park will be interpreted as a school subject? work = force * distance So, just plug in your numbers.
June 25, 2015

how about you provide the function, instead of naming a file we cannot see? Is it p(t) = a*e^(kt) with suitable values of a and k?
June 24, 2015

Math
the properties of logs are the same as those of exponents. √2 = 2^1/2 because √2 * √2 = 2 and 2^a * 2^b = 2^(a+b) 2^1/2 * 2^1/2 = 2^1 = 2 And, 2^-n = 1/2^n so, 1/√2 = 2^-1/2
June 24, 2015

Math
4x - e^(-(4x-y+3)) = -e^(-2) e^(-(4x-y+3))= 4x + e^(-2) -(4x-y+3) = ln(4x + e^-2) 4x-y+3 = -ln(4x + e^-2) y = 4x+3 + ln(4x + e^-2)
June 24, 2015

Math
since y(2) = 2, e^(2-2) = -2+c 1 = -2+c 3 = c So far, so good. e^(x-y) = -x+3 x-y = ln(-x+3) y = x-ln(-x+3) Somehow you got an extra "-" sign in there
June 24, 2015

assuming in and out mean up and down, then I get -2-19+7 = -14 You have the bait 10 feet above the water!
June 24, 2015

math
θ=42°
June 24, 2015

Math - oops
June 24, 2015

Math
log(√x) = 1/2 log(x) since log(x^n) = n log(x) So, what you have is √36 = 6, so √72 = 6√2 So, assuming by log2 you mean log2, log26 + log26 + log22 but log22 = 1, so that is = 2log26 + 1/2 Now, what is log26? You don't have a log2 button on your ...
June 24, 2015

physics
Unless the pilot can track a speeding bullet, I don't see how he can take any of those measurements. I guess he could turn the gun backwards and fire it when passing over an observer. If the observer sees the bullets come straight down, the speeds are ok.
June 24, 2015

physic pls help
how long does it take to fall 45m? 4.9t^2 = 45 t = 3.03 seconds So, how fast do they have to be moving to cover the 15m in 3 sec? 5m/s How fast is 5m/s in terms we can really relate to? That's 100m in 20 sec. Great athletes cover 100m in about 10 seconds, so it's only ...
June 24, 2015

statistics
ummm that would be .3 + .12 * 1.3 = ?
June 24, 2015

physics
just solve for t in 24 + 24.5t - 4.9t^2 = 0
June 24, 2015

Physics
the max height is (v sinθ)^2/19.6 the speed at time t is √(Vx^2+Vy^2) = √((v cosθ)^2 + (v sinθ - 9.8t)^2) The speed at max height is just Vx = v cosθ So, find t when h(t) is half the max height. That is, when vsinθ t - 4.9t^2 = (v sinθ...
June 24, 2015

Algebra
Suppose there are x price decreases. so, price is 400-x membership is 300+3x revenue is thus (400-x)(300+3x) = -3x^2+900x+120000 So, just find the vertex of the parabola to determine price and max revenue.
June 24, 2015

math
friction coefficients? mass of man? force of man's steps?
June 23, 2015

English
2 and 4 are the same 1 and 3 are almost self-contradictory. If he kept in touch, that means he got in touch on a regular, continuing basis. You can't do that every day. So, 1 and 3 are really not good English.
June 23, 2015

algebra
if x is at 5%, the rest (30000-x) is at 9%. So, you want x in .05x + .09(30000-x) = .08(30000)
June 23, 2015

algebra
x^4 + 2x^3 - x^2 - 2x x(x^3 + 2x^2 - x - 2) x(x^2(x+2)-(x+2)) x(x^2-1)(x+2) x(x-1)(x+1)(x+2) I expect you can take it from there, yeah?
June 23, 2015

maths
if cot x = 3/4 sec x = 5/3 csc x = 5/4 So, plug in the values and see whether it's true.
June 23, 2015

maths
So, is it ever true? tanθ/(1+tan^2θ) = sinθ/cscθ tanθ/sec^2θ = sin^2θ sinθ cosθ = sin^2θ sinθ(cosθ-sinθ) = 0 θ = π/4
June 23, 2015

maths
If you can't spell theta you might as well just use x. secθ = 5/4 so, sinθ = 3/5 cscθ = 5/3 tanθ = 3/4 tanθ/(1+tan^2θ) = sinθ/cscθ (3/4)/(1+9/16) = (3/5)/(5/3) (3/4)/(25/16) = 9/25 3/4 * 16/25 = 9/25 12/25 = 9/25 Hmmm. I suspect a ...
June 23, 2015

Guru found Singh
If I said A product of two integers is 10. If one number is 5, find the other number. could you find the other? Follow the same step here.
June 23, 2015

Science
a = v^2/r, so .18 = v^2/5 Now just find v.
June 23, 2015

Differential Equation
as you know, |ai+bj| is √(a^2+b^2) and ai+bj + ci+dj = (a+c)i+(b+d)j so what do you get?
June 23, 2015

vectors
two sides are <8,6,-4> and <9,10,14> The cross product is <124,-148,26> Its magnitude 194.823 is twice the area of the triangle.
June 23, 2015

maths
well, all four angles add up to 360, so 30+50+d+d = 360 . . .
June 23, 2015

statiSTIcs
52 is 2 std above the mean of 44. So, look up Z=2 in your table, and subtract that from 1. Or, mosey on over to http://davidmlane.com/hyperstat/z_table.html and enter 2 in the "Above" box and it will calculate the Z value and show the tail of the graph.
June 22, 2015

Calculus
well, recall what you were told: The price(in dollars) p,and the quantity sold x obey the demand equation p=-1/10x+150 You found that maximum revenue R occurs at x=750, so p = -75+150 = 75
June 22, 2015

algebra
c = k-4 c+2 = (k+2)/2 + 11 c = 24
June 22, 2015

math
AB = 12, BC = 4, CD = 7, and DA = 15 Start off my assuming that the largest number is the whole line. That might not be so, but it's a good place to start. B must be to the right of C, since BC < CD That means we have ACBD. Check: AC=8 CB=4 BD=3 You just have to play ...
June 22, 2015

algebra
just find t when 5422(1.037^t) = 29000000 (I dropped 3 zeros on each side) 1.037^t = 5348.57 t = log(5348.57)/log(1.037) It'll be a while
June 22, 2015

algebra
You don't say whether the dividing fence is to be parallel to the river or not. If not, then let x be the length of the side parallel to the river. Then you have x+3y = 4700 so, x = 4700-3y The area is a = xy = (4700-3y)y = 4700y - 3y^2 The vertex of this parabola is at (...
June 22, 2015

algebra
same as the others. Give it a try. period
June 22, 2015

algebra
this is just like the river field. Why do you insist on saying "comma" and then writing the number with the comma? question mark
June 22, 2015

algebra
if the side parallel to the river is x, and the other two sides are y, you have x+2y = 9000 the area a = xy = (9000-2y)(y) = 9000y-2y^2 The vertex of this parabola is where you have maximum area. That is at y = 9000/4 You have y, so you can get x, and can find the area.
June 22, 2015

Algebra
why all the words, when you have the symbols? demand quantity at price x is p(x) = 1/40 x + 19000 The cost is C(X) = 15450x + 20000 (a) So, the revenue (price * quantity) is R(X) = xp(x) = 1/40 x^2 + 19000x (b) P(x) = R(x)-C(x) = (1/40 x^2 + 19000x)-(15450x + 20000) = 1/40 x^2...
June 22, 2015

Geometry
42 u2004-42-42-42-00_files/i0060042.jpg
June 22, 2015

Math
see related questions below
June 22, 2015

math
June 22, 2015

Math
If the number of 37,50,58-in tv's are x,y,z, then x = 2(y+z) y = z 1800x+2000y+4800z = 168000 Now just solve the three equations.
June 22, 2015

physics
F = ma = 1.2*10^3kg * (20m/s)/(5s) = 4.8*10^3 kg-m/s^2 = 4.8*10^3 N
June 22, 2015

Algebra
If the number of 37,50,58-in tv's are x,y,z, then x = 2(y+z) z = ? (which are equal?) 1800x+2000y+4800z = 168000 Fix the second condition, and then solve the three equations.
June 22, 2015

algebra
√42 By the way, your files cannot be seen anywhere except on your computer.
June 22, 2015

programming ( qbasic)
I did google searches for qbasic input to find how to do input and print qbasic math to see how math was done. It also showed the DIM statements and a FOR loop qbasic strings to find string functions like Val and CHR and ASC
June 22, 2015

programming ( qbasic)
DIM WORD AS STRING DIM SUM AS INTEGER INPUT "Enter a word: ", WORD\$ SUM = 0 FOR N=1 to LEN(WORD\$) SUM = SUM + ASC(MID\$(WORD\$,N,1)) NEXT N PRINT "Word value: ",SUM google is your friend. I have never used qbasic, but in about five minutes I found enough code...
June 22, 2015

Physics
you assumed g/min was gallon/minute Not so. It is grams/minute So, keeping track of the units, you want to convert volume to time: 196gal * 231 in^3/gal * (2.54cm/in)^3 * 1g/cm^3 * 1min/g = 741940 min = 1.41 yr Hmmm. check my math or your supposed answer
June 22, 2015

Math - not
I'm sure an acronym is not what you are after. An acronym is a word whose letters come from the words of a phrase represented, such as LASER - Light Amplification by Stimulated Emission of Radiation Maybe you are supposed to write a list using the letters of the word as in...
June 22, 2015

mathematics
type that into google or, what the heck -- use your calculator stop wasting time here with such nonsense.
June 22, 2015

Math velocity
The second ball hits when 60-4.9(t-2)^2 = 0, t = 5.5 v = 19.6(1 - 1/5.5) = 10.036 m/s So, you want v where 60 + 5.5v - 4.9*5.5^2 = 0 v = 16.04 m/s check:
June 22, 2015

math conversion
I don't know about Chinese, but from metric to English units, 1kg = 2.2046 lb so, now just multiply by the number of kg you have.
June 21, 2015

Algebra II
5x+12x+13x <= 120 30x <= 120 x <= 4 so, the shortest side can be no more than 20.
June 21, 2015

math-urgent
you have constant acceleration h" = -9.8 m/s^2 so, the speed is h' = -9.8t+Vo m/s Vo=20, so h' = -9.8t+20 h= -4.9t^2+20t+Ho Ho=20, so h = -4.9t^2+20t+30
June 21, 2015

math-urgent
the mass of the ball does not matter. The height as a function of time is h(t) = 30 + 20t - 4.9t^2 so, just find the vertex of the parabola, and solve for t when h=0. Just good old Algebra I.
June 21, 2015

calculus
each triangle has a base 2y. So, since the area of an equilateral triangle of side s is √3/4 s^2, our triangles have area √3/4 (9-x^2) Now all we have to do is sum up all the triangular plates of thickness dx, from -3<=x<=3. Or, because of symmetry, twice the...
June 21, 2015

Calculus AB
a) well, cosh(0) = 1 b) 211.49-20.96cosh(0.03291765x) = 70 20.96cosh(0.03291765x) = 141.49 cosh(0.03291765x) = 6.75 x = arccosh(6.75)/0.03291765 c) y' = -(20.96)(0.03291765x)sinh(0.03291765x) so, just plug in the values from (b). Use the graphs's symmetry to eliminate ...
June 21, 2015

maths
Angle RPQ is 75+30 = 105° Now just use the law of cosines to find the distance x from R to Q: x^2 = 32^2 + 24^2 - 2(32)(24)cos105°
June 21, 2015

Calculus
since the line 1-15x is the tangent line at (0,1), we could just find where |1/(1+3x)^5) - (1-15x)| < 0.01 -0.008353 < x < 0.008872 Using differentials, we have y(0) = 1 dy = -15/(1+3x)^6 dx So, if we want |dy| < 0.01, we need x such that 1/(1+3x)^5 - (1-15x) < ...
June 21, 2015

Calculus
However, given axis h, with 26 <= h <= 51 (why?) and angular speed ω, the height h(t) = h + 26sin(ωt) dh/dt = 26ω cos(ωt) so, solve for t when h=25, and then find dh/dt.
June 21, 2015

Maths Problem
their speed difference is 50m/min, so it will take Gerald 600/50 = 12 minutes to run the extra distance. So, how many laps does Gerald run in 12 minutes?
June 21, 2015

gips ghoman
fix the typo. 2nd equation has no "y" term. Then, note that 18 = 18x+18y and you can eliminate the 18x stuff.
June 21, 2015

jdt trignometric
using more conventional symbols, I assume we have tanθ = 7/24, in the 1st quadrant. So, cosθ = 24/25 I expect you can do the arithmetic now, eh?
June 21, 2015

algebra
If \$x is invested at 2.3%, the rest (80000-x) is at 3.1% So, adding up the interest, we get .023x + .031(80000-x) = 2000
June 20, 2015

ALGEBRA
If his rowing speed is r, and the current speed is c, then (r+c)/4 = (r-c)/3 48/(r+c) + 48/(r-c) = 14 c = 1
June 20, 2015

ALGEBRA
Let's say the cop's leaps are 4 ft, while the snatcher's are 3 feet, and the cop's leaps take 6 seconds, while the snatcher's take 5 seconds. So, after x seconds, the distances and times must match up: (x/6)(4) = (x/5)(3) + 72*3 x = 3240 So, it will take ...
June 20, 2015

pre-calculus
http://www.wolframalpha.com/input/?i=x%2F%28x^2-100%29 as you can see from the graph, the concentration appears to be negative until x=10. Then it explodes and then drops down. I cannot think what the vertical asymptote can represent, unless there's some delayed-release ...
June 20, 2015

Math
P(x) = 750x(20-x) So, since x is always positive, where do you think P(x) is negative?
June 20, 2015

Algebra
each graph is a line. You don't need to use y=mx+b to "start." 18x+3y=12 or, 6x+y=12 If x=0, y=12 if y=0, x=2 So, plot the points (0,12) and (2,0) and join them in a line. Using the Ax+By=C (standard) form is very convenient, since you can easily get both ...
June 20, 2015

Algebra
You don't have to use any particular form of the equation. In fact, this problem asks you to graph the lines, and solve the system of equations using the graphs. For example, http://www.wolframalpha.com/input/?i=plot+6x+-+3y+%3D+24+%2C+18x+%2B+3y+%3D+12+
June 20, 2015

pre-calculus
The horizontal asymptote shows that the level of medicine approaches a constant level over a long time. A vertical asymptote? Got me. The level of medicine is always finite. Of course, it might be helpful if you actually provided the function under discussion. Just sayin'
June 20, 2015

Geometry
so, why not just follow the steps described, and see which way produces the desired result?
June 20, 2015

algebra
you know that the vertex of the parabola y = ax^2+bx+c is at x = -b/2a. So, your maximum height is at t = 90/32 Just find h(90/32) Or, rewrite the equation by completing the square: h(t) = –16t^2 + 90t + 15 = -16(t^2-90/16 t) + 15 = -16(t^2 - 90/16t + (90/32))^2 + 15 + 16...
June 20, 2015

algebra - PS
Or, you can think of it like this: all lines of the form 3x – 4y = C are parallel to the line 3x – 4y = 8 So, plug in your point (0,4) and you have 3(0)-4(4) = -16 So, your new line is 3x – 4y = -16 which is the same line derived above with the point-slope form.
June 20, 2015

algebra
3x-4y=8 has slope 3/4 So, you want the line through (0,4) with slope 3/4: y-4 = 3/4 (x-0)
June 20, 2015

algebra
If there were g general tickets, then the rest (416-g) were reserved. Now add up all the receipts: 8g+14(416-g) = 4840 Now just solve for g.
June 20, 2015

ST MICHAEL NURSERY SECONDRY AND PRIMARY SCHOOL KONTAGORA
force = mass * g work = force * distance power = work/time
June 20, 2015

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