Monday
April 21, 2014

Posts by Steve


Total # Posts: 21,808

5TH GRADE MATH
If you mean that the sum of the three perimeters is 140 yards, then you can divide 140 up any way you like. If you pick, say, 30,50,60 yards as your three perimeters, then you can divide the values up as you will. For example perimeter 30: 7x8 yards perimeter 50: 25 ft by 50 f...

Mathematics
P is in QI, so if cosP = 5/13, tanP=12/5 Q is in QIII, so if tanQ = 8/15, sinQ = -8/17 17tanPsinQ = 17(12/5)(-8/17) = -96/5

trigonometry
h/63 = sin 45

calculus help
There's a nice discussion here: http://math.stackexchange.com/questions/126755/lhospitals-rule-with-indeterminate-powers

Math
to figure a percentage, just divide and multiply by 100. 2023.60/55953.77 = 0.0361 = 3.61%

Calculus Help!!!!!
should be no problem. That's just Algebra II. Anyway, y = x^3/(x+1)^2 y' = x^2(x+3)/(x+1)^3 y" = 6x/(x+1)^4 see the graph and some analysis here: http://www.wolframalpha.com/input/?i=x^3%2F%28x%2B1%29^2

Precalculus
tan does not become 2tan expand (a+b-1)^2 and you will see the 2's, just as (a+b)^2 = a^2 + 2ab + b^2

Precalculus
You have (tan+sec-1)/(tan-(sec-1)) multiply top and bottom by tan+sec-1 and you have (tan+sec-1)^2/(tan^2-(sec-1)^2) tan^2+sec^2+1+2tan*sec-2tan-2sec)/(tan^2-sec^2+2sec-1) (sec^2+tan*sec-tan-sec)/(sec-1) (tan+sec)(sec-1)/(sec-1) tan+sec

Calculus Help Please!!!
As mentioned, let BC = x distance over water: √(x^2+49) distance over land: 11-x (a) energy expended: y = 1.3√(x^2+49) + 11-x dy/dx = 1.3x/√(x^2+49) - 1 y'=0 at x = 70/√69 what do you get for the other parts?

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

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