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\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...
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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...
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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).
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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...
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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...
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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
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1/2=16/32, 3/4=24/32 so 3 27/32" is closer to 3 3/4".
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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...
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A problem with mimetex notations:
\frac{1.998\times 10^{27}}{8.700\times 10^{22}}=2.297\times 10^4
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Mass of Sun/Mass of Uranus is
\frac{1.998\times 10^27}{8.700\times 10^22}=2.297\times 10^4
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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...
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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...
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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...
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I think ebaines's guess makes more sense, but it is unusual to write "square root" in this case.
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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...
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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} .
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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).
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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?
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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...
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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...
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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...
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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...
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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...
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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%...
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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...
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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...
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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...
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Yes, ebaines is right, I have not considered wire length.
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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.
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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...
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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...
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Hi Tut,
Thank you for the quantum part.
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Use the formula
acceleration=\Delta v/t
where t is time and \Delta v the variation in velocity.
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F(x)=x^2-t^2
then
F(t)=t^2-t^2=0
F(4t)=(4t)^2-t^2=15t^2
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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...
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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...
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\vep_0 is a constant, not influent for your question.
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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...
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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...
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If it is y=(x+5)(x^2+3) then use the chain rule and
\frac{dy}{dx}=(x^2+3)+2x(x+5)
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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}.
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The plot is not clear, please repost using "math" environment, and explain what are G and r.
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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...
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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...
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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...
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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...
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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...
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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...
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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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