Monday
April 27, 2015

Posts by STEVE


Total # Posts: 30,837

math
you should recall that for y = ax^2+bx+c the vertex is at x = -b/2a So, figure that for x, then evaluate y there. Since this parabola opens downward, its vertex is the maximum value.
April 18, 2015

AP Physics
conserve momentum. The sum of the two momenta after the collision must be the same as the original momentum of the moving ball. No diagrams here, so there's no way to tell the direction of the first ball.
April 18, 2015

Math
clearly both those equations cannot be true, since 99≠57. The sum of T5 to T8 is S8 - S4 = 8/2(2a+7d) - 4/2(2a+3d) = 4a+22d = 114 Similarly, S15-S11 = 15/2(2a+14d) - 11/2(2a+10d) = 4a+50d = 198 Subtract those two to get 28d=84, or d=3 So, a=12 T21 = 12 + 20*3 = 72
April 18, 2015

Math
oops typo. I hit 2 instead of 3. I'm sure you noticed that, and can fix it.
April 18, 2015

Math
just get all the y stuff on one side of the equation. x = 2r + 3ty 3ty = x - 2r y = (x-2r) / 3t
April 18, 2015

Math
8x3 * 3 = 24x9 8x3 * 4 = 32x12
April 18, 2015

maths
If you're talking about exponents, 5x^-3 = 5/x^3 If not, please explain "index" to poor ignorant me.
April 18, 2015

Physics
it will be the same as if it were just dropped. So, how long does it take to drop 60m? technically, this is not quite true, since the aerodynamics of flight will probably keep it aloft longer than just dropping it.
April 18, 2015

math
d = (T12-T5)/(12-5) = (50-8)/7 = 6 T5 = a+4*6=8, so a = -16 Thus, the sequence is -16 -10 -4 2 8 ...
April 18, 2015

Further maths
f(x) = 2x-3 so, f(g) = 2g-3 since g = x^2+5, g(x-1) = (x-1)^2+5 so, f(g(x-1)) = 2((x-1)^2+5)-3 = 2x^2-4x+9
April 18, 2015

trig
You know that A(b) = 43+b so, if b=22, plug that in wherever there is a b: A(22) = 43+22
April 18, 2015

Algebra
(8a^3b^6)^(1/3) = 2ab^2 (16a^8b^-4)^(1/4) = 2a^2b^-1 2ab^2 / 2a^2b^-1 = a^-1b^3 = b^3/a
April 18, 2015

calc
marginal cost is dC/dx = 49(-3x+3lnx+28)/(28-3x)^2 so at x=7, dC/dx = (7 + 3 ln7)/49
April 18, 2015

Physics
since the volume is constant, 4^2 * 2 = .5^2 * v
April 17, 2015

Math plane or spherical trig?
which kind of trig are we using?
April 17, 2015

geometry
the length of AB is √45 = 3√5 the length of CD is √80 = 4√5 So, since dilations scale lengths linearly, CD/AB = 4/3 No idea what EF is supposed to be for...
April 17, 2015

Math
assuming you want integer ratios, the medium rectangle must be 3 times as large, or 24x9 Similarly, since 3 does not divide 32, and 8 does, the large one is 32x12
April 17, 2015

math
There is a nice discussion and a good example here: http://en.wikipedia.org/wiki/Frobenius_method where do you get stuck?
April 17, 2015

Math
h/30 = tan 24
April 17, 2015

Math
If x students transfer, (480-x)/16 = (192+x)/12 x = 96
April 17, 2015

Math
ok, I'll bite. what is 2* ?
April 17, 2015

Math 222
when you multiply, you add powers: a^3 = a*a*a a^5 = a*a*a*a a^3 * a^5 = (a*a*a)(a*a*a*a*a) = a^8 similarly, when you raise powers to powers, you multiply them (a^3)^2 = (a^3)(a^3) = a^(2*3) = a^6 (a^1/2 b)^(1/2) = a^(1/2 * 1/2) b^(1 * 1/2) = a^1/4 b^1/2 so, now you have a^1/4...
April 17, 2015

Math
clearly, a = 0.5 d = 0.4 so, S10 = 10/2 (2*0.5 + 9*0.4)
April 17, 2015

Algebra
(x+5)(x-5)(3x-2) = 0
April 17, 2015

Algebra
4t + 16t^2 = 72 4t^2 + t - 18 = 0 (t-2)(4t+9) = 0 t = 2
April 17, 2015

mathematics
DE = √(1^2+9^2) = √82 DF = √((x+3)^2+5^2) = √(x^2+6x+34) So, x^2+6x+34 = 82 check my math, and solve for x.
April 17, 2015

algebra
8/12 = 2/3 24/36 = 20/30 = 2/3 So, you can see how to adjust either a or b. 5/3 = 25/x
April 17, 2015

pre-calc
if n is even, so is n^2, so the sum is even if n is odd, so is n^2, and since the sum of odd+odd is even, so is the whole thing. But that's just logic. To prove it, take S1: 2 is a factor of 1^1+1-2 = 0 So, assume Sn. Sn+1: 2 is a factor of (n+1)^2 - (n+1) + 2 = n^2+2n+1...
April 17, 2015

Math
w <= 6/2
April 17, 2015

Algebra
#5: T1 = 50 Tn+1 = Tn+20 #6: T1 = 1452 Tn+1 = Tn * 2/3 I expect you can tell an AP from a GP
April 16, 2015

5th grade (math)
since 5+8 = 13, one obvious combination is 2.35 in 5-cent stamps, and one 8-cent stamp Since 5*8=40, decreasing the 5-cent count by 8 and increasing the 8-cent count by 5 will keep the total at 2.43 So, just build a table 5¢ 8¢ 47 1 39 6 ... 7 26
April 16, 2015

Ap Calculus
You have a problem. x^2+y^2 cannot ever be negative.
April 16, 2015

Ap Calculus
The curves intersect at (-1,1) and (1,1) So, using discs, and allowing for symmetry, v = 2∫[0,1] π(R^2-r^2) dx where R = 2+√(2-x^2) r = 2+x^2 using shells, and taking advantage of symmetry, v = 2∫[0,1] 2πrh dy + 2∫[1,2] 2πrh dy where r = ...
April 16, 2015

Calculus check and help
A and B look good. The curves intersect at (0.1366,-3.9814) and (2.3977,1.7490) For C, you can either use washers, as you did for the horizontal axis. They are of thickness dy: x = 1/2 e^y x = √(y+4) v = π∫[-3.9814,1.7490] (√(y+4))^2-(1/2 e^y)^2 dy or, ...
April 16, 2015

Math
since rate*time is constant, 5*20 = 4*t
April 16, 2015

Calculus check
A is OK B is v = ∫[0,4] 2πrh dx, where r = 4-x h = (16-2x)-√x^3 For C, you need to split the Region into two parts at y=8, because we have to integrate along dy. The rectangles have a base of x, which changes at y=8 v = ∫[0,8] ∛y^2 h(y) dy + ∫...
April 16, 2015

Math
after n breaths, the amount left is 500*.88^n
April 16, 2015

math
area changes by the square of the linear ratio so, the area becomes 729*3^2
April 16, 2015

Integration by Parts
since sin(t) = (e^-t - e^-it)/2, isin(t) = i/2 (e^it - e^-it) i sint e^it = i/2 (e^2it - 1) so, the integral is just i/2 ((1/2i) e^2it - t) = -1/4 e^2it - t/2 do that from 0 to 2π and you have [1/4 e^4πi - π]-[1/4] = 1/4 - π - 1/4 = -π I haven't ...
April 16, 2015

calculus word prob
if the cable goes from A along the 360-ft side for a distance x past the indent at A's corner to y from the indent at B's corner, then the cost will be 8(60+x) + 11√((300-x)^2+(240-y)^2) + 8(60+y) Now, I don't think you have studied multi-variable derivatives...
April 16, 2015

calc
that's where E' is a max E' = .004(4x^3-24x^2) = .008(x^3-6x^2) E' is max where E" = 0 E" = .008(3x^2-12x) = .024x(x-4) so, |E'| is max when x=4, as you can see at http://www.wolframalpha.com/input/?i=.004+%28x%5E4-8x%5E3%29%2B2
April 16, 2015

math 8th!
since the slope is 2, y changes by 2 whenever x changes by 1. So, pick a point 1 unit to the right or left of (-2,3) These would be (-3,?) and (4,?) Since y changes by 2 for every 1 in x, the two points would be 2 units above or below (-2,3): (-2,1) and (4,5) You could have ...
April 16, 2015

Geometry
the ant has gone 3 times the distances, or 30 inches along, and 24 inches up. Using your distance formula, the final displacement is √(30^2+24^2) = 6√(5^2+4^2) = 6√41
April 16, 2015

pre-calc
I'll get you started. But you clearly need to study the examples in your text. Or, just do a google and you will find lots of examples online. You start with your matrix of coefficients: 4 -1 3 | 12 1 4 6 | -32 5 3 9 | 20 You want to work things so that you have a final ...
April 16, 2015

pre-calc
well, when I do it, it says I'm right, so why don't you show your work here and we can see how things go?
April 16, 2015

pre-calc
Enter your coefficients here and see all the details: http://www.gregthatcher.com/Mathematics/GaussJordan.aspx
April 16, 2015

algebra
after t days, the amount left is (1/2)^(t/13) So, after 3 days, the amount left is (1/2)^(3/13) = .852 = 85.2%
April 16, 2015

Math
we see that the length of the beam is 8/sin40 = 12.45 ft At 60 degrees, the top is 12.45sin60 = 10.78 ft high So, the wire is 12.78 ft up. Since the beam is only 12.45 ft long, it will not touch the wires.
April 16, 2015

MATH
40*9.25 = 370.00 The deductions are .0765*370 = 28.31 .12*370 = 44.40 .08*370 = 29.60 But, what's discretionary? The taxes and slacks are mandatory, but the transportation and lunches could be adjusted if necessary. So, I'd say 247.74 Hmmm. Maybe transportation is also...
April 16, 2015

calculus
The volume is just a stack of discs, each of radius y and thickness x, so v = ∫[a,b] πr^2 dx y(1) = 0 y(e) = 1 so, v = ∫[1,e] πr^2 dx so, what's r? If we were revolving around y=0, r would just be y. But the axis is 3 units farther away than that, and...
April 16, 2015

calc
just figure f(1)...f(4) since the rectangles have width 1, your approximation is just the sum of the four values of f. The value will be a little high, since f is concave downward, so using the right ends of the intervals means the rectangles are a bit too tall.
April 16, 2015

MATH HELP
well, what is 3+5 ? If you even considered (B) you clearly have not studied the Fibonacci sequence too closely.
April 16, 2015

calc(very urgent)
something wrong with the solution I posted a few hours ago? http://www.jiskha.com/display.cgi?id=1429156887
April 16, 2015

precalculus
we know that the center is at (0,0) and the axis is vertical, so y^2/a^2 - x^2/b^2 = 1 If the distance between the vertices is 2a = 8, then 4^2 + b^2 = c^2 Since (3,-5) is on the graph, 25/a^2 - 9/b^2 = 1 a=4, so 25/16 - 9/b^2 = 1 b^2 = 16 y^2/16 - x^2/16 = 1 See the graph at ...
April 16, 2015

pre-calc
You have Sn, but you have a typo, or the copy/paste mangled it. It should be Sn: 1^2+...+(3n-2)^2 = n(6n^2-3n-1)/2 So, S1: 1^2 = 1(6*1^2-3(1)-1)/2 S2: 1^2+4^2 = 2(6*2^2-3*2-1)/2 S3: 1^2+4^2+7^2 = 3(6*3^2-3*3-1)/2 which are all true We have not shown it to be true for all n. To...
April 16, 2015

pre-calc
8x+7y >= 336 Unless we're discussing pirates, that's borders.
April 16, 2015

math
well, clearly, the marble has a height of 2r, so the water must be that deep to cover it. Since the cylinder is said to have a radius of 4, I think you want the radius of the marble that requires the most water to cover it. The volume of water is v = π*16(2r) - 4/3 π...
April 16, 2015

pre - CALCULUS
enter your values here to see all the details: http://www.gregthatcher.com/Mathematics/GaussJordan.aspx
April 15, 2015

Pre-calculus
vehicles and winds travel on a heading, not a bearing. Sadly, this distinction is ignored or unknown to many textbook writers and teachers. But on to the math. the Cessna in still air travels be at (180 sin35°,180 cos35°) = (103.24,147.45) The wind blows it an ...
April 15, 2015

calculus (please help. URGENT!)
v = π/3 h^2 (3r-h) = πrh^2 - π/3 h^3 dv/dt = 2πrh dh/dt - πh^2 dh/dt = πh(2r-h) dh/dt Pluggin in your numbers, then, we have π*5(20-5) dh/dt = 3 dh/dt = 3/(75π) = 0.021 m/min
April 15, 2015

Math (ASAP)
well, just plug and chug a1 = 32 a2 = 1/2 (32) = 16 a3 = 1/2 (16) = 8 ...
April 15, 2015

math
I got 111.32, so I guess it depends on how you want to round it.
April 15, 2015

Math
4321 = 29*149 we know that 149 divides the product, so the question is, is any other number in teh product a multiple of 29? There are only 21 consecutive factors, so it's not guaranteed, so you'll have to check whether there is a multiple of 29 between 140 and 160. ...
April 15, 2015

Math
oops. 10*42^2 = t*60^2
April 15, 2015

Math
t = k/v^2 so, tv^2 is constant. Therefore, 10/42^2 = t/60^2
April 15, 2015

Science/Physics
3.9 + 2.4 + (3.9+3.1) = 13.3 How did you arrive at 10.5?
April 15, 2015

geometry
the midpoint is the average of the endpoints. So, for BC, P=(h,k) Now just use your distance formula to get the required lengths.
April 15, 2015

math
plug in your numbers and play around with Z table stuff at http://davidmlane.com/hyperstat/z_table.html
April 15, 2015

math
.42
April 15, 2015

even wurse spelling
yet correct, withal.
April 15, 2015

More math
and yes, you are correct.
April 15, 2015

maths
after 6 jumps, he has descended 6 steps The 7th jump will take him to the 9th step.
April 15, 2015

geometry
The inner rectangle is 70x105 the inner circle has radius 35 the outer rectangle is 84x105 the outer circle has radius 42 now just figure the areas and subtract inner from outer
April 15, 2015

trig table?
Excuuuuuse me! How long ago did you take trig? No one uses tables any more. However, the trig book I used was titled "Trigonometry with Tables." I remember our library had huge volumes from the National Bureau of Standards with 12-place tables for trig, log, and ...
April 15, 2015

maths
PAD is not necessarily congruent to PBC. They have two sides congruent, but that is not enough.
April 15, 2015

Precalc
f(x) = (3x)^-4 + 3x^4 f' = -4(3x)^-5(3) + 12x^2 = -12/(3x)^5 + 12x^2 where is 15x^2-30x = 0? where is 6x^2+12x = 0?
April 15, 2015

math
60mph = 88ft/s, so you want k where 88-kt=0 so t = 88/k 88t-1/2 kt^2 = 100 88(88/k) - 1/2 k (88/k)^2 = 100 k = 38.72 ft/s^2 now you can solve the other part.
April 15, 2015

algebra
recall that the slope-intercept form of a line is n = mt+b where m is the slope. Here, that is -2.23 It means that the number of refineries is declining by 2.23 per year, or about 9 refineries every 4 years.
April 15, 2015

math
(20+14)(30+14)-(20)(30)
April 14, 2015

math
just using the measurements, the tiled area is 8*6 - 2*3 = 42 ft^2 11" is nearly a foot, so we can estimate that about 42 tiles will be needed. Naturally, since the tiles are a bit smaller, more of them will actually be used.
April 14, 2015

geometry
Assuming a logical arrangement of W,X,Y,Z, your answer appears correct.
April 14, 2015

math
recall that the product of the roots of ay^2+by+c=0 is c/a. Here, a is 1, so y1*y2 = -c clearly, 12 and 0 only work if c=0. suppose c is -36. The roots are 6 and 6.
April 14, 2015

math - eh?
eh?
April 14, 2015

AP CALC
looks good to me.
April 14, 2015

calculus multiple choice
#1 v = ∫[0,lnπ] π sin^2(e^x) dx That will take some numerical methods to figure. #2 ∫[1,3] 2/x dx ----------------- 3-1 #3 s(t) = ∫[0,2] -2t^2+4 dt
April 14, 2015

PRE - CALCULUS
so, did you graph it?
April 14, 2015

Chemistry
1.05 g/mL * 5500 mL * 1lb/454g = ? lb
April 14, 2015

Science
all are metals except sulfur
April 14, 2015

Technical Physics
it falls the anchor displaces its volume in water when it sinks, but it displaced its weight when it was in the boat.
April 14, 2015

maths
-2*2*5
April 14, 2015

math
for the same reason that spelling should
April 14, 2015

math
what makes you think anyone "found" it?
April 14, 2015

Physics
after 25 seconds, v=25*.8 = 20 when it starts to decelerate, a = -1 m/s^2, since it takes 20s to decrease v to 0. so, the total distance is s = 1/2 .8*20^2 + 20*77.5 + 20*10 - .5*400 = 1710 m avg speed is thus 1710/(20+77.5+20) m/s
April 14, 2015

Pre-Calculus (Check)
If the middle table has side x, then the three squares (x-1)^2 + x^2 + (x+1)^2 = 677 3x^2 + 2 = 677 3x^2 = 675 x^2 = 225 x = 15 and the tables have sides 14,15,16 how did you come up with 3x^2-6x = 677?
April 14, 2015

physics
correct.
April 14, 2015

Math
#1 is correct #2 is 11 it is a vertical line whose y-coordinates differ by 11, so that is its length. How did you come up with 18?
April 14, 2015

Fourier Series
well, you have to break f(x) into two parts for x<0, f(x) = 0 for x >= 0, f(x) = 2x so, a0 = 1/π ∫[0,π] 2x dx = π and for the others just use integration by parts for integrals of x cos(nx), etc.
April 14, 2015

Math
(12.7*7.5 m^2) * (10.76 ft^2/m^2) * (1 bdl/33ft^2) * ($29.95/bdl) = $930.17 That is the cost for one side of the roof. The cost will actually be a bit higher if only whole bundles can be purchased.
April 13, 2015

Polygons on the coordinate plane
plural of vertex is vertices. So, draw a rectangle where the length + width = 8.
April 13, 2015

Calculus
oops.The printed area is 8x12, so the page is 10x15
April 13, 2015

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