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PLEASE ANSWER ALL PARTS! Thank you in advance. 2. Prove the vector triple product ĀX (B...
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(1) Prove that 75 is irrational. (State the Lemma that you will need in the proof. You do not need to prove the lemma.) (2) Disprove: The product of any rational number and any irrational number is irrational. (3) Fix the following statement so that it is true and prove it: The product of any rational number and any irrational number is irrational. (4) Prove that there is not a smallest real number greater than...
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To prove that N(A) = C(AT)- we will be showing that a vector from either set is also in the other. 1. Prove Claim 1: If Xe N(A) then it is perpendicular to C(A) Outline: Let x be a vector in N(A), and consider the system of equations formed by Ax = 0. This will show that x is orthogonal to each row of A. Finally, show that x...
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If F is a continuous vector field on an oriented surface S with unit normal vector n, then llo F.JS = : Finds Select one: True False Let S be the bottom half of the unit sphere, oriented upward. Let C be the boundary of S, the unit circle in the zy-plane, oriented counterclockwise as viewed from above. Then for any vector field F with continuous first-order partial derivatives, SP.d -...
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5. An eigenvalue problem: (a) Obtain the eigenvalues, In, and eigenfunctions, Yn(x), for the eigenvalue problem: y" +1²y = 0 '(0) = 0 and y'(1) = 0. (5) Hint: This equation is similar to the cases considered in lecture except that the boundary conditions are different. Notice how each eigenvalue corresponds to one eigenfunction. In your solution, first consider 12 = 0,...
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Please help in all parts of the question. Thank you in advance. Find at least 3 different organisms (yeast cannot be one of the 3) that produce ATP without the use of oxygen. Search the WWW to find information on this phenomenon and write a paragraph for each (200-250 words in total) in your own words, addressing at least the following points: 1. What is the name of the organism and what general kind of organism is it? 2. What is...
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CHEM61041 Question 2 continued (b) Answer ALL parts (i) - (iii) Sulfate ion 5 forms a 1:1 host-guest complex in methanol with cation 6, with a binding constant of 313 M . Complexation of sulfate 5 to the dication 7 also gives a 1:1 host- guest complex, with a binding constant of 6.8 x 10M- da НН НН 6 OCH2Ph (i) Sketch a possible structure for the 1:1 complex of sulfate...
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With respect to the independent variable as indicated. Obtain the derivative of the following functions. y = sec 2t y = x Arcsin 2x Arc tan 2x Y x = e(cos2t + 2 sin 2t) y=xel
differential equations. PLEASE answer both parts. These have
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Find the general solution to y" + y, + y = et +2e-t. Find the general solution to y +4y (t +2)e t.
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[2] X is continuous uniform (1,7) while Y is exponential with mean 2. If the variance of (X+2Y) is 20, find the correlation coefficient of X and Y.