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20b(4b3)3
Find the Taylor polynomial of degree n=4 for each function expanded about the given value of x 0 . f ( x ) = x , x 0 = 1
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Limit of cos(kt+kux) as k→0wherek=21−a2u=b(6−k2)and a and b are real numbers?
A wire 15 m long is stretched tight from the top of a radio mast to a point on the horizontal ground. The distance of the point on the ground from the foot of the radio mast is 8 m. How high is the radio mast above the level ground?
What does it mean to differentiate a vector?I didn’t quite understand what does it mean to differentiate a vector, i suspect that the derivative of a vector valued function is just answering the question : What vector should i added to the previous one to get the next one. For example :Consider the vector X → ( t ) = ⟨ 1 , t ⟩ X → ′ ( t ) = ⟨ 0 , 1 ⟩Now if i take a random vector from the vector valued function ⟨1,t⟩ , say for example ⟨1,3⟩ If i add to it the derivative of ⟨1,t⟩ which is ⟨0,1⟩, i get ⟨1,4⟩ which is the next vector.But this is only true for t ∈ Z because in the real numbers the next vector is not defined, it could be ⟨ 1 , 3.0001 ⟩So how can i really understand what is the derivative of a vector.
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struggling to derive Lorentz transformations for a sine wave, which is traveling at random direction. I started by prooving that phase ϕ is invariant for relativity and that equation ϕ = ϕ ′ holds.By using the above equation i am now trying to derive Lorentz transformations for angular frequency ω, and all three components of the wave vector k, which are k x , k y and k z .This is my attempt: ϕ ′ = ϕ ω ′ Δ t ′ + k ′ Δ r ′ = ω Δ t + k Δ r ω ′ Δ t ′ + [ k x ′ , k y ′ , k z ′ ] [ Δ x ′ , Δ y ′ , Δ z ′ ] = ω Δ t + [ k x , k y , k z ] [ Δ x , Δ y , Δ z ] ω ′ Δ t ′ + k x ′ Δ x ′ + k y ′ Δ y ′ + k z ′ Δ z ′ = ω Δ t + k x Δ x + k y Δ y + k z Δ z ω ′ γ ( Δ t − Δ x u c 2 ) + k x ′ γ ( Δ x − u Δ t ) + k y ′ Δ y + k z ′ Δ z γ ( ω ′ Δ t − ω ′ Δ x u c 2 ) + γ ( k x ′ Δ x − k x ′ u Δ t ) + k y ′ Δ y + k z ′ Δ z γ ( ω ′ Δ t − k x ′ c c Δ t u c 2 ) + γ ( k x ′ Δ x − ω ′ c u Δ x c ) + k y ′ Δ y + k z ′ Δ z Δ t γ ( ω ′ − k x ′ u ) + Δ x γ ( k x ′ − ω ′ u c 2 ) + k y ′ Δ y + k z ′ Δ z From this I can write down the Lorentz transformations. γ ( ω ′ − k x ′ u ) = ω γ ( k x ′ − ω ′ u c 2 ) = k x k y ′ = k y k z ′ = k z What am i doing wrong?
Find fractional notation for the ratio 1.6 to 9.8
division by fraction proofI was trying to figure out the property of dividing by fraction : x a b = x ⋅ b a An other representation for this problem is to show X ÷ ( A ÷ B ) = ( X ⋅ A ) ÷ BA simple proof, is by multiplying and dividing by b a which leads to the wished result of x ⋅ b a My questions are, Is there a reason why this method of proving works? for me it seems like a "trick". A second question, do you have an other way to prove it? My searching so far led mostly to intuitive explanations about the concept of dividing.
Solving an example with imaginary units.θ=arctan(3+2)θ=75∘=5π12
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