Wednesday
September 2, 2015

Posts by steve


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

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