Saturday

November 28, 2015
Total # Posts: 35,833

**Calculus - typo**

or, (-1/r) e^[(-1/r) t] since d/dt e^(kt) = ke^(kt)
*November 23, 2015*

**College Alg.**

If the amounts in A and B are x and y, then (suppressing all the extra zeros), maximize p=.13x+.07y subject to x >= 65/2 y >= 65/4 x+y <= 65 Now use your favorite tool to solve. A good one is at http://www.zweigmedia.com/RealWorld/LPGrapher/lpg.html
*November 23, 2015*

**Math**

Jiskha and facebook
*November 23, 2015*

**Geometry**

well, the side lengths are CB=10 Note that A is halfway from C to B (6=(1+11)/2), so ABC is an isosceles triangle, and AB=AC=√74 Now all you have to do is scale up the dimensions by a factor of 20'/1" = 240 to get the actual side lengths. We weren't asked ...
*November 23, 2015*

**Geometry - incomplete**

I assume you meant ACB rather than ACV. Since the angles total to 180, we have for angle ABC, 180-(5x+1)-(3x+12.5) = 162.5-8x That is all we know. You have given no side lengths, nor even any way to determine the actual angles. Knowing all the angles would not help, since we ...
*November 23, 2015*

**math**

10+16 = ?
*November 23, 2015*

**math**

2L/5child = 2/5 L/child
*November 23, 2015*

**math**

well, just add 'em up and divide by 5. The numbers are 36,49,64,81,100
*November 23, 2015*

**math**

y = x^x^x^... lny = x^x^x^... lnx = y lnx lny/y = lnx Now differentiating implicitly, 1/y y' - lny/y^2 y' = 1/x y' = (1/xy)/(1 - lny/y) You can massage that in various ways.
*November 23, 2015*

**Calculus**

I think we can safely assume that the max volume occurs when h+r is in fact 12, and not less. So, h = 12-r v = πr^2 h = πr^2(12-r) dv/dr = 3πr(8-r) So, max v occurs at r=8 v(8) = π*8^2(4) = 256π I think you can easily show that if h < 12-r, max v ...
*November 23, 2015*

**Maths**

the dimensions of the box are x,x,y where x^2 y = 2592, so y = 2592/x^2 Around the square, the distance is 4x Around the length, the distance is 2x+2y So, we want the minimum length. No maximum is possible, as the package may be arbitrarily long and thin. So, the length z is z...
*November 23, 2015*

**Calculus**

f' = 9x^(4/5) - 36/x^(1/5) = 9/x^(1/5) (x-4) f increases where f' > 0, or x>4 or, where x<0
*November 23, 2015*

**Math**

f' = x (lnx)^2 f" = lnx(lnx+2) f is concave down where f" < 0, or -2 < lnx < 0 That is, on the interval (1/e^2,1) You can see the graph of f(x) at http://www.wolframalpha.com/input/?i=1%2F4+x^2+%282%28lnx%29^2-2lnx%2B1%29+for+0%3Cx%3C2
*November 23, 2015*

**math**

height = 26 sin75° base is 26 cos75° feet from wall
*November 22, 2015*

**Pre-Algebra**

solve for t where 6 + 46t - 16t^2 = 39
*November 22, 2015*

**math**

4.50x + 5.50*20 = 5.00(x+20)
*November 22, 2015*

**Math**

35*.70 + 45*.30 = ?
*November 22, 2015*

**physics**

If the car stops in t seconds, the deceleration a is 35.5/t The distance traveled is s(t) = 35.5t - (35.5/2t)t^2 = 52.7 so, t = 2.97 seconds. a = 35.5/2.97 = 11.953 m/s^2 F = ma = 2165.7 * 11.953 = 25,886 N
*November 22, 2015*

**math**

(b+B)/2 * 2 = 36 b+B = 36 4x+5x=36 x=4 The bases are 16 and 20
*November 22, 2015*

**Physics IB**

see related questions below.
*November 22, 2015*

**Math**

if they are dependent they are the same line. So, the solution set is all real numbers. Any solution to one equation is a solution to the other.
*November 22, 2015*

**Calculus**

you have ∫[-∞,+∞] (x-μ)^2 1/r e^-(x/r) dx This just boils down to ∫x^2 e^(-x) dx with suitable constants thrown about. Do it with integration by parts twice to get -(x^2+2x+2)e^(-x) Now substitute in (x-μ) and x/r and things work out ok.
*November 22, 2015*

**Algebra**

If it takes him x hours, then 1/9 + 1/x = 1/5
*November 21, 2015*

**trigo**

You want <x,y> such that <x,y> + <0,-45> = <20,0> clearly that is <20,45> Now just convert that to speed and direction.
*November 21, 2015*

**wcccd**

looks like a good description...
*November 21, 2015*

**math**

original area: (x)(x) = x^2 larger area: (2x)(2x) = 4x^2 area goes up as the square of the scale factor, because both dimensions are multiplied. BTW, did you actually draw the squares? The answer would have been clear.
*November 21, 2015*

**Calculus**

and watch out for that "c"
*November 21, 2015*

**Science**

clearly, 2/3 mole NH3. So, just convert that to grams.
*November 21, 2015*

**Calculus**

∫[0,∞] xe^-x dx = -(x+1)e^-x [0,∞] lim -xe^-x = 0 x->∞ by lHospital's Rule so, ...
*November 21, 2015*

**College Algebra**

consider 4000 pieces one "job". The classic work problem now becomes 1/5 + 1/x = 1/3 x = 15/2 So, he can sort 2000 mails (1/2 job) in 15/4 hour
*November 21, 2015*

**Maths**

y = (x^2+5x^7)/x y = x + 5x^6 y' = 1 + 30x^5
*November 21, 2015*

**Math**

assuming base 3, log((4x+1)(13x-5)) = 2 (4x+1)(13x-5) = 3^2 = 9 52x^2 - 7x - 5 = 9 Now just solve the quadratic
*November 21, 2015*

**math**

total money = x .10*0.80x*2 - r*0.20x*2 = 3300 Without knowing x, there is no way to determine .10-r
*November 21, 2015*

**mathematics**

draw each line. Then shade the area below the two slanting lines, above the x-axis, and between the y-axis and the vertical line at x=80. The solution is the part where all the shaded areas intersect. A good start is shown here: http://www.wolframalpha.com/input/?i=solve+3x%...
*November 21, 2015*

**interes rate**

(1+r)^16 = 2 Now just solve for r.
*November 21, 2015*

**math**

x+y = 120, so y = 120-x z = x^2y = x^2(120-x) dz/dx = 240x - 3x^2 = 3x(80-x) absolute maximum of x^2y is at x=80 so, x=80, y=40 Note that this is very like the fencing problems, where the length is divided equally among the lengths and widths. Here, the powers of x and y are ...
*November 21, 2015*

**Calculus**

dz/dt = 2t e^z e^-z dz = 2t dt -e^-z = t^2 + c e^-z = c-t^2 -z = ln(c-t^2) z = -ln(c-t^2) at(0,0) 0 = -ln(c) c = 1 z = -ln(1-t^2) I like your answer. Maybe they want z = ln(1/(1-t^2))
*November 20, 2015*

**Calculus**

Hmmm. I get y = -e^(x/2) - 7e^(-3x) Better check your algebra. 2t^2+5t-3 = (2t-1)(t+3)
*November 20, 2015*

**World History**

thank you
*November 20, 2015*

**World History**

Sorry my answer is d
*November 20, 2015*

**World History**

Leaders in the industrialized world see booming populations in the least industrialized nations as a threat to? a= the continued expansion of their own nations b= technologymadvancement c= the global balance of power d= the existing food supply
*November 20, 2015*

**Math**

because one solution will lie on the positive real axis. The rest are evenly spaced above and below that axis, giving conjugate pairs.
*November 20, 2015*

**math**

He finds mc022-1.jpg and mc022-2.jpg.
*November 20, 2015*

**math**

If the depth is x dm, then we have 48*31.5*6.5 = 27*18.2*x If his speed is x in still water then 12/(x-4) = 5 Use that x to evaluate 15/(x+4) Draw a diagram. If you draw a radius perpendicular to the chords, you bisect them. You then have two 3-4-5 triangles (the radius of 5 ...
*November 20, 2015*

**trigonometry**

r = 7cos(θ+π/4) r^2 = 7rcos(θ+π/4) x^2+y^2 = 7/√2 r(cosθ-sinθ) x^2+y^2 = 7/√2 (x-y) You can massage that into the standard circle form if you want. Or, cheat here: http://www.wolframalpha.com/input/?i=x^2%2By^2+%3D+7%2F%E2%88%9A2+%28x-...
*November 20, 2015*

**conversions**

of course, the gauge does not matter for area. So, you have 30500 ft * 1m/3.28ft * 117in * 1ft/12in * 1m/3.28ft = 27640 m^2
*November 20, 2015*

**Maths**

it's just a flat line of any length. That is, its altitude is zero. Or, maybe it has an altitude, but a zero-length base, so it's a vertical line.
*November 20, 2015*

**physics**

huh? It does. Ever seen moist soil after a hot afternoon?
*November 20, 2015*

**English**

no such word as longly What does Mr. Spock always say? "shortly" means in a short time, not for a short time. That is it describes an event in the near future.
*November 20, 2015*

**Calculus**

along the line from (0,0) to (3,0), dy=0, so that part is just ∫[0,3] G(x,0) dx For the 2nd part, use the usual polar coordinate conversion with r=3, and you have ∫[0,π/4] G(3cosθ,3sinθ) dθ I can't tell what your radicals are supposed to be...
*November 20, 2015*

**math**

x < x-1 subtract x: 0 < -1 no solutions
*November 20, 2015*

**Calc**

v = π/6 d^3 so, you have dv/dt = π/2 d^2 dd/dt and just plug in your numbers.
*November 20, 2015*

**Kaah**

8v + .025*320 = 0 assuming the mass of the expelled gases is negligible ...
*November 20, 2015*

**functions**

x = 5+19
*November 20, 2015*

**Science**

First consideration: what does it mean for one color to be "better" than another?
*November 20, 2015*

**Math**

multiply all the values by 4, so you have 8:20:28 Now you can see the quantities that go with 20 cups of pineapple juice.
*November 20, 2015*

**Math**

34/.54 - 34
*November 20, 2015*

**Science**

their combined speed is 79 km/hr. So, they are 59.4 km apart after 59.4/79 hours
*November 20, 2015*

**geometry**

well, how about (x+5y)(x-3y) You just need two factors of 15 that differ by 2 in value; one added, the other subtracted.
*November 20, 2015*

**geometry**

well, let's see... +5 * -3 = -15 that help?
*November 20, 2015*

**math 5th grade**

HUH? She started with 2 lbs. How could she possibly wind up with 19.2 lbs??? When you get an answer, at least check to see whether it makes sense! 2/5 * 2 = 4/5 = 0.8 3/10 * 2 = 3/5 = 0.6 So, she used 1.4 lbs of flour, leaving 2.0-1.4 = 0.6 left over Hmmm. Maybe you meant she ...
*November 19, 2015*

**Calculus**

yep.
*November 19, 2015*

**algebra**

6C2 diagonals
*November 19, 2015*

**math**

If there are b bagels and m muffins, then just add up the revenue from each: .85b + 1.10m = 400.00
*November 19, 2015*

**math**

7x+5x=48 x=4 5x=20
*November 19, 2015*

**Physics [Help, need answer in 10 min]**

Never come here expecting instant help. Someone who can do it may not be available just now. Still, this problem seems pretty straightforward: F = GMm/r^2 = 6.673*10^-11 * 1.99*10^30 * 7.36*10^22 ------------------------------------------- (1.496*10^11 + 3.84*10^8)^2 = 4.345*...
*November 19, 2015*

**physics**

Just use the formula for each point and add 'em up. They're all in a nice straight line, so there are no vector calculations involved. Take a peek at http://hyperphysics.phy-astr.gsu.edu/hbase/electric/potpoi.html
*November 19, 2015*

**physics**

midway between the charges, of course.
*November 19, 2015*

**Math: Geometry**

huh? An easy isosceles trapezoid? Mark off P and Q on AB so you have a rectangle PQCD. That means that AP=QB=(9-8)/2 = 1/2 Now the height h of the trapezoid is h^2 = 7^2 - (1/2)^2 And the area is h(8+9)/2
*November 19, 2015*

**Math**

Just looking at the factors will not work, because you can't see the translations. Expanding and then completing the square, (x+3)(x-1) = x^2+2x-3 = (x^2+2x+1)-4 = (x+1)^2 - 4 So, that's x^2, translated left 1 and down 4 Or, using symmetry, you know the axis of ...
*November 19, 2015*

**Algebra 2**

As I read it, the directions were to list the possible rational zeros, not to actually find them. Looks to me like Truda did it just right.
*November 19, 2015*

**function rule**

a(w) = w(w+4)
*November 19, 2015*

**algebra**

common denominator is 60, so 15x-12x-20=64 3x=84 x=28
*November 19, 2015*

**Algebra 2 (Math)**

well, geez - start substituting! y=z+1 x=-3z+6, so (-3z+6)+2(z+1)+z=14 Now just solve for z, then you can get x and y.
*November 19, 2015*

**Calc**

f(t) = 800(1/2)^(t/5700) You can see that every time t increases by 5700, you have another power of 1/2, or a half-life. So, using that, just plug in your values for t. You can get an estimate by noting that 11400 = 2*5700 45000 ≈ 8*5700
*November 19, 2015*

**Math**

a scale factor of 3 means that all distances are multiplied by 3. So, multiply all your coordinates by 3.
*November 19, 2015*

**math**

assuming you mean (4x^3-x)/((2x+1)(6x-3)) = (x(2x-1)(2x+1))/(3(2x+1)(2x-1)) = x/3 = 3333 well, 7 men for 7 hrs for 1 day = 1 work unit 7 men for 1 hr for 1 day = 1/7 wu 1 man for 1 hour for 1 day = 1/49 wu 5men * 5hrs * 5days = 125/49 wu or, just do the ratios in-line (5/7)(5/...
*November 19, 2015*

**math**

At interest rate x, 2100(1+2x) = 2352 x = (2352/2100 - 1)/2 = .06 = 6% so, x-1 = 5% My age=m grandfather is g (g-16) = 9(m-16) (g+8) = 3(m+8) so, solve for m and g, and you want (m-8)/(g-8) = ?
*November 19, 2015*

**Algebra**

.06p = 7500 Now using that p, find .07p Or, just calculate (7/6)(7500)
*November 19, 2015*

**Algebra 2**

take a look at http://www.zweigmedia.com/RealWorld/LPGrapher/lpg.html Enter your problem. It will find a solution and even provide a graph. Be sure to set the x- and y-ranges appropriately. You can get an example to show the syntax. For this problem, just copy/paste minimize c...
*November 19, 2015*

**Algebra 2**

y = z+1 and x = -3z+6, so (-3z+6)+2(z+1) + z = 14 so, find z, then x and y
*November 19, 2015*

**algebra 2a help**

correct you have trouble with the word "minimum"?
*November 19, 2015*

**algebra 2a help**

true It's clear you need to review your introduction to complex numbers.
*November 19, 2015*

**Algebra**

clueless? check the topic of this section of your text. Review the definition of tan(x). Draw a diagram. Then it is clear that the height is given by 1.5 + 4.2 tan 74°
*November 19, 2015*

**Math**

maybe
*November 19, 2015*

**Calculus**

well, of course A,B,C depend on their denominators. But if you list them in the same order after solving for the values, the result should be (44/9)/x - (44/9)/(x+3) - (44/3)/(x+3)^2
*November 19, 2015*

**Pre-Calc**

No, but there are only a few points. Describe the picture. If a and b are on the same side of the vertical line down from the tower, then a-b=9°. If not, a+b=115° Where does the 43° angle come into play?
*November 19, 2015*

**Calculus**

forgotten your Algebra I? x/(6x-5) = 1/6 + 5/6 * 1/(6x-5)
*November 19, 2015*

**math**

AB => x+5 = y BA => 11-y = x So, just solve for x and y.
*November 19, 2015*

**math**

If the amounts in A and B are x and y, then .10x + .15y = 4000 .10(1.2x) + .15(1.1y) = 4000+500
*November 19, 2015*

**algebra**

since a=πr^2 = 78.5 = 25π, r=5 since s=rθ = 6π, θ = 6π/5 = 216°
*November 19, 2015*

**Calculus 1**

by l'Hospital, (a) -> (1/x + 2)/(2x) -> 3/2 (b) -> 2x/e^x -> 2/e^x -> 0
*November 19, 2015*

**Algebra I**

all correct. good work
*November 19, 2015*

**Maths**

xy=800, so x == 800/y x+2y = 800/y+2y for minimum value, you need -800/y^2 + 2 = 0 y=20 This is just like the fencing problems where minimum fencing for 3 sides of a rectangle is desired. The amount is evenly divided between the x's and the y's
*November 19, 2015*

**math**

sounds like the response to a question on Jeopardy! Want to revise the syntax?
*November 19, 2015*

**math**

that would be correct, since then the sin curve is above the cos curve.
*November 19, 2015*

**math**

To get the algebraic (signed) area, just do ∫[-π/2,π/2] cos(t)-sin(t) dt = 2 But that value subtracts the area where cos < sin. If you want the physical area, you need to break up the region at π/4. http://www.wolframalpha.com/input/?i=%E2%88%AB[-%CF%80...
*November 19, 2015*

**math**

cost: 40 desired revenue: 40*1.10 = 44 now divide that by the 80 good bananas to get the price for each banana.
*November 18, 2015*

**math**

cost: (120 * 1/6) + (120 * 1/5) = 44 sales: (120+120)/4 = 60 profit: 60-44=16 % profit = 60/44 = 15/11 15/11 - 1 = 4/11 = .3636 = 36 4/11 % It makes it harder to arrive at the solution when you have typos in the problem...
*November 18, 2015*

**Math**

clearly, the extra 4 balls added 760 g now do the math.
*November 18, 2015*