Sunday
April 20, 2014

Posts by steve


Total # Posts: 21,799

algebra
you just have a right triangle with legs 5 and 8. So, the rope, forming the hypotenuse is √(25+64) = √89

Calc 2
and the (-2/3)^k part is just a geometric series S = (-2/3)/(1+2/3) = -2/5

geometry
x^2 + 6371^2 = (6371+353)^2 x = 2150

Algebra
2 hours

Math
√(25^2 + 10^2)

math
(P2-P1)/P1 * 100

Calc
dQ/dt = kQ (if you please)

CHEM
since PV/T is constant, if P is held constant, then V/T is constant. if T is increased by a factor of 296/90, then V is increased by a factor of 296/90. So, multiply 3.3 by that factor.

math (Matrix algebra)
Enter your data at http://www.gregthatcher.com/Mathematics/GaussJordan.aspx to see all the details

math (Matrix algebra)
assuming you mean a determinant, and calling your matrix M, I get |M| = 31-3x So, if 31-3x = 25, x=2 The inverse can be seen at http://www.wolframalpha.com/input/?i=inverse+{{-2%2C+1%2C+x%2B2}%2C{3%2C+x-4%2C+5}%2C{0%2C+1%2C+3}}+ substitute in x=2 if you just want the numbers.

maths
since one line is slanting, and the other is horizontal, I'd say they are not parallel. Even is there's an x missing from the 2nd line, it will still not be parallel.

maths
x y -4 13/2 -3 5 -2 7/2 ...

Algebra
since time = distance/speed, we have 5/x + 5/(2x) = 15/(2x)

Math
5% growth is just 1200000*1.05^n after n years for #c, we have 1200000*(1.05)^7*(0.92)^8 = 866,581

Algebra
x^2+8x+15 = (x+3)(x+5) so, you have (x+3)(x+5)/(x-4) * (x-4)(x+4)/2(x+3) the x+3 and x-4 cancel, leaving (x+5)(x+4)/2

math
out of 36 possible rolls, only 4 have the sum < 5: 12 13 21 22 What's the chance of no 6's? 5/6 * 5/6 so, take 1-P(~6,~6) = 11/36

Algebra
the point of Reiny's question is to remind you that division by zero is undefined. So, when b+4=0, the expression cannot be evaluated. That is, when b = -4, the expression is undefined.

Math
I get zero. ∫[-1,2] 1-x^2 dx = x - x^3/3 [-1,2] = (2 - 8/3) - (-1 + 1/3) = 0 yeah, I know, we have to divide by 3 ...

Trig - heh
now, just change all those 225's to 255's and redo the calculations.

Math
PR/QR = sin(Q) PR/120 = sin(10.5)

Calculus Help Please Urgent!!!
1/3 pi r^2 h = 30, so h = 90/(pi r^2) surface area = 2 pi r s where r^2+h^2 = s^2, so a = 2 pi r √(r^2 + (90/(pi r^2))^2) = 2/r √(pi^2 r^6 + 8100) for minimum paper, we need da/dr = 0, so, as wolframalpha so ably shows at http://www.wolframalpha.com/input/?i=2+pi+r...

mathematics for management
5^x 25^2y = 1 5^x 5^4y = 1 5^(x+4y) = 1 x+4y = 0 3^5x 9^y = 1/9 3^5x 2^2y = 3^-2 5x+2y = -2 x = -4/9 y = 1/9

math
Assuming you mean (8^y)^y, we have 8^y^2 = 2^3y^2 1/32^y = 2^-5y 4 = 2^2 3y^2-5y = 2 y = 2 or -1/3

mathematics for management
2log(a+b) = log (a+b)^2 = log (a^2+2ab+b^2) 2log a + log(1 + 2b/a + b^2/a^2) = log (a^2 (a^2+2ab+b^2)/a^2) looks the same to me

math
Assuming a 360-day year, 8000 * .095 * 1/3 = 253.33

math
ignoring all those trailing zeros, 58/6 = 9.67

calculus
1/10 ∫[0,10] 3/(x+1) dx = 3/10 ln(11)

math
the bisector BD and half the chord CD form a right triangle with the radius BC BC^2 = 3^2+5^2

math
the one with an x term, but no higher powers.

calculus
So, the height is 40/x^2 c(x) = 2x^2*5 + 4x(40/x^2)*2 = 10x^2 + 320/x set the derivative to zero, and you find minimum cost at x = 2∛2

Precalculus
for #2c, there is a second point at about (-1.38,3) see the graph at http://www.wolframalpha.com/input/?i=solve+5x^3-3x^5%2B1+%3D+3

statistics
C

cal
false. These are formulas for interest compounded k times per year.

math
have you tried your calculator?

Math
850000(1+.06/4)^(4*3.5)/4.75 = 220,419 850000(1+.06/4)^(4*5)/5.10 = 224,476

statistics
well, who has a negative z score?

Math
As I showed you earlier, it is ∫[0,8] 7/(x+1) dx ---------------------- (8-0) = 1/8 (7log(x+1) [0,8]) = 7/8 (log9-log1) = 7/8 log9 what were your solution steps?

Algebra
(r+2)/(r+4) - 3/(r+1) = (r^2-10)/(r^2+5r+4)

math
5n + 25q = 325 q = n-5 now just plug in q and solve for n.

Algebra
1/(g+2) + 3/(g+1) = (4g+7)/(g^2+3g+2)

Math
using FOIL, you get (2n)(6n) + (2n)(1) + (2)(6n) + (2)(1) = 12n^2 + 2n + 12n + 2 = 12n^2 + 14n + 2

math trigonometry
the law of cosines says 68^2 = 53^2 + 71^2 - 2*53*72 cosθ so, cosθ = (68^2-53^2-71^2)/(-2*53*72) = 0.42269 θ = 65°

Algebra
the common denominator is 2b, so you have 1/2b + b^2/2b = (1+b^2)/2b

Math
and there's your answer.

Math
17 is 17*1 so, what is 17*23.125?

Mean, Median and Mode HELP!
sort the data to get 4 6 7 9 10 11 11 12 15 16 Now it is easy to see mode = 11 median = 10.5 mean = 10.1

Math
distance is ∫[0,8] 3t√(640t^2) dt = 512

Math
that would be ∫[0,3] 300t^2/(t^3+32) + 5 dt let u = t^3 + 32 du = 3t^2 dt and now you have ∫[32,59] 100/u du + ∫[0,3] 5 dt = 15 + 100log(59/32)

Math
∫[-1,2] 1-x^2 dx ----------------------- (2-(-1))

Math
∫[0,8] 7/(x+1) dx ---------------------- (8-0)

Math
that would be (∫[0,8] 5e^-x dx)/(8-0) = 5/8 (1-e^-8)

Algebra
since the denominators are equal, just subtract the numerators: ((5x-2)-(x-2))/(4x) = (4x)/(4x) = 1

trying to understand math
in March, total sales were 9.00 * 125 * 31 = 34875.00 In April, (assuming 30 days, 15 days per half-month) 1st half: 9.00*125 * 15 = 16875.00 2nd half: 11.00*125 * 15 = 20625.00 total: 37500 avg at 11.50 = 43125 so she falls 5625 short. Two items need clarification... There...

math
(pi * .8^2 * .5 m^3) ----------------------- = 32 s (pi * .1^2 * 1 m^3/s)

Algebra
just solve your equation: x^2-81 = 115 x^2 = 196 x = 14 so, the base is 14+9 = 23 height is 14-9 = 5

Algebra
√(5x^2)+7x+2-√(4x^2+7x+18) = x-4 √(5x^2)-√(4x^2+7x+18) = -6x-2 now square both sides to get (5x-2) - 2√(5x^2)(4x^2+7x+18) + (4x^2+7x+18) = (6x+2)^2 4x^2+12x+16 - 2√(20x^4+35x^3+90x^2) = 36x^2 + 24x + 4 √(20x^4+35x^3+90x^2) = -16x^2-6x+...

algebra 1
both correct However, I'd have written #2d as (5x+2 + 3x-1)/2 just to show it's the average of two numbers, rather than half of each.

algebra1
looks like A to me

College Cal 1
if the 2-strand dimension is x, then we have f(x) = 2x + x + 2(15000/x) df/dx = 3 - 30000/x^2 min fence when df/dx = 0, at x = 100 so, the field is 100x150 as usual, the fencing is divided equally among the dimensions. ** f(x) = fencing(x) !

alg
since f(1) = 5, f-1(5) = 1

Algebra
probably not any better than the user's manual that came with it.

Alg.
well, just plug in the values g(-4+h) = (-4+h)^2 - 3 = 13-8h+h^2 g(-4) = (-4)^2 - 3 = 13 so, the numerator is -8h+h^2 divide that by h and you wind up with -8 + h

math
v1 - 3v2 = (1+2j)-3(1+j) = 1+2j-3-3j = -2-j v1*v2 = (1+2j)(1+j) = 1+3j+2j^2 = -1+3j v1*v1 = (1+2j)(1+2j) = -3+4j v1/v2 = (1+2j)/(1+j) * (1-j)/(1-j) = (3+j)/2 you can practice you skills at wolframalpha.com, but use i instead of j.

trigonometry
since 10*468 = 13*360, if we can find all the values of n < 10, then just adding 10 to those values will produce all the possibilities. Finding n<10 should not take too long. For example n=1 works, since 468 = 108(mod 360)

caculus
from the product rule, d(uv) = v du + u dv so, u dv = d(uv) - v du now integrate

MATH HELP
2 kg is about 4.5 pounds So, what do you think?

Calculus Help Please Urgent!!!
Hmmm. we all know that tan x -> x as x->0 so, cot x -> 1/x as x->0 so the limit ought to be zero.

M A T H
no, cost = 4800 + 1400x

Algebra
.04x + .30(200-x) = .08(200) x = 169.2 lbs whole milk so, 30.8 lbs of cream.

Math
Hmmm. we have ∫[0,2] 0.18t^2 + 0.16t + 2.64 = 0.06t^3 + 0.08t^2 + 2.64t [0,2] = .48 + .32 + 5.28 = 6.08 What did you do to arrive at your answer? 1.04 is obviously way off, since f(0) = 2.64 just to start with.

trig/ vectors
he needs to head upstream at an angle θ (measured from the line CD), such that tan θ = 4/12 so, θ = 18.4° The speed required is √(16+144) = 12.65 mph

Math
call the 2 piles x and y P(x) = 3/5 P(y) = 2/(b+2) 3/5 * 2/(b+2) = 6/45 6 / 5(b+2) = 6/45 5(b+2) = 45 b+2 = 9 b = 7

Calc III
well, just plug them in ∂x/∂u = 0 ∂x/∂v = 7 ∂x/∂w = 14w ∂y/∂u = 18u ∂y/∂v = 0 ∂y/∂w = 9 ∂z/∂u = 2 ∂z/∂v = 4v ∂z/∂w = 0 So J = (0 7 14w) (18u 0 9) (2 4v 0) |J| = 1008uvw ...

maths
the area of a sector is 1/2 r^2 θ So, the volume of the cake slice of height h is 1/2 r^2 θh subtract that from the volume of the cake, which is pi r^2 h v = r^2 h (pi-θ/2)

college algebra
If the hole has depth h, then √h/4 + h/1100 = 3.0 h = 132'8"

math trigonometry
if the two towers have heights a and b, then (b-a)/31 = tan 25° a/31 = tan 31° Now just solve for a and b.

math
sinA = 1/2, so tanA = 1/√3 tan(A-B) = (tanA-tanB)/(1+tanAtanB) = (1/√3 - 3/4)/(1+(1/√3)(3/4)) = (25√3 - 48)/39

math
I get AC+B = 3x^^3+14x^2+6x-6 AC has to be 3rd degree, since A is 1 and C is 2 (A+B)(B-C) = -3x^3-5x^2-6x+24 Somewhere you're messing up. Visit calc101.com and click on the "long multiplication" link, and it will show all the details of polynomial multiplication.

math
just substitute in. For example, ABC = (3x+4)(x^2+2)(x^2+3x-2) = 3x^5+13x^4+12x^3+18x^2+12x-16 what do you get for the others?

college algebra
max height when t = 1 h(1) = 576 -16t^2+32t+560 = 0 when t = 7

algebra
recall that lna-lnb = ln a/b, so ln (x+3)/(x-5) = ln 7 (x+3)/(x-5) = 7 x+3 = 7x-35 x = 19/3

algebra
643 e^10k = 813 e^10k = 813/643 = 1.2644 10k = ln 1.2644 = 0.2346 k = 0.02346 now just solve for t in 643 e^0.02346t = 2x10^9

science
well, 1 mole = 22.4 L, so you have 1.15/22.4 moles. that should help.

math
common ratio, so ...

math
identify the sequence 1.6, .8, .4, .2 as arithmetic, geometric, or neither and why.

math
C(g) = 2.19g

math
a gas station charges $2.19 per gallon of gas. use function notation to describe the relationship between the total cost C(g) and the number of gallons purchased g.

math
looks like 8 11 14 17

math
find the 1st 4 numbers of the sequence 3 n + 5

math
625cm/2500cm = 1:4 so, what's 5000/4 ?

Math
since you give no information as to their directions, I will assume they are traveling in opposite directions. So, if the .1kg mass is moving in the + direction, we have 0.1*0.4 - 0.2*1.0 = (0.1+0.2)v v = -8/15

science
why do people have a hard time moving a large rock out of the road

science
what animal would have less momentum then a 52 kg cheetah running at 10 m/s.

science
what is the momentum of a 20kg scooter traveling at 5.o m/s.?

math
this is bogus. Maybe X,Y,Z are all disjoint. So, Z – (X U Y) = Z maybe Z⊆(XUY) so Z – (X U Y) = Ø Looks like you're on your own for this one.

math
well, duh: (2,-3)

Math
w(2w+4) = 400 w = √201 - 1

linear algebra
3/4 as big as or 25% smaller than

Math
assuming you mean a 1 ft cube, then it has 4^3 = 64 smaller cubes. The 8 corners have 3 faces yellow The 12 edges have 2 blocks each with 2 faces yellow, making 24 The 6 faces have a 2x2=4 set of cubes with 1 face yellow, or 24 That leaves the interior 2x2x2=8 cubes all green

Math 10
the graph is a parabola, with vertex at t=1 h(1) = 20 see a picture and analysis at http://www.wolframalpha.com/input/?i=-5t^2+%2B+10t+%2B+15

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