Monday

April 20, 2015

April 20, 2015

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*