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Question 9 (ii) and Question 10
9. For F as in 8, define N:F-Q by N(a+bv2)--22 (i) Prove that N(a3)-N(a)N(8), for all α, β E F. (ii) Find an element u E F such that N(u)-1 and such that all of the powers un are distinct. 10. Use 9 above to prove that the equation 2-2U2-1 has infinitely many solutions over Q. What can you conclude about the number of solutions over Z.
9. For F as in 8, define...
9 – in 5. Prove that lim n+ 8 + 13n -7 13
k110 9 +5=14 -4 n-3=-11 8 17-3 C) 10-8=-24 3 nd 9、 the (L) The quotient of a number and-7, decreased by 2, is 10. Find the number.
(9) 8. Show how you would accomplish the following multistep synthesis: Synthesize the insect repellent N,N-diethyl-n-toluamide from m-toluic acid. Use compounds with no more than 5 carbons as your other reagents. NC CH 3 2 from
#8-#9
Four identical 100 N boxes are initially at rest on a rough horizontal surface. In all cases, the coefficient of static friction between the box and the surface is 0.70 and the coefficient of kinetic friction is 0.25. Forces are applied as shown. 8. Circle the letter of the box (or boxes) subject to a frictional force of 25 N. A.C. P U 9. Circle the box(es) in equilibrium. A+B .70 25 N 50 N 12 Sa 100 N...
Find C(n, x)pxqn − xfor the given values of n, x, and p. (Round your answer to four decimal places.)n = 9, x = 8, p = 0.4
00 (1 point) For what values of 3 does the series (-1)"(5x)" converge? (n+8)(n +9) The series converges when is in Use interval notation to enter your answer. If the series converges at only one number, enter a closed interval or a single point, e.g., "[5,5]" or {5} Otherwise, enter an open interval (don't worry about whether the series converges at endpoints)
The following set of data is from a sample of n=6. 7, 10, 9, 7, 8, 12 a. Compute the mean, median, and standard deviation. (Round to two decimal places as needed.) b. What is the shape of the dataset? Why?
In questions 1-8, find the limit of the sequence. sin n cos n 2. 37 /n sin n 3. 4. cos rn 5. /n sin n o cos n n! 9. If c is a positive real number and lan) is a sequence such that for all integer n > 0, prove that limn →00 (an)/n-0. 10. If a > 0, prove that limn+ (sin n)/n 0 Theorem 6.9 Suppose that the sequence lan) is monotonic. Then ta, only if...
a. For n= 4 and pi=0.19, what is P(X= 0 )? b. For n= 9 and pi =0.40, what is P(X= 8 )? c. For n= 9 and pi=0.60, what is P(X= 7 )? d. For n=5 and pi =0.89, what is P(X=4)? When n= 4and pi =0.19 , P(X= 0)equalsnothing.