Friday

July 3, 2015

July 3, 2015

Total # Posts: 32,086

**pre-calculus 11**

numerator zero is no problem. 0/x = 0 for any nonzero x. The only restrictions you need worry about are where the denominator is zero.
*June 15, 2015*

**Physics**

did you try drawing the figure? You just wind up with a right triangle, where one angle is 40° and the hypotenuse is 10. x = 10 cos40° y = -10 sin40° Looks like time to review your trigonometry.
*June 15, 2015*

**Area/volume of hollow figure**

It occurs to me that I gave you the volume of the box's material. The interior volume is just (10-2)(10-2)(100-2)
*June 15, 2015*

**Area/volume of hollow figure**

the volume is the volume outside the box, less the volume inside the box. Assuming you are given the outside dimensions, and the box has no open sides, then the interior volume would be (10)(10)(500) - (10-2)(10-2)(100-2) You do the same for the area. Each interior face has ...
*June 15, 2015*

**Math**

That's what I get. x/31 = 60/50 x = 37.2 Looks closer to 37 than 38, even using your rounded-off figures.
*June 15, 2015*

**physic**

v changed by -1.5m/s in 1.2s a = -1.5/1.2 = -1.25 m/s^2
*June 15, 2015*

**E.s groly**

5(a+4d) = 10(a+9d) 5a+20d = 10a+90d a = -14d So, there is no unique solution. Some examples are a = 14 d = -1 14,13,12,11,10,9,8,7,6,5 5*10 = 10*5 a = -7 d = 0.5 -7,-6.6,-6,-5.5,-5,-4.5,-4,-3.5,-3.-2.5 5(-5) = 10(-2.5)
*June 15, 2015*

**Math**

first, find the length of a $50 note.
*June 14, 2015*

**Math**

depends on the weight of the people. It might also depend on the size of the people, since the elevator car might not hold enough bodies to max out the weight.
*June 14, 2015*

**pre-calculus 11**

Not only are the signs backwards, but the intervals are incorrect as well. Take a look at the graph and see whether you can fix it. http://www.wolframalpha.com/input/?i=-|x^2-9|+for+-5+%3C%3D+x+%3C%3D+5 The trick to getting signs right is remembering that |x| = x if x >= 0...
*June 14, 2015*

**pre-calculus 11**

wolframalpha is your friend. Just type in your request, as shown below: http://www.wolframalpha.com/input/?i=|1%2F2x+%2B1|+%3Dx%2B1
*June 14, 2015*

**geometry**

a = pi(8^2 - 5^2) = 122.52 You were correct, if they are asking about the area of the top or bottom surface of the cylinder. However, maybe they are asking about the area of the curved surface. In that case, it would be 2pi(8-5)h and you'd need to know the height of the ring.
*June 14, 2015*

**math**

since the x-coordinate is the same for all of the points, they lie on a vertical line. So, just pick any three values for y and plot the points. For example, (-2.8,0) (-2.8,-5) (-2.8,1.73)
*June 14, 2015*

**Math**

Your algebra is correct. Your logic is wrong, however. x=0,8 are roots of the function. That is, where the area is zero. If you rewrite it as 20x - 5/2 x^2 you see it is a parabola with its vertex at x = -b/2a = 20/5 = 4 So, y=10 and the largest area is 4*10 = 40 http://www....
*June 14, 2015*

**math**

since the period of sin and cos is 2pi, the function clearly satisfies Rolle's Theorem. So, we want to find c (possibly more than one value) where f'(c) = 0 f'(x) = cosx - sinx so, f'(c) = 0 if cosx = sinx That is when x = pi/4 or 5pi/4 See the graph at http://...
*June 14, 2015*

**physics**

start with F = ma
*June 14, 2015*

**Algebra2**

or, look at it like this: 2|3x-5|-8=8 2|3x-5| = 16 |3x-5| = 8 |x - 5/3| = 8/3 so, x = 5/3 ± 8/3 x = 13/3 or -1 or, you can use the "extraneous root" introduced by squaring both sides. |3x-5| = 8 (3x-5)^2 = 64 3x-5 = ±8 3x = 5±8 x = 5/3 ± 8/3
*June 14, 2015*

**Algebra**

1 < y < 6 why?
*June 14, 2015*

**queen's science Academy**

Since the height of the falling stone is the same as that of the projected stone after 2 seconds, h-4.9t^2 = 20t-4.9t^2 h = 20t = 40
*June 14, 2015*

**math**

Still a typo. Is that 180+x or 180-x? 180x makes no sense. And where do the A's fit in?
*June 14, 2015*

**math**

so. what have you got so far? How can a digit have no value?
*June 14, 2015*

**math trigonometry**

sin(360-x) = -sin(x) tan(-x) = -tan(x) cos(180-x) = -cos(x) so, you have sin(x)tan(x)/cos(x) = sin^2(x)/cos^2(x) = tan^2(x) Not sure where the A comes from, but you get the idea. Just reduce everything to simple trig functions and then combine them. If you need further help, ...
*June 14, 2015*

**math trigonometry**

Simplify the following expression to a single trigonometric term sin(360-x)*tan(-x)/cos(180 x)*(sin^2A cos^2A) answer= -sinx*-tanx/cosx*(1) after that how do i continue?
*June 14, 2015*

**Math**

the volume of water hitting the roof is just the area of the roof's horizontal projection, times the depth of the rainfall. That is just 12√48 * .30 m^3 = 24.94m^3 1 m^3 = 1000L, so the barrel needs to hold 24900L. v = πr^2h, so π(3/2)^2h = 24.94 h = 3.53m ...
*June 14, 2015*

**maths**

as long as you multiply top and bottom by the same thing, the value is unchanged. So, 2/3 * 3/3 = 6/9 2/3 * 9/9 = 18/27 2/3 * 1.2/1.2 = 2.4/3.6 2/3 * 100/100 = 200/200 and so on
*June 14, 2015*

**Matsogella**

Is there a question somewhere in there? Heck, or even a subject?
*June 14, 2015*

**math**

There are 36 possible outcomes. List the ones you want. For example, sum < 6: 1 4 2 3 3 2 4 1 There are 4 ways to get that, so P(sum<6) = 4/36 Same for the other one.
*June 14, 2015*

**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*