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20b(4b3)3
How to find the initial and the future population based on today's data?A certain species of bird was introduced in a certain county 25 years ago. Biologists observe that the population doubles every 10 years, and now the population is 27,000.(A) - What was the initial size of the bird population? (Round your answer to the nearest whole number.) n (initial) = 27 , 000 2 ( 25 / 10 ) ⟹ [ n ] (initial) = 4773 - correct.(B) - Estimate the bird population 8 years from now. (Round your answer to the nearest whole number.) n (8 years later) = 4773 × 2 ( 8 / 10 ) ⟹ [ n ] (8 years later) = 8310 - wrong.
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Rearrangement inequality and minimal value of sin3xcosx+cos3xsinxFor x∈(0,π2), is the minimum value of sin3xcosx+cos3xsinx=1? So considering (1cosx,1sinx) and (sin3x,cos3x) is it right to use the rearrangement inequality and conclude that sin3xcosx+cos3xsinx is more than or equal to sin3xsinx+cos3xcosx which is equal to 1?
I have the following representation: ( a + β ′ X ) 2 where a is a constant and both β and X are k by 1 vectors.The representation is further written as follows: a 2 + 2 a β ′ X + X ′ β β ′ X )While the first part is clear to me, I struggle to understand why it is shown once with ′ (X′ and β ′ ) and once without ′ (X and β).
Subtract the following matrices. [ − 2 − 9 9 − 7 0 − 1 ] − [ 8 − 7 6 6 − 9 − 7 ]
limx→0x(1+acosx)−bsinxx3=1, how to find the constants a,b?
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Let f : R → R be a continuous function and g : R → R be a Lipschitz function. Would you help me to prove that the system of differential equation x ′ = g ( x ) y ′ = f ( x ) ywith initial value x ( t 0 ) = x 0 and y ( t 0 ) = y 0 has a unique solution.Could I prove the uniqueness solution of x ′ = g ( x ), x ( t 0 ) = x 0 by Gronwall Inequality first then use the result to prove the second?
For the experiment of tossing a coin three times, how do you find the probability of getting a head on the first toss?
Double union notationThe Cantor set C is defined as C = [ 0 , 1 ] ∖ ⋃ n = 0 ∞ ⋃ k = 0 3 n − 1 ( 3 k + 1 3 n + 1 , 3 k + 2 3 n + 1 ) Does the double union of sets work like the double summation?I start counting from n = 0 and then all of the k's.I.e.For n = 0...0, k goes from 0 to 0 ⋃ n = 0 0 ⋃ k = 0 0 = ( 1 3 , 2 3 ) For n = 1, k = 0...2. ⋃ n = 0 1 ⋃ k = 0 2 = ( 1 3 , 2 3 ) ∪ ( 3 ⋅ 0 + 1 3 1 + 1 , 3 ⋅ 0 + 2 3 1 + 1 ) ∪ ( 3 ⋅ 1 + 1 3 1 + 1 , 3 ⋅ 1 + 2 3 1 + 1 ) ∪ ( 3 ⋅ 2 + 1 3 1 + 1 , 3 ⋅ 2 + 2 3 1 + 1 ) = ( 1 3 , 2 3 ) ∪ ( 1 9 , 2 9 ) ∪ ( 4 9 , 5 9 ) ∪ ( 7 9 , 8 9 ) = ( 1 3 , 2 3 ) ∪ ( 1 9 , 2 9 ) ∪ ( 7 9 , 8 9 ) For n = 2, k = 0...8 ⋃ n = 0 2 ⋃ k = 0 8 = ( 1 3 , 2 3 ) ∪ ( 1 9 , 2 9 ) ∪ ( 7 9 , 8 9 ) ∪ ( 3 ⋅ 0 + 1 3 2 + 1 , 3 ⋅ 0 + 2 3 2 + 1 ) ∪ ( 3 ⋅ 1 + 1 3 2 + 1 , 3 ⋅ 1 + 2 3 2 + 1 ) ∪ ( 3 ⋅ 2 + 1 3 2 + 1 , 3 ⋅ 2 + 2 3 2 + 1 ) ∪ ( 3 ⋅ 3 + 1 3 2 + 1 , 3 ⋅ 3 + 2 3 2 + 1 ) ∪ ( 3 ⋅ 4 + 1 3 2 + 1 , 3 ⋅ 4 + 2 3 2 + 1 ) ∪ ( 3 ⋅ 5 + 1 3 2 + 1 , 3 ⋅ 5 + 2 3 2 + 1 ) ∪ ( 3 ⋅ 6 + 1 3 2 + 1 , 3 ⋅ 6 + 2 3 2 + 1 ) ∪ ( 3 ⋅ 7 + 1 3 2 + 1 , 3 ⋅ 7 + 2 3 2 + 1 ) ( 3 ⋅ 8 + 1 3 2 + 1 , 3 ⋅ 8 + 2 3 2 + 1 ) = ( 1 3 , 2 3 ) ∪ ( 1 9 , 2 9 ) ∪ ( 7 9 , 8 9 ) ∪ ( 1 27 , 2 27 ) ∪ ( 4 27 , 5 27 ) ∪ ( 7 27 , 8 27 ) ∪ ( 10 27 , 11 27 ) ∪ ( 13 27 , 14 27 ) ∪ ( 16 27 , 17 27 ) ∪ ( 19 27 , 20 27 ) ∪ ( 22 27 , 23 27 ) ∪ ( 25 27 , 26 27 ) = ( 1 3 , 2 3 ) ∪ ( 1 9 , 2 9 ) ∪ ( 7 9 , 8 9 ) ∪ ( 1 27 , 2 27 ) ∪ ( 7 27 , 8 27 ) ∪ ( 19 27 , 20 27 ) ∪ ( 25 27 , 26 27 ) For n = 3, k = 0...26.
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