Monday
April 27, 2015

Posts by steve


Total # Posts: 30,825

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

MATH
looks like output grows by 18 when input grows by 1. So, starting at f(2) = 30 = 36-6, f(x) = 18x-6
March 18, 2015

math
ns = k, a constant value. or, it is often written as n = k/s direct variation is n = ks
March 18, 2015

trig
assuming you mean line-of-sight distance, 300/x = sin 25° If you mean how far long the ground has he traveled, then 300/x = tan 25°
March 18, 2015

Algebra
As I said at 6:42 pm, check your signs. I get -3.125 or +1 Naturally, the negative answer may be disregarded.
March 18, 2015

math
ummm. hold the ruler next to the object and count the marks. Never done that?
March 18, 2015

Math
full price is 12*14 = 168 Since she bought 12 or more, she gets 1/4 off that amount, or 42 So, she pays 168-42 = 126 Or, you can say that with 1/4 off, each ticket costs $9 instead of $12. 14*9 = 126
March 18, 2015

Math
There were a total of 8000 seats for the two nights. The empties are therefore 8000-6109=1891 you got the right answer, but 6109-4000 is not 1891.
March 18, 2015

Math
5 * 7/8 = ?
March 18, 2015

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