Wednesday

September 2, 2015
Total # Posts: 33,233

**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*

**Geometry - incomplete**

depending on the labeling, any one of those could work.
*June 9, 2015*

**math**

100x + 200y <= 1400 0.6x + 0.8y <= 7.2 x/y >= 2/3 volume is .8x+1.2y Now just follow the usual optimization steps.
*June 9, 2015*

**gwalior glory school**

1st digit is 4 ones digit is 2 tens is 2+4 the number is 462 or, 451 if you only have one eye ...
*June 9, 2015*

**math**

3n+p = 70 n+3p = 50 add them together and you have 4n+4p = 120 so, 2n+2p = 60
*June 9, 2015*

**Algebra**

Just realize that a negative exponent switches the factor between numerator and denominator. (c^-3)^2d^4/d^-2 = c^-6 d^4/d^-2 = d^6/c^6 (e^4)^-3f^-5/f^-2 = e^-12 f^-5/f^-2 = e^-12 f^-3 = 1/(e^12f^3) (8^-7/8)^-2 = (8^-8)^-2 = 8^16
*June 9, 2015*

**MATH**

(ar)(ar^3) = 2ar^4 a^2r^4 = 2ar^4 ar^4 = 2r^4 a = 2 a(r^4-1)/(r-1) = 80 1+r+r^2+r^3 = 40 r = 3 So, the GP is 2,6,18,54,162,... (6)(54) = 2*162 2+6+18+54 = 80
*June 9, 2015*

**Algebra**

-5c^-3 = -5/c^3 So, (-5/c^3)^4 = 625/c^12
*June 9, 2015*

**Algebra**

here's one way. You want the concentration to be reduced by a factor of 15/25 = 3/5 So, the volume must be increased by a factor of 5/3. 5/3 * 120 = 200 ml So, if you add 80ml of water, the concentration is reduced from 25% to 15% Or, you can solve the equation .25*120 + ...
*June 9, 2015*

**maths**

factor out the x and you have (5/3 - 3/5)x = (25-9)/15 x = 16/15 x
*June 9, 2015*

**calculus1**

The graphs intersect at (0,-1) and (0,1). If this area is spun around the y-axis, you can think of the solid as a bunch of thin discs, of thickness dy, each with a hole in the middle. So, the area is a = ∫[-1,1] π(R^2-r^2) dy where R = 2-2y^2 and r = 1-y^2 a = &#...
*June 9, 2015*

**Calc 1**

true If the perimeter is p, then 2x+2y = p y = (p-2x)/2 = p/2 - x The area is a = xy = x(p/2-x) = p/2 x - x^2 This is just a parabola, with vertex at x = p/4 so, y = p/4 as well, and you have a square to get max area.
*June 9, 2015*

**science**

I believe it is C water can act as either a polar or nonpolar solvent.
*June 9, 2015*

**Calc 1**

what do you mean you "tried 0.5"? Tried for what? In my solution, the slope is 2, not 1/2.
*June 9, 2015*

**Calc 1**

clearly, s(0) = 0 s(1/2) = 1 So, the line is y=2t. since t is time and y is position, say, cm, then the slope of the line (cm/s) is the average velocity during the interval [0,0.5] See http://www.wolframalpha.com/input/?i=plot+y%3Dsin%28pi*x%29%2C+y%3D2x
*June 9, 2015*

**Kainantu sec..science(chemistry)**

PV=kT That is, PV/T is constant. (10)(1.93)/(273+100) = 1V/273 so just solve for V.
*June 9, 2015*

**Kainantu sec..science(chemistry)**

1 mole at STP is 22.4L 2.00g of CS2 is 2/76.14 = 0.0263 moles CS2 CS2+3O2 = CO2 + 2SO2 so, each mole of CS2 produces 2 moles of SO2. I expect you can take it from there...
*June 9, 2015*

**Maths**

assuming you measure the 12m along the ground, we have the horizontal distance from the base of the building is 12cos5° = 11.95 So, from eye level, the vertical distance to the top of the building is 11.95tan35°15' = 8.45 Add to that the 1.6m of your height, and ...
*June 8, 2015*

**math**

65*3 = 5x x = 39
*June 8, 2015*

**Physics**

since s = 1/2 at^2, the truck moved for t seconds, where 42 = 1/2 * 2.15 t^2 t = 6.25 seconds The car moved 1/2 * 3.47 * 6.25^2 = 67.77 meters so, it was 25.77 m behind the truck v = at, so you can figure out the speeds, I expect.
*June 8, 2015*

**Physics**

h(t) = 22.0 + 17.0t - 4.9t^2 v(t) = 17.0 - 9.8t So, find t when h=0, and use that to find v at that instant.
*June 8, 2015*

**Physics**

x(t) = 2.17+4.80t^2−0.100t^6 v(t) = 2.17+ 9.60t - 0.600t^5 a(t) = 9.6 - 3.0t^4 As you say, v(2) = 0, so a(2) = -38.4
*June 8, 2015*

**algebra**

x/(x-5)-3=5/(x-5) x/(x-5)-5/(x-5)=3 (x-5)/(x-5) = 3 1 = 3 not true for any value of x.
*June 8, 2015*

**Maths**

since the circumference is πd, just find d where πd*480 = 1200 m
*June 8, 2015*

**geometry**

clearly AD and BC are horizontal, and thus parallel. since B is 1 to the left of A, and C is one to the left of D, BA || CD. since AD and AB are not the same length, ABCD is a parallelogram and not a rhombus.
*June 8, 2015*

**Math**

can't see the diagram, but the area of a semi-circle is π/2 r^2 So, the area between two semi-circles of radii r and R is π/2 (R^2-r^2) You have circles of radii 14 and 16. So, plug in your numbers.
*June 8, 2015*