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20b(4b3)3
How many permutations can be made from the word assassin?
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If h has positive derivative and φ is continuous and positive. Where is increasing and decreasing fThe problem goes specifically like this:If h is differentiable and has positive derivative that pass through (0,0), and φ is continuous and positive. If: f ( x ) = h ( ∫ 0 x 4 4 − x 2 2 φ ( t ) d t ) .Find the intervals where f is decreasing and increasing, maxima and minima.My try was this:The derivative of f is given by the chain rule: f ′ ( x ) = h ′ ( ∫ 0 x 4 4 − x 2 2 φ ( t ) d t ) φ ( x 4 4 − x 2 2 ) We need to analyze where is positive and negative. So I solved the inequalities: x 4 4 − x 2 2 > 0 ∧ x 4 4 − x 2 2 < 0That gives: ( − ∞ , − √ 2 ) ∪ ( √ 2 , ∞ ) for the first case and ( − √ 2 , √ 2 ) for the second one. Then (not sure of this part) h ′ ( ∫ 0 x 4 4 − x 2 2 φ ( t ) d t ) > 0 and φ ( x 4 4 − x 2 2 ) > 0 if x ∈ ( − ∞ , − √ 2 ) ∪ ( √ 2 , ∞ ) . Also if both h′ and φ are negative the product is positive, that's for x ∈ ( − √ 2 , √ 2 ).The case of the product being negative implies: x ∈ [ ( − ∞ , − √ 2 ) ∪ ( √ 2 , ∞ ) ] ∩ ( − √ 2 , √ 2 ) = [ ( − ∞ , − √ 2 ) ∩ ( − √ 2 , √ 2 ) ] ∪ [ ( √ 2 , ∞ ) ∩ ( − √ 2 , √ 2 ) ] = ∅ .So the function is increasing in ( − ∞ , − √ 2 ) , ( − √ 2 , √ 2 ) , ( √ 2 , ∞ ). So the function does not have maximum or minimum. Not sure of this but what do you think?
Discrete Math logically equivalent?Show that ( p ∧ q ) ∨ ( ¬ p ∧ ¬ q ) ≡ p ↔ qHow would I go about doing this?Do I use a truth table or a more "algebraic" process?
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Find the indefinite integral. ∫x(x2+1)2dx
What is a solution to the differential equation d y d x = 1 x + 1 ?
Solve y ′ ( t ) = sin ( t ) + ∫ 0 t y ( x ) cos ( t − x ) d x by Laplace transformMy try:I applied Laplace transform on both sides of the equation. s L { y ( t ) } = 1 s 2 + 1 + L { c o s ( t ) ∗ y ( t ) } ⟹ s L { y ( t ) } = 1 s 2 + 1 + L { c o s ( t ) } × L { y ( t ) }Now, I'm stuck on applying the inverse Laplace transform on (*) to find y ( t )
Bounding the order of tournaments without transitive subtournaments of certain size.A tournament of order N is a directed graph on [N] obtained by assigning a direction to each edge of K N . A tournament D is transitive if for every triple a , b , c ∈ N, ( a , b ) , ( b , c ) ∈ E ( D ) implies that ( a , c ) ∈ E ( D ). For n ∈ N let f(n) be the maximum integer such that there exists a tournament of order f(n) without a transitive sub-tournament of size n. Show that f ( n ) > ( 1 + o ( 1 ) ) 2 n − 1 2 .
What is the highest spectral order that can be seen if a grating with 6500 slits per cm is illuminated with 633-nm laser light? Assume normal incidence.
Prices starting at $5/week., cancel anytime
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