Saturday
August 1, 2015

Posts by STEVE


Total # Posts: 32,558

calc
I see several similar questions in the Related Problems below. I expect they will help out.
June 13, 2015

statistics
it is the correlation coefficient. Better read your text, or google some articles.
June 13, 2015

Calculus
If he lands x miles from the nearest point on the shore to P (call it O), and O is m miles from Q, then the distance traveled is z = √(x^2+1) + m-x The time taken is thus t = 1/3 √(x^2+1) + (m-x)/5 You want to minimize t, so dt/dx = x/3√(x^2+1) - 1/5 dt/dx = ...
June 13, 2015

Calculus
There are several similar related questions below. I'm sure you can adapt one of those solutions to your specific numbers.
June 13, 2015

Algebra
I'm assuming you meant "starting with n=1". If so, just start substituting in values for n: a1 = 2^(1-1) = 2^0 = 1 a2 = 2^(2-1) = 2^1 = 2 and so on.
June 13, 2015

math
the raise increases the mean from 34600 to 34600+3900/5 = 35380. The median will not change, since only the highest salary has increased. The number of salaries above and below the median has not changed. Same for the mode, since the wording of the question implies that there ...
June 13, 2015

Math
clearly, since 0 <= |sin x| <= 1, the extrema are where sin^2(2x) = 1 or 0 That is, sin(2x) = ±1 or sin(2x) = 0 In the indicated domain, that leaves 2x = π/2 or 3π/2 or 0 or π or 2π x = π/4 or 3π/4 or 0 or π/2 or π See the ...
June 13, 2015

Alg 2 HELP!!
#1 since y=ab^x, just plug in the two points you are given: ab^2 = 48 ab^5 = 3072 Divide the 2nd by the first and you have b^3 = 64 b = 4 a*4^2 = 48, so a = 3 and y = 3*4^x #2 inverse variation means xy = k, a constant. Plug in your values and you have (6)(-1) = (3)(y) y = -2...
June 13, 2015

Alg 2
8^log(8)x = x I stated it clearly as one of the examples. Similarly, log(8) 8^x = x
June 13, 2015

Alg 2
^ and log are inverse operations x+8 - 8 = x x/8 * 8 = x (√x)^2 = x log88x = x 8log8x = x The thing that makes logs initially so confusing is the notation. If we had a cute symbol like + or / or √ things would be a lot easier. The definition of log8x is that power ...
June 13, 2015

trigonometry
Of course the answer is complete. I have evaluated every trig function given. What else can there be? What makes you think that there might be something missing?
June 13, 2015

trigonometry
sin 150 = sin 30 = 1/2 cos 315 = cos 45 = 1/√2 cos(90-x) = sin x sin (360-x) = -sin x cos -240 = cos 240 = -cos 60 = -1/2 sin 135 = 1/√2 So you have 2(1/2)(1/√2)(sin x) ------------------------- (-sin x)(-1/2)(1/√2) Think you can handle it now? As I ...
June 13, 2015

trigonometry math help
Reduce things to reference angles in Quadrant I: sin 250 = sin(270-20) = -cos 20 = -m since sin^2+cos^2 = 1, sin 20 = √(1-m^2)
June 13, 2015

university
it will take 0.69 seconds for the water to fall 2.35 meters. At 1.70 m/s, the water will be 1.177 m from the wall when it hits. So, how wide is your walk? More important, how tall do you expect the pedestrians to be? The water must be far enough from the wall not to hit the ...
June 13, 2015

math
well, 150*48 = 7200 150*43 = 6450 what do you think?
June 13, 2015

algebra
You want 200((1.06^71 - 1)/(1.06-1) - 1) Better study your annuity formula and how it arises.
June 13, 2015

Algebra 1
Well, I doubt that -5.26 is a solution, but you can easily check that 7.58 works just fine. Don't you check your answers when you get them?
June 13, 2015

chemistry
Oxalic acid is H2C2O4 with a mol wt of 126.07 grams I expect you can take it from there . . .
June 13, 2015

Math
You must surely have discussed this topic, for otherwise there would be no need to ask such a question. The brief discussion in wikipedia sheds some light on the topic. http://www.geneseo.edu/~bearden/socl211/chisquareweb/chisquare.html google is your friend on questions of ...
June 12, 2015

physics
x/2.5 = 48/5.0 and do the same for the other question.
June 12, 2015

Differential equation
oops typo that should be √(1+x^4) everywhere. I seem to have slipped in some 1+x^2...
June 12, 2015

Differential equation
y′=12x^3 √(1+x^4)(1+y^2) Man, after the last one, this should not have caused you any headaches. It's basically the same thing dy = 12x^3 √(1+x^4)(1+y^2) dx dy/(1+y^2) = 12x^3 √(1+x^4) arctan(y) = 2(1+x^2)^(3/2) + c y = tan(2(1+x^2)^(3/2) + c) y(0)=...
June 12, 2015

Physics
y = a(x-h)^2 + k y'(0) = tan 50° = 1.1917 k = 0.0674 a(1.06-h)^2 + k = 0 2a(-h) = 1.1917 y = -0.7782(x-0.7657)^2+0.0674 y = -0.7782x^2 + 1.1917x - 0.3887 Let the height y be given by y = ax^2+bx+c y(-b/2a) = 0.0674 y(1.06) = 0 y'(0) = 2ax+b = tan 50° = 1.1917 ...
June 12, 2015

Differential equation
dy = 8e^(4x)(1+y^2) dx dy/(1+y^2) = 8e^(4x) dx arctan(y) = 2e^(4x)+c y = tan(2e^(4x)+c) at x=0 you have tan(2+c) = -2 c+2 = arctan(-2) = -1.107 c = -3.107 y = tan(2e^(4x)-3.107)
June 12, 2015

math
(3a)^2 = 9a^2 ((3a)^1/2)^-1/2 = (3a)^-1/4 There's just no valid way to come up with what you got.
June 12, 2015

math
when you multiply, you add exponents. For example, 2^3 x 2^4 = 2^(3+4) = 2^7 Recall that negative exponents are the reciprocals of positive exponents. 2^-3 = 1/2^3 = 1/8 SO, you have (3a)^1/2 * (3a)^-1/2 = (3a)^1/2 / (3a)^1/2 = 1 or, by adding exponents, (3a)^1/2 * (3a)^-1/2...
June 12, 2015

maths
what does "between a ... triangle" mean?
June 12, 2015

Physics
wikipedia has a nice article on trajectory. If you scroll town a bit, you come to the equations in terms of θ, x and t.
June 12, 2015

Alg 2 HELP!
x = -b/2a only works with quadratic functions. When the polynomial is of degree 3 or higher, all bets are off. In this case, there is a local max or min when 3x^2+4x-13=0
June 12, 2015

Alg 2 HELP!
On the first one, it's easy enough to find the intercepts. Coming up with the max and min is a bit tricker, if you don't have calculus as a tool.
June 12, 2015

Maths
in QIII, tan is positive and csc is negative. (doesn't really matter, since they're both squared in the expression.) So, sinA = -√3/2 tanA = √3 csc^2 = 1+tan^2, so 4tan^2-3csc^2 = tan^2A-3 = 0
June 12, 2015

math
P(A and B) = 1/2 * 1/15
June 12, 2015

Alg
It might help if you provided the function. . .
June 12, 2015

add maths
see Related Questions below.
June 12, 2015

maths
the curved surface is just a rectangle of width 2πr=140π and height 1 the top and bottom are circles of area πr^2 = 4900π So, add it all up.
June 12, 2015

Calculus
If you let u = x^2, then du = 2x dx But you only have x dx, which is 1/2 du
June 11, 2015

math
12 / (5/4) = 12*4/5 = 48/5 So, 9 bags with 3/5 bag (3/4 cup) left over
June 11, 2015

Algebra
nope. Just take the factors in pairs, as I did, working your way in from the ends. Actually, even that's not necessary, unless you just want to verify the results. There are 12 factors, so that means there are 6 pairs like the two I showed above. So, there are 6 pairs of ...
June 11, 2015

Algebra
you want x^2-y^2 = 495 (x+y)(x-y) = 495 495 = 3^2*5*11 so, the factors are 1 3 5 9 11 15 33 45 55 99 165 495 so, if you have x+y=495 x-y=1 248^2-247^2 = 495 x+y=165 x-y=3 84^2-81^2 = 495 and so on
June 11, 2015

physics
since pressure is force/area, a smaller area means greater pressure.
June 11, 2015

math
3^-3 + 3^-4 = 3*3^-4 + 3^-4 = (3+1)*3^-4 = 4*3^-4 Recall that a negative exponent switches between top and bottom in fractions. So, 4*3^-4/3^-5 = 4/3^4 * 3^5 = 4*3 = 12
June 11, 2015

algebra 2
The terms shown cannot all be part of an AP. So, assuming that 192 and 196 are the first two terms, d=4. No idea what 48 is doing there. Now, 1,2,4 is the start of a G.P with a = 1 r = 2 So, an = 1*2^(n-1)
June 11, 2015

algebra 2
That would be a^2 = B Note that the base of the log and the base of the exponent are the same. The log (in this case, 2) is the exponent.
June 11, 2015

Algebra
r-2 and s-2 are the roots of (y+2)^2 - 19(y+2) + 7 = 0 y^2 - 15y - 27 = 0 The product of the roots of the shifted function is -27
June 11, 2015

physics
since the height h = Ho+Vo*t-4.9t^2, the top ball will hit after t seconds, where 10+0t-4.9t^2 = 0 t = 1.429 seconds its final speed is v = 0-1.429*9.8 = -14.00 m/s The middle ball must then be thrown downward with velocity v such that v-9.8t = -14.00 7.5+v*t-4.9t^2 = 0 v = -7...
June 11, 2015

physcis
the height h is h(t) = vt-4.9t^2 So, the max height is achieved when t = v/9.8 So, we have v(v/9.8)-4.9(v/9.8)^2 = 0.85 v = 4.08 So, the height is roughly h(t) = 4t-4.9t^2 Now you can figure the other answers, I expect.
June 11, 2015

math
You are correct, since 12*7/2 = 42.
June 11, 2015

Frequency Distribution
total sales: 6*25+7*20+8*10+9*0+10*5 = 420 That's 420sales/60hr = 7 sales/hr
June 11, 2015

geometry - My bad.
oops. My bad. I neglected to read that the areas were 5:2, not the sides. Go with Damon. Right, as usual.
June 11, 2015

geometry
the question asked for the corresponding side, not the area. So, 10.00 is the correct answer.
June 11, 2015

chemistry
Assuming the reaction is Ca(HCO3)2 = CACO3 + CO2 + H2O then 200g of limestone is 200/162.11 = 1.234 moles So, you have that many moles of CO2 1 mole occupies 22.4L at STP, and contains 6.023x10^23 molecules. So, I guess you can now answer the questions, eh?
June 11, 2015

math
Assuming you meant (√3+√2)/(3-√2) multiply top and bottom by 3+√2 and you have (√3+√2)(3+√2)/7 = (3√3+√6+3√2+2)/7 I suspect a typo. Maybe you can repost with standard characters.
June 11, 2015

Math
try using some standard math notation x^-3 * x^9 * y^5 * y^3 = x^6 y^8 you are correct.
June 11, 2015

math - oops
oops. misspoke on the first solution cos(θ+60) = cosθ cos60 - sinθ sin60 = (-4/5)(√3/2) - (-3/5)(1/2) = 3/10 - 2√3/5
June 11, 2015

math
since θ is in QIII, cosθ is also negative, and so is -4/5. If you really meant what you wrote, then since 180/3 = 60, you want cos(θ+60) = cosθ sinθ - cos60 sin60 = (-4/5)(-3/4) - (1/2)(√3/2) = 3/5 - √3/4 If you meant cos (θ+180)/3 = ...
June 11, 2015

Maths
study math, and stop wasting your time. Better yet, study how the lotto works, and realize that there is no such equation.
June 11, 2015

physics
It takes the car 10/8.7 = 1.149 seconds to stop s = 10t - 4.35t^2 so plug in t = 1.149 to find the distance
June 11, 2015

Math (Finite)
since no digits are to be repeated, the number of possible valid combinations is just the number of permutations of 10 things, taken 5 at a time: 10!/5! However, unless the burglar knows that, he still has only one chance in 10^5 of getting it right, as PsyDAG showed above.
June 11, 2015

math
well, you can start by listing the even numbers between 50 and 60 52 54 56 58 Now, which of those is divisible by 3?
June 11, 2015

linear algebra
The symmetric matrix for Q is (1 1 3) (1 1 -2) (3 -2 1) Can you now reduce that to diagonal form?
June 11, 2015

calculus1
Ok. Using parentheses to disambiguate the function, we have y = 1/(4x) + x^3/3 y' = -1/(4x^2) + x^2 so, the arc length is ∫[2,3] √(1+(y')^2) dx = ∫[2,3] √(1+(-1/(4x^2) + x^2)^2) dx = ∫[2,3] x^2 + 1/(4x^2) dx = 1/3 x^3 - 1/(4x) [2,3] (1/3*...
June 11, 2015

Physics
when will it hit? 190 + 170t - 4.9t^2 = 0 t = 35.777 what is its speed? v = 170-9.8t = 170-9.8*35.77 = -180.546 Or, using conservation of energy, max height is reached when v=0, so 170-9.8t=0 t=17.346 h(17.346) = 1664.49 At that point, the PE = mgh = 1664.49*9.8m = 16312m So, ...
June 11, 2015

calculus1
If you meant y = 1/4 x + x^3/3 s = ∫[2,3] √(1+(1/4 + x^2)^2) dx If I got it wrong, fix it and edit the integral.
June 10, 2015

calculus1
#1 cos(1/x^3) oscillates between 1 and -1, but the x^2 out front forces the limit to zero http://www.wolframalpha.com/input/?i=x^2cos%281%2Fx^3%29+ #2 for x < 1, x^2+2x-3 < 0 So, you have 4*1/(small negative) -> -∞ #3 same thing here. sin(x) > 0 for x<&#...
June 10, 2015

calculus1
use l'Hospital's Rule: #1 the limit is the same as sec^2(x)/(4x-8) = -1/8 Factoring top and bottom, you have (x+2)(x^2-2x+4) / (x-2)(x+2)(x^2+4) So, at everywhere except x = -2, f(x) = g(x) = (x^2-2x+4) / (x-2)(x^2+4) g(-2) = (4+4+4)/(-4(8)) = 12/-32 = -3/8 Since f(x) ...
June 10, 2015

k92 sec.
how many moles of CS2 is 2g? how many moles of So2 are produced by one mole of CS2? Then, since 1 mole fills 22.4L of volume at STP, you can figure the volume. Or, check the related questions below
June 10, 2015

Pre Calculus
If the amounts of 5%,15% and 25% are x,y,z then we have x+y+z = 50 .05x + .15y + .25z = .20(50) x = 2y Replace x with 2y and you have 2y+y+z = 50 .05(2y) + .15y + .25z = .20(50) or, 3y+z = 50 .25y + .25z = 10 3y+z = 50 y+z = 40 So, subtracting, we get 2y=10 y=5 so, x=2y=10 10+...
June 10, 2015

math
120 tiles in all 6 * 2*2 = 24 gray so, 96 white 96-24 = ? more white than gray
June 10, 2015

algebra2
since you have 8x+47 = 8x+40 there are no solutions
June 10, 2015

math
since 1/3 = 2(1/6), you have 5/3 - 5/6 = 2(5/6)-(5/6) = (2-1)(5/6) = 5/6
June 10, 2015

Geometry
1/2 of the chord is r sin(B/2) So, the area of the triangle is 2 * (1/2 r sin(B/2)(r cos(B/2)) = r^2 sin(B/2)cos(B/2) = 1/2 r^2 sinB The area of the whole sector is 1/2 r^2 B So, the segment's area is as noted above: the sector minus the triangle.
June 10, 2015

pre-calculus 11
if f(x) = 1/(x-c), then there is a vertical asymptote at x=c. This is the graph of f(x) = 1/x, shifted right by c. If f(x) = 1/x - c then the graph is f(x)=1/x, shifted down by c, and the vertical asymptote is at x=0. And you have your shifts backwards. Plugging in x=1 in ...
June 10, 2015

Math
let's start plugging in numbers as we figure them out: xxxxxxx the last digit is even, so we have xxxxx0 xxxxx2 ... xxxxx8 the 1000's is twice the ones', so we can't have the last digit more than 4: xx0xx0 xx4xx2 xx8xx4 the 100,000 is the 1000's+3, so we ...
June 10, 2015

kapahi
If the box has 4 blue balls, then that means the one remaining ball is red. So, there is only one way to have a 5-ball box with 4 blue balls: It must have one red and 4 blues. That is if all the balls of a color are identical. If they are somehow distinguishable, then there ...
June 10, 2015

Math
you are correct. as an even simpler example, let g(x) = x-1 (neither even nor odd) f(x) = x (odd) f∘g = x-1
June 10, 2015

pre-calculus 11
perhaps it will help to view the two functions graphed individually: http://www.wolframalpha.com/input/?i=+|1%2F2x+%2B1|+%3D+x%2B1
June 10, 2015

calculus1
#1 Let u = x^2+9 du = 2x dx and you have ∫ 1/2 √u du That's easy, right? From the 2nd Fundamental Theorem of Calculus, F'(x) = f(x) = x√(x^2+4)
June 10, 2015

calculus1
sin u sec^5 u = tan u sec^4 u = sec u * tan u * sec^3 u du if v = sec u, then that is v^3 dv So, you have ∫ sin2x sec^5(2x)dx 1/2 ∫ sin2x sec^5(2x) 2 dx = 1/2 ∫ sec^3(2x) d(sec(2x)) = 1/8 sec^4(2x) + C There are lots of good Riemann sum calculators online. ...
June 10, 2015

math trigonometry
can you not use the same name for all your posts? cos(-200) = cos(200) = -cos(20) = -m work with the other angles in a similar way. Draw triangles on the axes to help see the transformation formulas.
June 10, 2015

math trigonometry
it's just an expression. Nothing to prove. But, in the spirit of the previous post, reduce all the angles to QI reference angles and see what drops out.
June 10, 2015

math trigonometry
what's the problem? cos 180 = -1 sin 225 = -sin 45 = -1/√2 sin 170 = sin 10 = cos 80 tan 135 = -tan 45 = -1 and you have (-1)(-1/√2)(cos 80) / (cos 80)(-1) = -1/√2 or -(-sin 45) / -tan 45 = -cos 45 = -1/√2
June 10, 2015

Physics 11th
h(t) = x + 4.9t - 4.9t^2 if h=0 when t=3, then x + 4.9(3) - 4.9(9) = 0 x = 29.4
June 10, 2015

Algebra
4! = 24
June 9, 2015

Alg 2
y-4=2(x+3) is the line parallel to y=2x-5 You want the line perpendicular. So, your equation is y-4 = -1/2 (x+3) you can massage that as you will.
June 9, 2015

Physics
it takes 120/200 = .6 seconds to reach the target. So, how far does the bullet fall in .6 s?
June 9, 2015

calculus1
f(x) = cosx+x-2 f'(x) = 1-sinx start with, say, x=3 x -> 3 - f(3)/f'(3) = 3-.01/.8588 = 2.98835 and proceed as needed
June 9, 2015

math trigonometry
that's theta, not theter. tan(180+θ)*cos(90+θ) + sin(360-θ)*tan(180-θ) = (tanθ)(-sinθ) + (-sinθ)(-tanθ) = 0
June 9, 2015

algebra 2
clearly, a = 13 d = -2 -25 = 13+19(-2), so -25 is A20 S20 = 20/2(13-25) = -120
June 9, 2015

math
no ideas on any of the? Review the distributive property -2r(8r+5) (-2r)(8) + (-2r)(5) -16r^2 - 10r Do the others the same way
June 9, 2015

pre-calculus 11
x^2/2 - 1 = x+3 x^2 - 2 = 2x+6 x^2 - 2x - 8 = 0 You multiplied x by 2, but not the 3.
June 9, 2015

solving two-step inequality
the difference between 5 times a number and 6 is less than 14.
June 9, 2015

Algebra
the slope is (2-4)/(6+2) = -1/4 So, in point-slope form, you have y-5 = -1/4 (x-2) Now massage that into slope-intercept form.
June 9, 2015

need ratio
(3/2):(9/2) = 3:9 = 1:3
June 9, 2015

physics
well, geez. The wall is 2m high. At the end the bug slides down 1 cm. So, he ends up 199cm from the foot of the wall. Not much of a physics problem.
June 9, 2015

math
540(1+.06)^3
June 9, 2015

Economic
even more important: who says so? Is it even true?
June 9, 2015

Algebra
or, just use the point-slope form of the line. You know the slope is 1/5 and it goes through (-3,-6). So, y+6 = 1/5 (x+3) You can massage that as you will.
June 9, 2015

Calc 1
Not at all. Just because the limit exists, that does not mean the function at x=a has the value L. It might not even be defined at all. recall your previous example, f(x)=(x^2+x-2)/(x^2-1), where the limit as x->1 was 1.5, but the function was not defined there. There was a...
June 9, 2015

math trigonometry
Not only that, I'm not sure what the sin^3x is even doing there. I will note that sin/cos^2 = tan/cos
June 9, 2015

Math - still no question
apparently you either did not read, or did not like my work on your previous posting. So, just what is your question? You have presented some data, but don't say what it is you want to know! You might also indicate how the semi-circles are arranged. Just in a long snaky ...
June 9, 2015

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