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Type: Posts; User: Aurora2000

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  1. Answers
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    6,101

    \frac{\cot x}{\csc x+1}=\sec x-\tan x ...

    \frac{\cot x}{\csc x+1}=\sec x-\tan x

    \frac{\cot x}{\csc x+1}=\frac{1}{\tan x(\csc x+1) }=\frac{1}{\tan x\csc x+\tan x}
    Now \tan x\csc x=\tan x\sin^{-1} x=\cos^{-1} x=\sec x , thus...
  2. Average score = 95, thus combined score of 12...

    Average score = 95, thus combined score of 12 students is 95x12=1140.

    If 11 students score 100, then their combined score is 11x100=1100. So the last student must score at least 40. The minimum is...
  3. Answers
    1
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    1,153

    If no friction are considered, and they have the...

    If no friction are considered, and they have the same mass, then their energy expense are the same: indeed let be h the height of the hill, they both must use mgh energy (g=9.81 m/s^2).
  4. Answers
    2
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    463

    I think OP means initial velocity of 500ft/s, all...

    I think OP means initial velocity of 500ft/s, all horizontal component, no vertical component.

    In this case the projectile flies 0.2s before reaching the target. In this time the gravitation will...
  5. Answers
    1
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    530

    If the satellite is in circular orbit, then the...

    If the satellite is in circular orbit, then the gravitation acceleration must equal the centripetal acceleration.

    Let be M,R the mass and radius of Mercury, r the distance from Mercury (here...
  6. Weight

    Weight
  7. Answers
    1
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    1,174

    Start from identity \cos^2x+\sin^2x=1 subtract...

    Start from identity
    \cos^2x+\sin^2x=1
    subtract 2\sin^2x both sides and you get
    \cos^2x-\sin^2x=1-2\sin^2x
  8. 1/2=16/32, 3/4=24/32 so 3 27/32" is closer to 3...

    1/2=16/32, 3/4=24/32 so 3 27/32" is closer to 3 3/4".
  9. Answers
    1
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    642

    Impose a coordinate system where positive x axis...

    Impose a coordinate system where positive x axis direction is east, positive y axis is north, negative x axis is west and negative y axis is south: plane's velocity is directed southeast (i.e. along...
  10. Question: I need help

    by Aurora2000
    Answers
    2
    Views
    2,657

    A problem with mimetex notations: ...

    A problem with mimetex notations:

    \frac{1.998\times 10^{27}}{8.700\times 10^{22}}=2.297\times 10^4
  11. Question: I need help

    by Aurora2000
    Answers
    2
    Views
    2,657

    Mass of Sun/Mass of Uranus is ...

    Mass of Sun/Mass of Uranus is

    \frac{1.998\times 10^27}{8.700\times 10^22}=2.297\times 10^4
  12. Answers
    1
    Views
    1,486

    You have done computations correctly, but the...

    You have done computations correctly, but the representation in base 8 is wrong.

    45 in base 8 is 4\times 8+5 , thus 37 in base 10; 7 in base 8 is the same as in base 10, thus 45\times 7 in base 8...
  13. Answers
    2
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    458

    Just eliminate the log (by applying its inverse...

    Just eliminate the log (by applying its inverse function exp):

    \log (2x+10)/2=\log(x+1)
    \log (2x+10)=2\log(x+1)=\log(x+1)^2
    and then
    2x+10=(x+1)^2

    Obviously you need x>-1 or the first line...
  14. Hi rpray2007, I have studied capacitors only...

    Hi rpray2007,

    I have studied capacitors only in books, thus I can be very unaccurate here :-)

    Polypropylene plastic film capacitors and Teflon plastic film capacitors have comparable lower...
  15. I think ebaines's guess makes more sense, but it...

    I think ebaines's guess makes more sense, but it is unusual to write "square root" in this case.
  16. I give my 2 cents (I am not an expert) :-) ...

    I give my 2 cents (I am not an expert) :-)

    You need something which stores pulse current, and converts voltage/amperage to reasonable levels. You can use first a capacitor to store the energy...
  17. Do you mean \sqrt{-27}^3 ? You cannot solve it...

    Do you mean \sqrt{-27}^3 ?

    You cannot solve it in the real numbers: \sqrt{-27}=3\sqrt{3}i , and \sqrt{-27}^3= -81\sqrt{3}i, where i:=\sqrt{-1} .
  18. Answers
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    339

    In base 2 you have only 0 and 1 as digits. 2+2...

    In base 2 you have only 0 and 1 as digits.

    2+2 of base 10 translates to 10+10 in base 2, and you have 10+10=100 in base 2 (100 base in 2 corresponds to 4 in base 10).
  19. Here is some hint:...

    Here is some hint:
    \sin^2\theta=1-\cos^2\theta=(1-\cos\theta)(1+\cos\theta)
    = \cos\theta (\sec\theta -1)(\cos\theta+1)

    Can you continue from this point?
  20. You have 15 orange sweeties and 10 yellow...

    You have 15 orange sweeties and 10 yellow sweeties, for a total of 25 sweeties. Probability can be thought as "favorable cases on total cases".

    (A) Sweetie is orange: favorable cases 15 as you...
  21. Question: Kinetic Energy

    by Aurora2000
    Answers
    1
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    542

    The ball has 850J of kinetic energy, thus it...

    The ball has 850J of kinetic energy, thus it converts all this energy into potential energy when boucing back. The potential energy at height h is mgh (m is the mass, here 1kg, g the gravitational...
  22. Answers
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    612

    I will assume you mean...

    I will assume you mean
    \sqrt{63}+13\sqrt{98}-5\sqrt{112} .

    You have 63=9\times 7, thus \sqrt{63}=\sqrt{9\times 7}=\sqrt{9}\times\sqrt{7}
    =3\sqrt{7} . Similarly...
  23. First from symmetry considerations, you have that...

    First from symmetry considerations, you have that the electric field is directed along the line y=x. So you need only to compute the total Electric field in the origin: this is

    From the figure the...
  24. Answers
    2
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    1,540

    This graph represents the position x as function...

    This graph represents the position x as function of time t. The instantaneous velocity is given by the derivative dx/dt, which corresponds to the tangent direction in the graph.

    From the graph you...
  25. In 5 litres of solution Y you have 5*8%=0.4...

    In 5 litres of solution Y you have 5*8%=0.4 litres of salt, and the rest 4.96 litres of water.
    Now you add t litres of solution X (t to be determined). This contains t*15% litres of salt, and t*85%...
  26. Question: Proportion

    by Aurora2000
    Answers
    1
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    787

    You contribute $2400, Jim $14750 and Susan...

    You contribute $2400, Jim $14750 and Susan $11200. The total is $2400+14750+11200=$32350.
    Thus your ratio is 2400/32350, Jim 14750/32350, Susan 11200/32350.

    When $20000 more are required, the...
  27. Answers
    1
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    465

    Let be x the number of students: the original...

    Let be x the number of students: the original price $129 is to be equally divided, thus each student will pay $129/x. If there were 2 more students, thus x+2 participants, the per capita cost will be...
  28. You need to translate "South" and "East" into...

    You need to translate "South" and "East" into directions.

    Draw a quadrant (up=north, right=east, left=west, down=south) and impose a coordinate system, with positive x axis corresponding to east...
  29. Answers
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    1,945

    Yes, ebaines is right, I have not considered wire...

    Yes, ebaines is right, I have not considered wire length.
  30. First graph the line y=3x-3. Then, as you are...

    First graph the line y=3x-3. Then, as you are interested in y>3x-3, you have to mark the entire open halfplane "above" (with greater y coordinate) the graph of y=3x-3.
  31. Answers
    4
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    1,945

    The candelier generates a force F=mg=66.5kg...

    The candelier generates a force F=mg=66.5kg \times 9.81m/s^2 due to gravity. The 3 wires
    must balance this force in order to create an equilibrium. Thus the combined force on the 3 wires is...
  32. Question: Physics help

    by Aurora2000
    Answers
    3
    Views
    626

    The skier starts from rest (thus 0 m/s), and...

    The skier starts from rest (thus 0 m/s), and skies 50 m. Let be a its acceleration. His speed at time t is
    v(t)=at, and the distance travelled is
    s(t)=\int_0^t v(x)dx=\frac{1}{2}at^2

    You know...
  33. Question: Absolute 0

    by Aurora2000
    Answers
    5
    Views
    442

    Hi Tut, Thank you for the quantum part.

    Hi Tut,

    Thank you for the quantum part.
  34. Question: Physics help

    by Aurora2000
    Answers
    3
    Views
    626

    Use the formula acceleration=\Delta v/t ...

    Use the formula

    acceleration=\Delta v/t

    where t is time and \Delta v the variation in velocity.
  35. F(x)=x^2-t^2 then F(t)=t^2-t^2=0...

    F(x)=x^2-t^2

    then

    F(t)=t^2-t^2=0
    F(4t)=(4t)^2-t^2=15t^2
  36. Question: Absolute 0

    by Aurora2000
    Answers
    5
    Views
    442

    I am not a physicist, but if I am not wrong, you...

    I am not a physicist, but if I am not wrong, you have spoken about two different ends: the first (where everything starts going apart) is called Big Rip, in which for each atom its observable...
  37. Answers
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    892

    I think you mean \lim_{x\rightarrow 0}...

    I think you mean
    \lim_{x\rightarrow 0} \frac{\sin x-\tan x}{\sin^2 x\tan x}.

    The case 0/0 is very common in limits, so you have essentially to simplify something in order
    to get a value (for...
  38. \vep_0 is a constant, not influent for your...

    \vep_0 is a constant, not influent for your question.
  39. Use Coloumb's formula: the force between point...

    Use Coloumb's formula: the force between point charges q_1,q_2 separated by a distance
    r is

    \frac{1}{4\pi\vep_0} \frac{q_1q_2}{r^2}

    Thus changing the distance from 2r to 5r will change the...
  40. Answers
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    782

    The acceleration is used to stop the plane, thus...

    The acceleration is used to stop the plane, thus it is opposite to the velocity. Velocity is due south, thus acceleration is due north. For the magnitude use

    2ad=v_f^2-v_i^2

    where a is...
  41. Question: Mathematics

    by Aurora2000
    Answers
    2
    Views
    604

    If it is y=(x+5)(x^2+3) then use the chain rule...

    If it is y=(x+5)(x^2+3) then use the chain rule and
    \frac{dy}{dx}=(x^2+3)+2x(x+5)
  42. Question: Mathematics

    by Aurora2000
    Answers
    2
    Views
    529

    The complement of {1,10} in E is the set of...

    The complement of {1,10} in E is the set of elements of E not in {1,10}. Thus it is {2,3,4,5,6,7,8,9}.
  43. Question: Help solving:

    by Aurora2000
    Answers
    1
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    308

    The plot is not clear, please repost using "math"...

    The plot is not clear, please repost using "math" environment, and explain what are G and r.
  44. Answers
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    2,037

    Let be x the speed of jet stream (in mph): in...

    Let be x the speed of jet stream (in mph):

    in the going out trip the plane travels 1200 miles at (500+x) mph, thus travel time is
    \frac{1200}{500+x}; in the return trip the plane travels 1200...
  45. Answers
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    721

    What do you mean with "just floats on water"? Is...

    What do you mean with "just floats on water"? Is it "does not sink but it is entirely immersed"?

    If yes, then use the following argument:

    It has mass 8kg, density 8 thus volume 1l. To receive...
  46. Answers
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    490

    It can be interpreted as "gravitation force...

    It can be interpreted as "gravitation force acting as centripetal force".

    Remember that a satellite in orbit around Earth must have variations for its velocity vector (in this case its direction...
  47. Answers
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    780

    If you want the roots of x^2+3x-10 (values for...

    If you want the roots of x^2+3x-10 (values for which x^2+3x-10 =0) then use the formula for II degree polynomials:

    the roots of ax^2+bx+c are

    \frac{-b-\sqrt{b^2-4ac}}{2a},\qquad...
  48. Yes. Without acceleration you cannot change...

    Yes. Without acceleration you cannot change velocity. The formula is

    a=\frac{dv}{dt},\ v(t)=v_0+\int_0^t a(t)dt

    where v_0 is initial velocity, a the acceleration. So if you have no...
  49. Question: Numbers sum

    by Aurora2000
    Answers
    1
    Views
    567

    The computations are a bit different. If you...

    The computations are a bit different.

    If you are summing from 1 to N, and the difference between 2 numbers is x , then put (assuming (N-1)/x integer):

    a_k=1+kx,\ k=0,1,2,\cdots

    and the last...
  50. Answers
    1
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    395

    The display is quite strange, I will interpret as...

    The display is quite strange, I will interpret as
    \frac{1-(2\sin x\cos x+\cos 2x)^2}{2\sin 2x\cos 2x}
    (if you meant another expression, repost using "math" environment)

    The problem is lot...
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