Saturday

May 23, 2015

May 23, 2015

Total # Posts: 31,335

**Physics**

as you said, the location of the center of mass does not change. So, since the boat weighs 4 times as much as the dog, it moves backward 1 foot for every 4 feet the dog moves forward. So, as you say, the boat has moved back 2 feet and the dog has moved forward 8 feet. That ...
*March 22, 2015*

**Math**

clearly it opens downward, since for equal increments of x, y is increasing, but more and more slowly. That means that soon it will turn around and start decreasing.
*March 22, 2015*

**Math**

first, there is no such word as miniscule. It is minuscule, and it is an adjective, not a noun. I have no idea which word you intended. you want to reduce the concentration by a factor of 10, so you need to increase the volume by a factor of 10. Since the original volume is ....
*March 22, 2015*

**Calculus Linearizations**

let y = √x that is, y^2 = x 2y dy = dx dy = dx/(2y) SO, given x = 16 y = 4 dx = -0.1, we have dy = -0.1/8 = -0.0125 That is, √(15.9) = y-dy = 4-0.0125 = 3.9875
*March 22, 2015*

**calc**

y = √x y^2 = x 2y dy = dx dy = dx/(2y) So, given x = 100 y = 10 dx = -0.4 dy = -0.4/20 = -0.02 so, √(99.6) ≈ 10-.02 = 9.98 actual value: 9.97998 As you can see, rather than using √(100-x) you just use √x and make a small adjustment. That way you ...
*March 22, 2015*

**Math**

The distance of (4,3) from (0,0) is 5. So, the circle is (x-4)^2 + (y-3)^2 = = 25 Now, you know that if the center were at (0,0), (±3,±4) and (±4,±3) would lie on the circle. So, shift those possibilities right and up, and see what drops out. (7-4)^...
*March 22, 2015*

**Maths**

well, you need to find the midpoint. That is at the average of the ends: (-1,0). Now just find the distance from there to (0,0). If the radii are a,b,c we have b = 5/4 a c = 4/5 b = 4/5 * 5/4 a = a so, the radii are the same, and hence the areas as well. Note that we don't...
*March 22, 2015*

**Pre ALGEBRA**

No idea, but it sure sounds like a dumb-ass way to model algebraic expressions. I can't decide just what means what You have black square white thin black thin white small square black small Clearly the question is garbled, or some geometric grouping is to suggest ...
*March 22, 2015*

**algebra. . please help**

rationalizing denominators depends on the fact that (a+b)(a-b) = a^2-b^2 So, if you multiply top and bottom by (3-√5), you have 4(3-√5) -------------- (3+√5)(3-√5) 4(3-√5)/(9-5) = 3-√5
*March 22, 2015*

**Math**

#1. I can't see where any n comes in at all. The chance of guessing the 3 digits in order is 1/5 * 1/4 * 1/3 That is, since there are 5P3=60 ways of picking 3 digits, and only one is correct, that's 1/60 chance of getting it right. #2 avg speed = totaldistance/...
*March 22, 2015*

**Algebra 1**

thank you
*March 22, 2015*

**Algebra 1**

what method would you use to solve y=x?
*March 22, 2015*

**math**

that works if she's now at 65.
*March 22, 2015*

**precalculus**

Take a look at the graph, and I'm sure you can justify your analysis. http://www.wolframalpha.com/input/?i=r%5E2+%3D+4cos2%CE%B8
*March 22, 2015*

**precalculus**

r = √(x^2+y^2) tanθ = y/x so, (-√6,-√2) = (√(6+2),arctan(-√2/-√6)) = (2√2,7π/6) To go the other way, just recall that x = rcosθ y = rsinθ
*March 22, 2015*

**mathematical physics**

∂f/∂x = 1/(1+xy^2) * y^2 = y^2/(1+xy^2) ∂f/∂y = 1/(1+xy^2) * 2xy = 2xy/(1+xy^2) ∂2f/∂x2 = -y^4/(1+xy^2)^2 ∂2f/∂y^2 = 2x/(1+xy^2) - 4x^2y^2/(1+xy^2)^2 = 2x(1-xy^2)/(1+xy^2)^2 ∂2f/∂x∂y = 2y/(1+xy^2) - y^2(2xy)/(1+...
*March 22, 2015*

**mathematical physics**

incompressible = solenoiodal iff ∇•F = 0 ∇•F = ∂F/∂x + ∂f/∂y + ∂f/∂z = (-x^2+y^2+z^2)/(x^2+y^2+z^2)^2 + (x^2-y^2+z^2)/(x^2+y^2+z^2)^2 + (x^2+y^2-z^2)/(x^2+y^2+z^2)^2 = 1/(x^2+y^2+z^2) ∇•F at (0,1,2) = 1/5 &#...
*March 22, 2015*

**social studies**

Explain the importance of accommodations to the tourism industry
*March 21, 2015*

**chemistry**

Induction will give you the correct answer. Which atom is the most electronegative?
*March 21, 2015*

**Analytical Chemistry**

What goes into Q exactly? I know activities are involved, but what species are in the Q expression? Would it be Cl-/O2? This is where I'm getting confused.
*March 21, 2015*

**Analytical Chemistry**

Indicate whether the following half-cells would act as an anode or a cathode when coupled with a S.H.E. in a galvanic cell. Calculate cell potential: Pt/O2(800 torr)/HCl(2.5E-5 M) I have not figured out a way to approach this problem. I know the nernst comes in, but I am at a ...
*March 21, 2015*

**chemistry**

Specifically, Lewis bases can donate their electrons, so they will have an excess amount of electrons. But, that doesn't mean that every negative charge will be a base.
*March 21, 2015*

**math**

Call AXB=ABX = a ABC = x ACB = XCB = x-39 We want XBC = x-a Then we have 2a+A = 180 x-a + x-39 + 180-a = 180 2x - 2a = 39 x-a = 19.5
*March 21, 2015*

**Math check**

#1: (2x)(10x) = (2*10)(x*x) = 20x^2 #2: -3m(m + 8) = (-3m)(m) + (-3m)(8) = -3m^2 - 24m #3: 4d(2d-9) = (4d)(2d) + 4d(-9) = 8d^2 - 36d #4: D #5: C
*March 21, 2015*

**application of differential equation**

this problem is discussed in detail at http://tutorial.math.lamar.edu/Classes/DE/Modeling.aspx just scroll down to where it talks about falling bodies.
*March 21, 2015*

**Math**

I don't think so. The tax rates are applied only to a portion of eligible income. Only the amount over $10K is taxed at 6% .02*2000 + .03*4000 + .045*4000 + .06(20900-10000) = 994
*March 21, 2015*

**Math**

#1 ok #2 26 + 3 who also liked Dalmatians but not Mickey = 29 #3 115-(39+43+56-(7+10+16)+4) = 6
*March 21, 2015*

**Algebra**

(x+a)(x+b) = x^2+5 x^2 + (a+b)x + ab = x^2+5 (a+b)x = 5-ab x = (5-ab)/(a+b)
*March 21, 2015*

**Math**

multiply each by 3/2
*March 21, 2015*

**algebra**

(5x)(7x+1)-(3x)(5x) = (7x+1-3x)(5x) = (4x+1)(5x)
*March 21, 2015*

**maths**

v = pi r^2 h = pi * 28^2 * 210 = 517231 cm^3 = 517.231 L
*March 21, 2015*

**physics**

well, the height in meters is h(t) = 0.60 + 0.15t - 4.9t^2 I presume you want to do something with its weight, which is 0.1*9.8 N . . .
*March 21, 2015*

**Algebra**

y/x = (x+y)/y since x+y=L, y/x = L/y Lx = y^2 Lx = (L-x)^2 x^2 - 3Lx + L^2 = 0 now solve as usual for quadratic. I expect you will get only one usable value Similarly, Lx = y^2 L(L-y) = y^2 y^2 + Ly - L = 0 now do the same for y. Make sure you choose positive values such that ...
*March 21, 2015*

**Algebra**

well, we all know that i = √-1. I assume you mean you want the expression rewritten as a standard complex number, a+bi. Since ... i^-3 = i i^-2 = -1 i^-1 = -i i^0 = 1 i^2 = -1 i^3 = -i i^4 = 1 ... #1 i^259 = i*(4*64+3) = i^3 = -i i^-22 = i^(-4*6+2) = -1 (3+4i^259)(2-3i^-...
*March 21, 2015*

**math - URGENT**

just take it step by step. The x-intercept is where y=0, so x = -79 Now, your line must have a slope of -7, so its equation is y-0 = -7(x+79) mq = -7(79) = -553
*March 21, 2015*

**MATH!!!**

y+9 = 5/32 (x+10)
*March 21, 2015*

**math -ans check**

looks right to me
*March 21, 2015*

**maths!!!!!!**

clearly, d = (3/16 - 24)/7 = -381/112 Now you can find a, since a+5d = 24 Now you can list the terms if you want.
*March 21, 2015*

**Pre-Calc.**

r^5 = 16807 r = 7 Now just write the terms
*March 20, 2015*

**Calculus**

Did you reall mean 5^x, or 5x^2? I will assume the latter. Since f" = -12x^2-48x+10 and that has two roots, those are where the inflection points lie.
*March 20, 2015*

**Calculus**

f = ax^b lnx f' = ax^b/x + ax^b lnx b/x = ax^blnx (1/xlnx + b/x) = f(x)*(1/xlnx + b/x) f'(1/5) = 1/(1/5 ln(1/5)) + 5b = -5/ln5 + 5b so, b = 1/ln5 f(x) = ax^(1/ln5) lnx a(1/5)^(1/ln5)(-ln5) = 1 a = -5^(1/ln5) / ln5 = -e/ln5 f(x) = -e/ln5 x^(1/ln5) lnx This has a minimum...
*March 20, 2015*

**math**

r:b = 5:2 b:g = 3:5 or, r:b = 15/6 b:g = 6:10 so, r:b:g = 15:6:10 so, see what you can do with part (b)
*March 20, 2015*

**math**

.04x + .05(2x) = 266
*March 20, 2015*

**math**

10x + 13(432-x) = 12(432)
*March 20, 2015*

**math**

since distance = speed * time, (x + x+10)(1.6) = 128 2x+10 = 80 x = 35 So, Mary's car goes 35 mi/hr, and John's car goes 45 mi/hr
*March 20, 2015*

**math**

Let s be the speed of the rowers, and c be the speed of the current since distance = time * speed, 3/2 (s+c) = 12 4(s-c) = 12 Now just solve for s and c
*March 20, 2015*

**math**

If there are x lbs of flour, then add up all the amounts of protein: .08x + .16(32-x) = .13(32) x = 12 lbs flour
*March 20, 2015*

**math**

Better talk to Nina, who did the very next post below yours. .04x + .05(2x) = 315
*March 20, 2015*

**math**

.04x + .05(2x) = 125 Now just find x and thus 2x.
*March 20, 2015*

**Pre-Algebra**

for two lines of the form y=mx+b to have infinitely many solutions, they must be the same line. That is, m and b must be the same. Your two lines are parallel, so they never meet; no solutions.
*March 20, 2015*

**Advanced Algebra**

n/2 (4+34) = 247 n=13 I expect you can now find the difference, eh?
*March 20, 2015*

**math104**

it's not a cross-product. It's just times. 10log(2.64*10^-5/10^-12) = 10log(2.64*10^7) = 10(7+.4) = 74 dB
*March 20, 2015*

**Math**

just use your formula for the FV of an annuity.
*March 20, 2015*

**Trigonometry - Oops**

My bad - switched x and y: (y/x + 1/√3)/(1 - y/x√3) = (y+35)/x x^2+y^2 = 25^2 x = 19.408, y=15.759 so, z = 54.343 not very far off, really, eh?
*March 20, 2015*

**Trigonometry**

as usual, draw a diagram. Let T be the top of the pole B be the bottom of the pole P be the point where the wire meets the ground. Draw a horizontal line from P, and extend TB into the ground, so that Q is the intersection of the horizontal from P and the vertical from T Then ...
*March 20, 2015*

**math**

so far so good. The complete solution turns out to be, as I'm sure you have worked out: y = c1 e^-x + c2 e^-2x + 1/4 (2x^2-6x+7)
*March 20, 2015*

**math(Discrete)**

As I recall, ∃! means "there exists exactly one" So, I guess the negation would be There exists at least one or there is none (∃ ∨ ∄) or, maybe ~∃!
*March 19, 2015*

**trig**

since cos(x+pi) = -cos(x), y = -3cos(x) - 3 Not sure what you want to know about it. -3cos(x)-3 is 3cos(x+pi)-3 shifted left or right by pi, and then flipped over. Since cosx has a period of 2pi, you can see why this would result in an identical graph.
*March 19, 2015*

**Geometry**

see the 1st related question below.
*March 19, 2015*

**Geometry**

since the circumference is 3π feet, it makes 45/3π = 15/π turns per second. That is π/15 seconds per turn. So, it takes 100π/15 = 20π/3 seconds to do the job.
*March 19, 2015*

**Math**

50m is the total length of the paths, but that was not the question. 30m*20m = 600m^2 you don't say which path runs the length and which the width. If the wider path is the longer, then the area used up by the paths is .8*30 + .7*20 - .8*.7 = 37.44 So, that leaves 600-37....
*March 19, 2015*

**Geometry**

12 turns/5s = 2.4 turns/s each turn of a wheel of diameter d is πd inches, so (225in/s)(1s/2.4rev) = 225/2.4 = 93.75 in/rev so, πd = 93.75 d = 29.84 in
*March 19, 2015*

**Geometry**

actually, that's not quite right. If the circumference is c, and the tire width is w (both in feet), the area of track made by one turn is cw. So, the tire makes 250/cw turns. Pick your own c and w.
*March 19, 2015*

**Geometry**

if the tire has width w and diameter d, then w*πd = 250 ft^2 wd = 250/π ft^2 so, pick any width and diameter (both in feet) that multiply to 250/π
*March 19, 2015*

**Math**

2.5 min = 150 sec, so A. 150+4*10 B. S10 = 10/2 (2*150 + 9*10)
*March 19, 2015*

**Math**

A: 1.6 * 0.8^5 B: 1.6 * (1 - 0.8^7)/(1-0.8)
*March 19, 2015*

**algebra**

I assume you mean y = -2√(3x-12)-5 = -2√(3(x-4)) - 5 so, the function √x has been shifted right by 4, scaled horizontally by a factor of 1/3, reflected over the x-axis, stretched vertically by a factor of 2, and shifted down 5.
*March 19, 2015*

**Calculus**

see the 2nd related question below. Just change the numbers.
*March 19, 2015*

**Algebra**

#1: √(11^2 - 7^2) #2: √((5+3)^2 + (6-1)^2) #3: ((-6+8)/2,(-2+4)/2) Better review your text for these topics.
*March 19, 2015*

**Alegbra 1**

just plug in the values for t, using the formula 25000 * 1.08^t For example, after 2 years, the salary is 25000 * 1.08^2 = 29160
*March 19, 2015*

**Math**

what's the trouble? Just plug in the values for t. For example, Q(800) = 300 e^(-0.000324*800) = 231.5006
*March 19, 2015*

**Math**

#1 False, if you meant (5x+1)/(x+2)(x-1) Do partial fractions just the way you add fraction of unlike denominators. 2/3 + 3/4 = (2*4 + 3*3)/(3*4) Now, you are given the result, and you want to find the parts. So, we are looking for (5x+1)/(x+2)(x-1) = A/(x+2) + B/(x-1) = (A(x-...
*March 19, 2015*

**Math**

oops. i gave the price per book. So, 60 books would cost p(60) = 60(86.45 - .055*60) = $4989.00
*March 19, 2015*

**Math**

No idea. Maybe there's a price break from $86.45/book to $80.95/book if you buy more than 100 books. In that case, 60 books cost 60*86.45 = $5187.00 There are many different functions that pass through those two points. I assume you are looking for a linear relationship. ...
*March 19, 2015*

**math**

x/25 = cos 63°
*March 19, 2015*

**math**

3500 * 1.04^6
*March 19, 2015*

**mathematics**

a+6d = 3 a+11d = -3 clearly, 5d = -6, so d = -6/5 that means a = 51/5
*March 19, 2015*

**Algebra**

Nope.
*March 19, 2015*

**Math**

always rearrange things into descending powers. Set equal to zero because after you factor it, you know that the product can be zero only if one of the factors is zero. f^2+7f-60 = 0 (f+12)(f-5) = 0 f = -12 or 5 6x^2-x-15 = 0 (2x+3)(3x-5) = 0 x = -3/2 or 5/3 6(y-3)^2 - (y-3...
*March 19, 2015*

**math**

each man can do 1/(20*24) = 1/480 of the job in a day. So, in 6 days, they have done 6*20/480 = 1/4 of the work. So, if the new men work at the same speed, you need to do 3/4 of the job in 15 days. m additional men can do 15m/480 = m/32 of the job in 15 days. So, we need m/32...
*March 19, 2015*

**math**

3-32 = -29 Divide that into two equal parts, and k has the same difference before and after: k = 32-29/2 = 35/2
*March 19, 2015*

**electrical principles**

the 4 240Ω resistors have a combined resistance of 60Ω Add that to the 40Ω in series, and the total is 100Ω P = E^2/R, so the parallel group dissipates 960W Now just figure the energy of the heater.
*March 19, 2015*

**Math**

1/6 + 1/3 + 1/(4/3*6) = 5/8 So, they will take 8/5 hr or 1 hr 36 min. Now just figure 1/3 - (1/6 + 1/8) = 1/24 so it takes 24 hrs to empty the pool
*March 19, 2015*

**math**

suppose y=0. That means x+z = 18 x-z = 26/5 x = 58/5 z = 32/5 So, the largest x can be is 58/5 Now, suppose we toss in y. If we subtract y/2 from both x and z, then the difference between x and z is still 26/5, and the sum is (x-y/2) + y + (z-y/2) = x+z = 18 For example, if y...
*March 19, 2015*

**Quick math help**

the one which includes the same variables and the same powers: A
*March 19, 2015*

**algebra**

as usual, just add exponents. 7^√3 * 7^√2 = 7^(√2+√3) Don't be spooked by radicals. They're just numbers.
*March 19, 2015*

**Geometry**

suppose you rotate around (0,0). That takes (x,y) -> (-y,x) Shifting the origin to (-8,3) changes the distance, and gives us (x+8,y-3). So, the shift takes (5,-9) -> (13,-12) Then the rotation takes (13,-12) -> (12,13) reflection through the line y=9 takes (x,y) ->...
*March 19, 2015*

**Advanced Algebra**

If you have the two points at the ends of the interval [a,b], then no matter how f(x) twists and turns in the interval, the average rate of change is the slope of the line joining (a,f(a)) and (b,f(b)). That is, (f(b)-f(a))/(b-a)
*March 19, 2015*

**Math**

clearly, 190 = 47*4 + 2 That means 47 whole cycles of digits 2,4,8,6 have been used, leaving 2 more: 2 and 4. 2^6 ends in the same digit as 2^2 and so on, till 2^190 = 2^(47*4) + 2
*March 18, 2015*

**Math**

Note that the powers of 2 end in digit that cycles: 2,4,8,6,2,4,8,6,... Since 190 = 47*4 + 2, 2^190 ends in 4 So, the remainder is 4 when divided by 5. If AC=32, the the hypotenuses AC and AD are in the ratio 2:1. So also are sides AD and AB. So, AB=12, making BC=24 And yes, ...
*March 18, 2015*

**Math**

I think you garbled your question, but since the cone and sphere share a radius, and the height of the cone is the same as the radius of the sphere, the volumes are hemisphere: 2/3 πr^3 = 2/3 π * 3^3 = 18π cone: 1/3 πr^2 h = 1/3 π * 3^2 * 3 = 9π
*March 18, 2015*

**Math**

the large triangle has base b and height h. So, its area is bh/2 The smaller triangle has base b/2 and height h/2, so its area is (b/2)(h/2)/2 = bh/8 = 1/4 (bh/2)
*March 18, 2015*

**Math**

This problem comes in many guises. One can be found here: http://math.stackexchange.com/questions/105084/a-line-which-bisects-two-sides-of-a-triangle-is-parallel-to-the-third Naturally, the area of the small triangle CBE is 1/4 the area of CAD, since it has half the base and ...
*March 18, 2015*

**Math**

You need to understand the concept of the slope of a line. It says how fast y changes as x changes by 1. That is, if the slope is 3, y increases by 3 whenever x increases by 1. If the slope is -2, y decreases by 2 when x increases by 1. So, given two points, the slope is the ...
*March 18, 2015*

**algebra**

R(x) = (8+x)(2000-100x) So, that is just a parabola, with its vertex (maximum revenue) at x=6 Now you can answer the other questions.
*March 18, 2015*

**algebra**

you might look at the many similar questions below. I'll give you the shortcut, which always works in this kind of situation. The maximum area is achieved when the fencing is divided equally among the lengths and the widths. In this case, we have one length and two widths...
*March 18, 2015*

**algebra**

150x300
*March 18, 2015*

**algebra**

x + 3y = 18 z = xy = (18-3y)(y) = 18y-3y^2 This is just a parabola with vertex (maximum value) at y=3 so, x=9, y=3
*March 18, 2015*

**Math**

the width and length are both reduced by 9.2cm on each side, so the new perimeter is 2((6.2-2*.092)+(5.6-2*0.92)) = 19.552 m
*March 18, 2015*

**math**

since y = -12x^2 has vertex at (0,0) and opens down, your function is reflected in the x-axis, shifted left 3 and up 2, so it is 12(x+3)^2 + 2
*March 18, 2015*