Monday
July 27, 2015

Posts by Steve


Total # Posts: 32,481

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

statistics
there were 15 cards, 5 of them diamonds. So, the chance of getting a diamond is 5/15 After that, having drawn a diamond, there are only 14 cards left, 4 of them diamonds. So, the chance that the 2nd draw is another diamond is 4/14.
June 8, 2015

pre calc
y = kx 9 = 12k, so k = 3/4 y = 3/4 x
June 8, 2015

physics
you have a right triangle, with the hypotenuse = 9 (his actual speed), and one leg=2 (the current) so, his resultant velocity must be upstream at an angle x such that sin(x) = 2/9 and the actual resultant speed s (due north) is √(9^2-2^2) Having gotten his speed s, the ...
June 8, 2015

maths
One subset is {1,3} I expect you meant to ask a little more . . .
June 8, 2015

Calculus
the revenue function is price * quantity, so R(x) = x(50-.01x) profit is revenue less cost, so P(x) = R(x)-C(x) = x(50-.01x) - (10+2x) = -0.01x^2 + 48x - 10 Now just set dP/dx=0 and evaluate P there. Or, just use your Algebra I skills and find the vertex of the parabola.
June 8, 2015

math
d/1400 = 8/450
June 8, 2015

Math
The digits are, as explained above, going right to left, 2 3 4*2=8 2+3=5
June 8, 2015

math
Grrrr! The Greek letter is pi The dessert is pie! Here is the graph. I expect you can use it to help with the other questions. http://www.wolframalpha.com/input/?i=-1800cos%289%CF%80%2F6+t%29%2B1800+for+0+%3C%3D+t+%3C%3D+10
June 8, 2015

science
at deceleration a, the velocity is v = 20-at so t = 20/a the distance traveled by the car is s = 20t + 1/2 at^2 = 20(20/a) - 1/2 a (20/a)^2 = 200/a So, to stop in 50 meters, 200/a = 50 a = 4 m/s^2 check: v = 20-4*5 s = 20*5 - 2*5^2 = 100-50 = 50
June 8, 2015

speed time distance
180 km/hr = 50 m/s the front of the train arrives at t=0. The front of the train leaves the platform at t = 365/50 = 7.3 The back of the train whose length is x leaves the platform at t = 7.3 + x/50 So, solve for x in 7.3 + x/50 = 21
June 8, 2015

math
Neither can I. You never asked a question.
June 8, 2015

math
The volume is x(30-2x)^2 The area is (30-2x)^2 + 4x(30-2x)
June 8, 2015

Math
also recall that cos(x) is negative in QII and QIII
June 7, 2015

Pre-Algebra
direct: y = kx, so k = y/x inverse: xy = k If y varies directly with x, find the constant of variation with x = 4 and y = -24 k = y/x = -24/4 = -6 If y varies inversely with x, find the constant of variation with x=5 and y = 10 k = xy = 5*10 = 50 and do the others in like wise.
June 7, 2015

calc
y is concave up if y" > 0 By the 2nd FT of Calculus, y' = -f(x) = -6/(x+1)^2 y" = 12(x+1)^3 so, where is y" positive?
June 7, 2015

Inequalities
Hmmm. I get (x-3)/(x-2) + 12/(x^2-x-2) > 8/(x+1) (x-3)(x+1) + 12 > 8(x-2) x^2-2x-3+12 > 8x-16 x^2-10x+25 > 0 (x-5)^2 > 0 So, all x except x = 2,5 and -1 Oddly enough, it appears that the real solution is x < -1 or x > 2 and x not 5. See http://www....
June 7, 2015

Math (PLEASE HELP!)
Evidently you do not understand the concept of a range. Your temperature is somewhere in 27±3 24 = 27-3 and 30 is 27+3 So, clearly the range is 24-30
June 7, 2015

math
as usual, maximum area is achieved in a square pen. To show this, note that if the dimensions are x and y, we have 2x+2y=200, so y = 100-x The area a = xy = x(100-x) = 100x-x^2 This is just a parabola, with its vertex at x=50. So, the pen is 50x50, or a square. Hmm. I see I ...
June 7, 2015

Math
you want m where 50 < 15+.10m
June 7, 2015

Math
total socks: 7 so, P(blue,red) = 2/7 * 2/7
June 7, 2015

calc
not sure what you mean by evaluate 4-x and 2x-8 Maybe a look at the graphs will help clarify your thinking: http://www.wolframalpha.com/input/?i=plot+y%3D4-x%2C+y%3D2x-8
June 7, 2015

Walk two moons need help
1st question: have you read it?
June 7, 2015

statistics
1569/23652 = 0.06633 You can do the rounding.
June 7, 2015

statistics
176/232 = 0.75862 You can round that as needed.
June 7, 2015

Statistics
since the yearly salary amounts to 2080*13.50 the benefits amount to 24% of that amount.
June 7, 2015

algebra
y = (10x+7)/(6x+3) now solve for x: (6x+3)y = 10x+7 6xy+3y = 10x+7 (6y-10)x = 7-3y x = (7-3y)/(6y-10) now x is y^-1, so to express f^-1(x), that is f^-1(x) = (7-3x)/(6x-10)
June 7, 2015

Algebra
for the survey, (b) looks better to me for the poems, you have (4/13)(2/12)
June 7, 2015

Algebra
(1.4*8)x10^(1+4) = 11.2x10^5 = 1.12x10^6
June 7, 2015

Math
if the base is x and the height is z, then x^2z = 4 The surface is the base and 4 sides, so a = x^2 + 4xz = x^2 + 4x(4/x^2) = x^2 + 16/x da/dx = 2x - 16/x^2 = (2x^3-16)/x^2 da/dx = 0 when x=2, so the container is 2x2x1
June 6, 2015

Math (PLEASE HELP!)
T = 27±3 |T-27| <= 3 Surely you can figure the range.
June 6, 2015

Math
1/7 = 3/(4x-1) 1 = 21/(4x-1) 4x-1 = 21 4x = 22 x = 11/2
June 6, 2015

Math/Physics
just given arbitrary vectors of some magnitudes, there is no way to compute their sum or difference. Unless you know the x- and y-components, you are stuck.
June 6, 2015

Algebra
x(x+18) <= 175 x^2+18x-175 <= 0 (x+25)(x-7) <= 0 So, -25 <= x <= 7 Or, for real-world tables, 0 <= x <= 7 There is probably a minimum positive width for a useful table.
June 6, 2015

math
The 4th row of Pascal's Triangle is 1 4 6 4 1 That is, (a+b)^4 = a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4 So, (3+b)^4 is 3^4 + 4(3^3)b + 6(3^2)b^2 + 4(3^1)b^3 + b^4 = 81 + 108b + 54b^2 + 12b^3 + b^4 That's all very nice, but if your question is to solve for b in (3+b)^4 = 1...
June 6, 2015

algebra
when you raise to powers, you multiply exponents. Consider: 2^3 = 2*2*2 (2^3)^4 = (2*2*2)*(2*2*2)*(2*2*2)*(2*2*2) = 2^(3+3+3+3) 2^(3*4) = 2^12 So, (x^4 y^5)^5 = x^20 y^25
June 6, 2015

Math
1/4 + 1/s = 1/3 Now just solve for s.
June 6, 2015

algebra
6C3 = (6*5*4)/(3*2*1) = 20
June 6, 2015

math
Draw radii to the points of tangency. Draw a line connecting the centers. Draw a parallel line, 2 units closer to the tangent points. Now you have a right triangle with legs 10 and 6, with the tangent line forming the hypotenuse.
June 6, 2015

math
It won't seem hard after you've done a few dozen of them... I assume you meant 9^(x+2)=240+9^x That is the same as 9^2*9^x = 240 + 9^x 9^x(81-1) = 240 80*9^x = 240 9^x = 3 x = 1/2
June 6, 2015

Math
make that 2n/10 + 5n/7 + 303 = n
June 6, 2015

Math
"several" sevenths? What kind of nonsense is that? Anyway if that means 5/7, then 2/10 + 5n/7 + 303 = n n = 3535
June 6, 2015

math
angle ADB is an exterior angle to triangle ACD. So, it is equal to angles ACD+CAD. Thus angle C is 45 degrees.
June 6, 2015

Math
In the absence of any other information about how the amplitude changes, I'd just use a linear rate of change. For instance, y = (2+0.3x) sin(x) Or, if you insist on a constant amplitude, then averaging them seems like a good option.
June 6, 2015

Math
Assuming even change in height, the rate is 0.5 m/hr So, at what time t do you have 1.4 + 0.5t = 1.71 ??
June 6, 2015

Math
see your original post.
June 6, 2015

math derivatives - eh?
The given information says nothing about the height or width of the building. Without that, we do not know enough to work the problem.
June 6, 2015

Math
see your previous post.
June 6, 2015

Math
come on, man! The common difference is A2-A1 or A3-A2, which they gave you. The difference is shown above: -2p+10 or -3p-13 In either case, it is 56. Now do you think you can write the sequence?
June 6, 2015

Math
since the difference is constant, (5p+12) - (7p+2) = (2p-1) - (5p+12) -2p+10 = -3p-13 p = -23 Now you can find the difference, and write the terms of the sequence.
June 6, 2015

Algebra II
that it is.
June 6, 2015

math
you want, for m miles, 26+.12m = 24+.19m
June 5, 2015

math
a quadratic has x^2 as its highest power. So, A. Note that y decreases by 3 when x increases by 1. So, it will look like y = -3x But, when x=0, -3x=0, and y is -8. So, y = -3x-8 again, A
June 5, 2015

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