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20b(4b3)3
Find the number of element in the power set of the set {x,(y,z)}
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If f ( x ) = a x − x 3 1 + x 2 show that ∀ x [ f ′ ( x ) ≥ 0 iff a ≥ 9 8 ]Part of answer found online: f ′ ( x ) = a − 3 x 2 ( 1 + x 2 ) − 2 x ( x 3 ) ( 1 + 3 x 2 ) 2 = a + x 4 − 3 x 2 ( 1 + x 2 ) 2 My problem:I don't understand why: a − 3 x 2 ( 1 + x 2 ) − 2 x ( x 3 ) ( 1 + 3 x 2 ) 2 = a + x 4 − 3 x 2 ( 1 + x 2 ) 2 When i try to rearrange the left i get: a − 3 x 2 ( 1 + x 2 ) − 2 x ( x 3 ) ( 1 + 3 x 2 ) 2 = a − 3 x 4 + 3 x 2 − 2 x 4 ( 1 + 3 x 2 ) 2 = a − x 4 + 3 x 2 ( 1 + 3 x 2 ) 2 And from there: a − x 4 + 3 x 2 ( 1 + 3 x 2 ) 2 = a + − 1 1 ⋅ x 4 + 3 x 2 ( 1 + 3 x 2 ) 2 = a + − x 4 − 3 x 2 ( 1 + 3 x 2 ) 2 Am i making a simple mistake in the interpretation of the minus in front of a fraction?
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Basketball concession stand sells a soda for 1.50 a bag of popcorn for 1.00 and a candy bar for 1.25 at one game 11 fewer candy bars were sold than bags of popcorn. that same night the number of sodas sold was 7 more than the number of candy bars and bags of popcorn sold altoghter. if the concession stand made 164 that night how many of each item were sold?
I'm given that E → = μ 0 p 0 ω 2 4 π r [ cos u ( x ^ − x r r ^ ) + sin u ( y ^ − y r r ^ ) ] implies − μ 0 p 0 ω 2 4 π r [ cos u x ^ × r ^ + sin u y ^ × r ^ ] = 1 c r ^ × E → ,but I don't follow how to get from the former to the latter.
Having trouble solving log ( x − 21 ) = 2 − log x for xI'm having trouble with this problem: log ( x − 21 ) = 2 − log x, solve for xI'm coming up with x = − 5 but that can't be right.
Explain the difference between a first and a second- order linear differential equation
If you double the net force on an object, youll
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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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