Previous 21 22 23 Next Question 21 of 23 (1 point) Apply the power property of logarithms. Assume that the variables represent real numbers. In 2y = Question 22 of 23 (1 point) Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. Assume that the variables represent positive real numbers. log3
3) Is {1 - 22 +23, 3+2x+6r%, 3+4x3, x+222 +23} linearly independent or linearly dependent?
22 & 23 please QUESTION 22 Which of the following statement(s) about electrolytes are true? 1. Electrolyte solutions conduct electricity because electrons are freely moving through the solution. 2. Electrolyte solutions conduct electricity because ions are moving through the solution 3. When methanol (CH3OH) is dissolved in water, an electrolytic solution results 4. When sulfuric acid acid is dissolved in water, a conducting solution results 5. If an aqueous solution containing sodium chloride is diluted, the conductivity will go down...
Q2) Let 21, 22, 23, 24, as be real numbers. Compute det ((a.) (1 :) ( ) ( ) ( .)) 1 1
By differentiating each side of (1 + x)" = 22=0 (3).x* and comparing the coefficients of xk-1 on each side show that for all natural numbers ( <ksn *(* = 1) =()
18. Let f(x) 4x2 +1 and gox)- 3x-4. Find (f+g)x), (f - g)(x). (I eg)X<), and (x). Determine the domain of seros d (t+g)0x)= (Simplify your answer. Do not factor.) 0o.o (Simplify your answer. Do not factor) = (x6-) (g)x) (Simplify your answer. Do not factor.) swer. Do not factor.) (Simplify your (x)= Choose the correct domain of B. All real numbers 1 A. All real numbers except t D. All real numbers except 4/3 C. All real numbers except...
For all real numbers x and y, if x is not equal to y, x>0,y>0 then (x/y)+(y/x)>2
#23 22, Use the definition of limit to prove Theorem 3.5. 23. Use Theorem 3.5 to prove that lim x? cost(1/x)-0. In addition, give a proof of th result without using Theorem 3.5. THEOREM 3.5 Squeeze Theorem for Functions Let I be an open interval that contains the point c and suppose that f, g, except possibly at the point c. Suppose that g(x) s f(a) s h(x) for all x in I If limn g(x)-L = lim h (x),...
Suppose 21, 22, 23, 24 ~ N(0, 1) where 21, 22, 23, 24 are all independent. Let X1 = zi + z2 42 = 22 + 23 23 = 23 + 24 Notice that Cov(21,13) = 0 so that Xi and X3 are independent. Which of the following is true? Var (21 | 22) = Var (21 | 22, 23) Var (x1 | x2) > Var (21 | 22, 23) Var (21 | x2) < Var (21 | 22, 23)
Problem 3. Let 21, 22, 23, 41, 42, y3 be some real numbers, and let A= (1 12 13 (41 42 43); Prove (slowly) that dim (ker(A)) > 2 # dim (col(A)) <1 # dim (raw(A)) <1 + X1y2 = 91.22, x1y3 = y123, 22y3 = 42.23. Show that dim(col(A)) = dim(raw(A)) = 3 - dim(ker(A)).