Friday
September 4, 2015

Posts by STEVE


Total # Posts: 33,310

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

algebra
Just use the distributive property: (3x+4)(x-2) (3x)(x-2)+(4)(x-2) 3x^2-6x+4x-8 3x^2-2x-8 Do #2 the same way Review the examples in your text, or google binomial multiplication
June 20, 2015

Algebra
from eq #1, you know y = 10-x substitute that into eq #2 and you have 5x-3(10-x) = 15 Now you can find x, and then y.
June 20, 2015

Math
you know: 7a+4.5c = 64 a = c-4 now just solve for a and c.
June 20, 2015

ALGEBRA
after each drain-fill cycle, there is 0.8 the amount of wine as before. So, after 20 cycles, the wine remaining is 20(0.8^20) liters
June 20, 2015

Ndmc - redux
Eh? I read it that the car passes the bus just as the bus starts to move. The car has constant speed, so at some point the accelerating bus will overtake the car. I haven't checked the math above, but the problem makes sense to me.
June 20, 2015

algebra
|4x+4| = 3 |x+1| = 3/4 x+1 = ± 3/4 x = -1 ± 3/4 x = -7/4 or -1/4 So, -1/4 is correct, as seen by using it: |4(-1/4)+4| = |-1+4| = |3| = 3 you can verify -7/4 for yourself.
June 19, 2015

algebra - ouch
I did check the other answer. Sure enough, √1 + 9 = 10 and I thought, "That's ok." Good catch. I had expected an extraneous root, and was surprised that there "wasn't" one.
June 19, 2015

algebra
Did you actually try using your values to see whether they satisfied the equation? √(10-x) + x = 8 √(10-x) = 8-x 10-x = x^2-16x+64 x^2-15x+54 = 0 (x-9)(x-6) = 0 x = 6 or 9 should have showed your work, so we could see what went wrong.
June 19, 2015

Graduated :math
I predict 67,07,71,69,76
June 19, 2015

algebra 1
standard form is Ax+By=C You can rearrange things to have 0.2x - y = 0.3 That's close, but we want integers. Now, how do you get rid of those pesky decimals?
June 19, 2015

Probablity
total marbles: 15 so, P(black,black) = 4/15 * 4/15
June 19, 2015

math
hint: any number ending in 0 or 5 is a multiple of 5.
June 18, 2015

math
actually, I get 14% The decrease was $11.71 11.71/80.77 = .1449 which is closer to .14 than .15 Pick 0.14 - 0.14 is 14% just expressed as a decimal. The wording is not optimal, but the two values are identical.
June 18, 2015

statistics
in your Z table you can easily find P(Z>1.05) also, P(Z>2.05) So, you just want P(Z>1.05) - P(Z>2.05) or, you do it the other way: P(Z<2.05) - P(Z<1.05) even easier, go to http://davidmlane.com/hyperstat/z_table.html and specify Z between 1.05 and 2.05 You ...
June 18, 2015

Algebra 2
1) x y d1 d2 d3 d4 0 8 1 7 -1 2 20 13 14 3 83 63 50 36 24 4 256 173 110 60 24 5 623 367 194 84 24 6 1292 669 302 108 24 Note how the 4th difference column is all 24 - 4th derivative of x^4 = 24 8^log_8(x) = x exponentiation and logs are inverse operations. b^log_b(x) = log_b(b...
June 18, 2015

Math Geometry
the sun rises 90° in 6 hours. That's 15°/hr So, at 11 am the angle of elevation of the sun is 75° If the shadow's length is s, then s/8 = cot75°
June 18, 2015

geometry
The area of all the exposed faces is 2(10*12 + 10*3 + 12*3) = 372 in^2 add to that the 7 in^2 of overlap.
June 18, 2015

Maths
8*6.50 + 4*2.10 ---------------------- 8+4
June 18, 2015

System of Equation
what methods of solution have you discussed?
June 18, 2015

Math (Need help Urgent)
#1 just solve for x in 4x-12 = -x^2+15x Then you can get y. #2 same thing. Just solve x^2-4 = 2x-4 to get x, then you can evaluate y.
June 18, 2015

math
you have to ask yourself. If a man can do the job in m hours, how much can he do in one hour? 1/m So, 2 men can do 2/m of the job in one hour. Same for the 6 boys. So, since they all can complete the job in 3 hours, in one hour they have done 1/3 of the job. You have to think ...
June 18, 2015

math
oops. I meant 9 men can do it in 2 hours.
June 18, 2015

math
2/m + 6/b = 1/3 1/m = (3/2)/b m = 18. That means one man can cut the field in 18 hours 2 men can do it in 9 hours
June 18, 2015

Math (PLEASE HELP!)
#1 eliminate y by equating the two: 2x^2-2x-3 = -x^2-2x-3 Now solve for x, and then you can get y #2 same thing #3 again, use the discriminant. We want kx^2-5x+2 = -3x+4 kx^2-2x-6 = 0 The discriminant is 4+24k
June 18, 2015

Math (PLEASE HELP!)
#1 well just solve -0.15(x-13)^2+7.6 = 7 just the usual quadratic stuff. #2 The discriminant gives this information. b^2-4ac: <0 no roots =0 1 root >0 two roots
June 18, 2015

Math (PLEASE HELP!)
(x+y)(x-y) = 24 x^2+y^2 = 74 you want some place where the tangent to the parabola has slope = -2 6x+4 = -2 x = -1 so, y=-2 The tangent line at (-1,-2) is y+2 = -2(x+1) y = -2x-4 b = -4 see http://www.wolframalpha.com/input/?i=plot+y%3D3x^2%2B4x-1%2C+y+%3D+-2x-4
June 18, 2015

Algebra
|z|^2-2z*+iz = 2i letting z = x+yi, x^2+y^2 - 2(x-yi) + i(x+yi) = 2i x^2+y^2-2x+2yi+ix-y-2i = 0 (x^2+y^2-2x-y)+(x+2y-2)i = 0 so, now just solve x^2+y^2-2x-y=0 x+2y = 2 x = 2-2y (2-2y)^2+y^2-2(2-2y)-y=0 5y^2-5y = 0 y = 0 or 1 so, x = 2 or 0 z = 2, i
June 18, 2015

Calculus
after t seconds, Q(t) = 9*0.996^t Now just solve for what you need.
June 18, 2015

Math
You want x where 3.00(x) + 4.25(8) = 4.00(x+8)
June 17, 2015

math
26 total marbles, so P(red,yellow) = 14/26 * 12/25
June 17, 2015

math
just divide both sides by 19.2L
June 17, 2015

calculus
It might help if you actually supplied the function. Clearly it looks something like -100x^2 --------------------- (x+10)(x-10)
June 17, 2015

logical statements-urgent
We want the truth table to look like this: PQR S TTT F TTF F TFT F TFF F FTT F FTF T FFT F FFF F Looks like it reduces to Q&~(P|R)
June 17, 2015

math
1/3 + 4/9 = 7/9 that help?
June 17, 2015

physics
this is one of the most basic setups. Clearly you need to do some reading. series: R = 1+2+3+5 = 11 parallel: 1/R = 1/1 + 1/2 + 1/3 + 1/4 R = 12/25
June 17, 2015

Calculus
Let side x be parallel to the barn. Then x+2y = 34 a = xy = (34-2y)y = 34y-2y^2 da/dy = 34-4y max area when da/dy=0, or y=17/2 So, the pen is 17 by 17/2 As usual, max area is when the fencing is divided equally among lengths and widths.
June 17, 2015

Finite Math
what do we know? if we let x = # dipped bananas y = # dipped apples z = # dipped strawberries so, to produce such a mix, we need 6x+6y+z = 60 3x+4y+z = 42 equating z, we wind up with 3x+2y = 18 So, let's see what we can do, using only integer values: x y z 0 9 6 2 6 12 4 3...
June 17, 2015

Physics
Recall that the range R = (v^2 sin2θ)/g so, just plug in your numbers.
June 17, 2015

math
the ones digit is 0,2,4,6,8 the 1000's digit is twice the one's, so must be 0,4,8 so far we have xx0xx0 or xx4xx2 or xx8xx4 now add 3 and we have 3x0xx0 7x4xx2 Now fill in the x's with whatever you want
June 17, 2015

Mathematics
r^4 = (1/4)/4 = 1/16 r = 1/2 so, the GP is 4, 2, 1, 1/2, 1/4
June 17, 2015

physics
velocity of ?
June 17, 2015

algebra
not so. Just pick a,b,c so that b^2-4ac is positive. f(x) = -x^2-10x-3 b^2 is positive whether b is positive or negative. It was all good until the last line. That's just rubbish.
June 17, 2015

Calculus
As I recall, you need Newton's law of cooling, which in this case would be T(t) = 2+23e^(-kt) where we try use a positive k. T(10) = 17, so 2+23e^(-10k) = 17 k = 0.0427 and we have T(t) = 2+23e^(-.0427t) So, after 30 minutes, T(30) = 2+23e^(-.0427*30) = 8.388 When T=4, we ...
June 17, 2015

Calculus
well of course if T(t) = 2+23e^kt T(10) will not equal T(30) You sure they're both supposed to be 17? So, what was the original problem?
June 17, 2015

math help please
company paid .80(2300)-250 Carol paid 250+.20(2300)
June 17, 2015

science chemistry
Since 1 dm^3 = 1L, .125 mol/dm^3 = .125M solution So, the 250mL amount needs .125*.250 = 0.03125 moles of KOH multiply that by the molar mass of KOH to get the number of grams.
June 17, 2015

science
Since weight varies directly with mass, Darren's weight would be half as much as on earth, given the same radius of the planet.
June 17, 2015

Chemistry
because each molecule contains 8 atoms. When figuring the mol wt, you need to use the number of molecules, not atoms.
June 17, 2015

Maths
depends on what you consider strengths. I suggest you list the various properties, and then decide what you consider to fit the bill.
June 17, 2015

algebra
try the quadratic formula: x = (-3±√(3^2+4*2*6))/4
June 16, 2015

trig
It occurred to me this might be a physics problem: sin(ωt-π)+sin(ωt+π) = -2sin(ωt)
June 16, 2015

trig
Not sure what the f is doing in there, but recall that sinA + sinB = 2sin((A+B)/2)cos((A-B)/2) I think you got too many π's floating around in there, as well. sin(x+π) = sin(x-π) = -sin(x)
June 16, 2015

Math
3*16 + 1.5*16 + 1*2 + 1 + 3*4 = 87
June 16, 2015

algebra
Sorry. That cannot be reduced. Assuming you mean (2x+1)/(4x^2+8x+5)
June 16, 2015

Algebra 2
draw the graphs as usual. Shade the area above the first. Shade the area below the second. Where the two shaded areas intersect is the solution. Note that the curve is included in the 1st, but excluded from the 2nd. http://www.wolframalpha.com/input/?i=plot++y+%3D+-x^2-8x-12+%...
June 16, 2015

Algebra
20-|7x+1| >= 6 |7x+1| <= 14 |x + 1/7| <= 2 x∊[-15/7,13/7] http://www.wolframalpha.com/input/?i=solve+20-|7x%2B1|+%3E%3D+6
June 16, 2015

Algebra
if |x-h| < n, that means that h-n < x < h+n |7-8x| < 10 | 7/8 - x| < 5/4 so, 7/8-5/4 < x < 7/8+5/4 -3/8 < x < 17/8 or, x∊(-3,8,17/8)
June 16, 2015

Maths
using the common difference of the AP, you know that x-2 = y-x Using the common ratio of the GP, you know that (x-1)/2 = y/(x-1) So, solve those two equations to get x and y.
June 16, 2015

Algebra
Read what I wrote. I guarantee that you will find the answer.
June 16, 2015

Algebra
well, you have 2m(n-8) - 7n So, if you want a common factor of n-8, you would need 56 That would give you 2m(n-8) - 7n + 56 = 2m(n-8) - 7(n-8) = (2m-7)(n-8)
June 16, 2015

pre-calculus 11
that is correct, except that you seem to be a bit fuzzy on how apostrophes are used. . .
June 16, 2015

Algebra
well, geez. You cant solve 3k+50 = 0? k = -50/3 (25 - 50/3 i)*(3+2i) = 325/3 which is a real number
June 16, 2015

Algebra
(25 + ki)*(3+2i) = 75+3ki+50i-2k = 75-2k + (3k+50)i So, you need 3k+50 = 0, since real numbers have zero imaginary part.
June 16, 2015

pre-calculus 11
Looks good to me.
June 16, 2015

Algebra
Hint: slope-intercept: y = mx+b point-slope: (y-k) = m(x-h) standard: Ax+By = C rise-run: ? never heard of it.
June 16, 2015

Math
If the area of the deck is 3 times the pool, then the total area of pool+deck is 4 times just the pool. If the width of the deck is w, you need (3+2w)(4+2w) = 4(3)(4)
June 16, 2015

pre-calculus 11
The round trip is 5400, so each half is only 2700 km. So, I get 2700/x + 2700/(95+x) = 7.6 x = 666 km/hr
June 16, 2015

math
I get the b and h for the triangular bases, but cannot figure out how the length can be both 7 and 15. Maybe you can clear that up.
June 16, 2015

Maths
If the depth is x cm, then since 1L = 1000cm^3, you have 100*140*x = 275*1000 x = 10.64 cm
June 16, 2015

pre-calculus 11
If you use some parentheses to properly specify the numerators and denominators, I think you have a typo and meant -x/(x-3) + 2x/((x+2)(x-1)) * ((x-2)(x+2))/((x-3)(x+3)) As usual, do multiplication before addition. In effect you have -x + y * z Do the y*z first, giving you -x...
June 16, 2015

pre-calculus 11
no, that would mean 8 <= t <= 16 That is an 8-hr window centered at 12:00 You want |10-t| <= 2
June 16, 2015

sgmic
I think you have it wrong: tan 3θ = tan(θ+2θ) tan 3θ = (tanθ+tan2θ)/(1-tanθtan2θ) tan3θ(1-tanθtan2θ) = tanθ+tan2θ tan3θ - tanθtan2θtan3θ = tanθ+tan2θ tan3θ - tan2θ - tan&#...
June 16, 2015

math
well, geez. Just list the even digits which sum to 12: 048 246 in whatever order you want to use them. Then sprinkle the 8's everywhere else.
June 16, 2015

Math
as you say, y = 70-2x, and the area a = xy = x(70-2x) You found the roots of that function which is where the area is zero! The vertex of a parabola is midway between the roots, at x = 17.5 So, y=35 and the maximum area is indeed 612.5
June 16, 2015

Math
If the digits, reading left to right, are abcde, then we are told b = a-2 b = c+2 So, abc are consecutive descending odd numbers. d = e+2 e = c-4 Looks like all 5 digits are in order: 97531
June 16, 2015

math
1/(2/7) = 7/2 So, there are 5/2 hours left to go.
June 16, 2015

Geometry
I must be missing something here. If AB and CD are diameters, then AD = BC, since the diameters must intersect in the center of the circle. No idea where E is.
June 16, 2015

Mathematics
see the related question below.
June 16, 2015

cubic function
That is clearly so. From the Rational Roots Theorem, you know that the only possible rational roots are ±1. So, the only way to find the roots are to graph it and try to read off the roots, or use some numerical method, such as bisection or Newton's method, or ...
June 16, 2015

science
Since you are given very little information, expect the math involved to be simple. How about you start with that most basic equation of motion: F = ma
June 16, 2015

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