Monday
April 20, 2015

Posts by Steve


Total # Posts: 30,680

geometry
1) in a 30-60-90 triangle, the sides are in the proportion 1:√3:2 2) h^2+10^2 = 20^2 3) a^2+4^2 = b^2 unless you know one of the other angles, there are lots of a and b which will work.
April 20, 2015

Calc 1
let u = 1/x then you have tan(3u)/u as u->0 we know that tan(u)/u -> 0, so tan(3u)/u -> 3
April 20, 2015

calculus
at height h, tanθ = h/50 sec^2θ dθ/dt = 1/50 so, plug in your numbers and evaluate dθ/dt
April 20, 2015

Math
if the sides are x,y,z, then the package (surface area) is 2xy + 2xz + 2yz So, the new dimensions will be x=3, y+3, z+3 plug in your numbers to find the area
April 20, 2015

math
Hmmm. Your question is ill worded. I suspect you mean g(x) is the integral of e^(3t^2)-3t dt from 4 to x. Otherwise, we'd need the integral of e^(3t^2) which is not elementary. So, with that in mind, dg/dx = e^(3x^2)-3x
April 20, 2015

derivatives
Assuming you meant 5√ and not 5th root, y = (12x-18x^4+3)/(5√(6x^2-11x^4+2)) Using the quotient rule, y' = (12-72x^3)(5√(6x^2-11x^4+2)) - (12x-x^4+3)(5 / 2√(6x^2-11x^4+2))(12x-44x^3) ------------------------------------------- 25(6x^2-11x^4+2) You ...
April 20, 2015

science 8th (:: 1 question
you are correct.
April 20, 2015

science 8th (::
R=E/I You did E-I
April 20, 2015

maths
after t minutes, the temperature T will be T(t) = 300 - 15(t/2)
April 20, 2015

maths
each cycle advances the drunk 2 meters So, after 4 cycles and 4(5+3)=32 seconds, the drunk has advanced 8 meters. The next 5 steps take him to the end, so it takes 32+5 = 37 seconds.
April 20, 2015

math
T4 = 3T1 T7 = 2T3 + 1 Now just plug in the values for Tn and you have a+3d = 3a a+6d = 2(a+2d)+1 Now just solve for a and d.
April 20, 2015

math
if x is at 2%, then the rest (23500-x) is at 7%. So, add up the interest: .02x + .07(23500-x) = 795
April 20, 2015

Math
#1. Draw the number line -9 is to the left of -4, so -9 < -4 #2 C? Excuse me? You say that -2 = -4? Again, use the number line. #3 Nope again. You want C though I suspect that is an accident. The logic is: |2-5| = |-3| = 3 so, -|2-5| = -3 -3 = 8-11
April 20, 2015

math
You are correct on all three. A and B could be true with various numbers, but C is only true if p or q is zero.
April 20, 2015

Trig
as usual draw a diagram. If the height is x, then from distance x, x/h = cotθ so, h cot 48° - h cot 68° = 1
April 20, 2015

Math
60% = 3/5, so (3/5)(3/5)x = 36 x = 36(5/3)(5/3) = 100 for the boys, we have the average as 16*50.25 + 8*45.15 ----------------------- = 48.55 16+8
April 20, 2015

Business Stats
well, what value z corresponds to P(Z>z) = .84?
April 20, 2015

chemistry
depends on the temperature and pressure, no? But at STP, 1 mole fills 22.4 L, so ...
April 20, 2015

Calc 1
how about I do this one, and you at least try on the others? x^2+3x-18 = (x+6)(x-3) So, everywhere except at x=3, f(x) = x+6 That means we expect the limit to be 3+6=9 Using the suggestion, the limit is (2x+3)/1 = 2*6+3 = 9
April 20, 2015

Math
Hmmm. xy=50 2(x+y) = 34 The only factor pairs of 50 are 1,50 2,25 5,10 None of those add up to 17, so the sides will not be integers. To find them, you will need to solve a quadratic equation: x+y=17 x + 50/x = 17 x^2-17x+50 = 0 Now just use the quadratic formula.
April 20, 2015

Math
clearly it is not a square. 192 has several factors: 4x48 6x32 8x24 12x16 ... so, which of those factor pairs adds up to half of 64?
April 20, 2015

Math
D is indeed correct.
April 20, 2015

Math
nope. C is what you get if there's a flat fee of 2.19 and each gallon costs 1 more.
April 20, 2015

algebra (urgent help needed)
see the related questions below.
April 20, 2015

Math
looks good to me
April 20, 2015

Calculus check and help
so far, I don't see any of your work, just the answers others have provided. For B, if you have to split the area into two equal parts, and the integration goes from 0 to 1.136, that means that there is some z in that interval which bounds exactly half the area. So, you ...
April 19, 2015

Calculus
well, 1-sin^2 = cos^2, so you really just have sin/cos^2 = sec tan which I'm sure you recognize.
April 19, 2015

Calculus
the graphs intersect at (0,1) and (1.136,1.764) A The cross-sections have base of f(x)-g(x) and height 5. So, we add them all up: v = ∫[0,1.136] 5(1+sin(2x)-e^(x/2)) dx = 5(x - 1/2 cos(2x) - 2e^(x/2)) [0,1.136] = 2.1455 B The same thing, but the height is the same as the...
April 19, 2015

Chem
If the reaction is Pb(NO3)2 + 2NaCl = PbCl2 + 2NaNO3 then each mole of PbCl2 uses one mole of Pb(NO3)2. So, with 3.264/278.11 = 0.0117 moles of PbCl2 produced, the 2.00mL was .0117/.002 = 5.868M 5.868*80.7/100 = 4.735M original concentration
April 19, 2015

Calculus
If you mean f(x) = √(x-3) f is only defined for x >= 3 For that domain, it is clearly integrable. So, the interval is [3,∞)
April 19, 2015

Calculus
clearly the intervals have width 1. So, with right-hand endpoints, we need 1*(f(1)+f(2)+f(3)+f(4)) = 1+4+9+16 = 30 what was so hard about that?
April 19, 2015

Science
I'm not sure. There are various chemical reactions taking place all the time (plant and animal respiration, mineral formation, etc.) that consume or release water. So, not only is C probably true, but we don't know the long-term effects of the various processes taking ...
April 19, 2015

statistics
you want z such that P(Z>z) = .63/2 z = .896 So, the scores are ±0.896
April 19, 2015

Math/Algebra
By the end of 2012, that's 3 years, not 2. A: 4000*.0315*3 = 378.00 B: 4000(1.0315^3-1) = 390.03 Looks like C to me.
April 19, 2015

Vectors
unless the normals are parallel, the planes must intersect in a line.
April 19, 2015

mass
1.3 = .000081x x = 16049.38 So, subtract the 1.3g from that
April 19, 2015

Math
least perimeter will be a square. So, what are the sides of such a square?
April 19, 2015

statistics
P(Z>z) = 0.2 z = 70
April 19, 2015

math
If there are x lbs of peanuts, then there are (100-x) lbs of cashews. So work with the value of the mixture and its parts: 2.80x + 5.30(100-x) = 3.30(100)
April 19, 2015

7TH MATH HELP
#1. Nope: -12(3)-3 = -36-3 = -39 #2 ok #3 Nope: as x increases, y decreases #4 Nope: 8*2+5 = 16+5 = 21 #5 ok #6 Nope J(10, 5) -> (15,9) #7 Nope: you didn't change anything!
April 19, 2015

math
how are the cubes arranged? 1x6 or 2x3?
April 19, 2015

math
π r^2 h = 355 r^2 h = 113 the area a=2πrh+2πr^2 which we want to be small 113 is prime, so there will not be integer values. However, using integers to approximate, r h a/2π(r^2+rh) 3 13 48 4 7 44 5 4 45 6 3 54 Looks like r is near 4
April 19, 2015

maths
625^2+4 = 360629 = 157*2297
April 18, 2015

Calculus
as always, n ∑ 2/n f(5+2/n) k=1 Since you didn't specify the endpoints or the number of intervals, you can fill in the numbers.
April 18, 2015

precalc
just look up the information for x^2 = 4py Figure p, and you're halfway there.
April 18, 2015

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

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