5. 6. Express 27 = 3 in logarithmic form a. log3 27=3 b. log+3=27 Which of the following do not exist? logarithms with fractional bases logarithms that equal zero a. C. C. b d. 10g273=3 d. log33=27 logarithms of negative numbers logarithms of irrational numbers

Q: I Let f(t) be a periodic function with period 7/2 with its window function given by fr(t) = {…

A:

Q: 4. Consider the matrix 1 0 0 0 0 0 -2a -a (a² + a) 0 (2-a²) - (2-a²) -2a (2-a²) 2+ 4a - a² Find all…

A: 4) Solution:According to the given data, find the all values of a for which given matrix is psd.

Q: 4. Prove that thereal 2 × 2 matrix a b ^-[22] A d is invertible if and only if ad – bc, in which…

A: The inverse of a square matrix A is another matrix denoted as A^(-1), such that when you multiply A…

Q: 2. Show that the following functions are convex by verifying the condition that V²f(x) 20 is…

A:

Q: Rita has 360 meters of fencing and wishes to enclose a rectangular field. Suppose that a side length…

A:

Q: Suppose you have $5400 deposited at 3.6% compounded semiannually. About long will it take your…

A: Given information:Initial deposit (principal), .Annual interest rate, Compounding frequency,…

Q: Question 3 Labor. Refer to Table 4. Find the average rate of change of hourly earn- ings from 1980…

A: The given table is year1970198019902000weekly hours37.135.334.534.3Hourly…

Q: Logic Problem 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. There are exactly five dorms.…

A: Now, let's use this information to deduce who drinks coffee and who has a dog:••We know that there…

Q: Find the Taylor series for the functions sinh x and coshx for all à € R.

A:

Q: Find a basis for the eigenspace corresponding to the eigenvalue of A given below. J A = 50 - 3 0 -…

A:

Q: (a) A signal applied to a servomechanism system is defined by the function as, 0 4 5 f(t) = 2t+1 9…

A:

Q: Evaluate the following integral by making an appropriate change of variables. Sfin[7(49x²…

A:

Q: Exercise 8.11.1 Find the (real or complex) eigenvalues and eigenvectors of the following matrices.…

A:

Q: Suppose U = {1, 2,..., 9}, A = all multiples of 2, B = all multiples of 3, and C = {3, 4, 5, 6, 7}.…

A:

Q: Question 1 (a) Fd parametric equations for the line segment that joins the point P(2, 3, -3) to the…

A: As per our company guidelines we are advised to solve only the first question.Kindly repost the…

Q: 6. Let g(x) = -1/² for x 0 and g(0) = 0. (a) Show g(n) (0) = 0 for all n = 0, 1, 2, 3,.... (b) Show…

A: We will use formula of taylor series to solve this problem.

Q: 2. Determine the values of a and b that lead to the smallest (based on area) convex set E₁ = {(x, y)…

A:

Q: Consider the curve e" + e- 2 Now imagine we rotate it around the y-axis. Find the surface area that…

A:

Q: 4. Use the definition to show that the following sequences are Cauchy: (a) {3n+2}n=1 (b) {1 n=1 (c)…

A:

Q: Use al-Kashi's method to approximate √3821953 (including the fractional part).

A:

Q: What's the conjecture?

A:

Q: The test function gx(x) given in the following figure: 8x(1)| a 0 FO-A Xo Fo+a Find the conditions…

A:

Q: Angle of a line with the positive direction of the x-axis is 0 (0 is a cute). The line is rotated…

A:

Q: Exercise 4: Recall that in Exercise 3 we looked at Euler's method applied to the equation x = x with…

A:

Q: To test this series for convergence n=1 4" +4 5n You could use the Limit Comparison Test, comparing…

A:

Q: Show that translations are commutative. That is, if matrix T(d) represents a translation by d₂…

A: To show that translations are commutative, we'll use the matrix representation of translation. Let…

Q: Consider the congruence a² + x + 1 = 0 mod 21. Solutions to the congruence above must also be…

A: The given congruence equation is .We will solve this congruence relation using the Chinese remainder…

Q: Exercise 1. (a) Prove (using direct proof) that Vn € {odd integers}, 3j € Z|n = 2j - 1. (b) Write…

A:

Q: Derive the formula for the curl of a field in spherical coordinates. In class we studied the…

A: The curl of a field in spherical coordinates is given by

Q: 2. Show that the following functions are convex by verifying the condition that V² f(x) 20 is…

A:

Q: Determine whether the and justify your answer. set S spans R following S = {(5,6,5), (1,1,-5),…

A:

Q: 5. Suppose the function f has the property that there exists a positive number B such that…

A:

Q: the product of the elements is the identity. 7 has order 2. of order 2.

A: Let us prove above result

Q: 16. Let V and W be vector spaces such that dim(V) dim(W), and let T: V → W be linear. Show that…

A: Answer (A),Let V and W be vector spaces such that dim(V) = dim(W) and let  be linear.Now, we need to…

Q: After making 21 payment of 625.78 on your car loan, you wanted to find out how much is left of your…

A:

Q: Find the general solution of the given system. X(t) = X' = 17418 I 0 7 7 2 11-1212 X

A:

Q: Fibonacci sequence. The Fibonacci sequence yo, y1, Y2₂, ... starts with yo = 0, y₁ = 1, and for t =…

A: As per the question, we have two distinct sequences: the classic Fibonacci sequence, defined by ,…

Q: A phone company charges for service according to the formula: C(n) = 30 +0.08n, where n is the…

A:

Q: 10ω Consider g(w) w² +4 Determine the intervals on which g is decreasing. O 9 is decreasing on: g is…

A:

Q: Show that the equation has at least one solution.

A: Here we will use Intermediate Value Theorem to conclude the equation has at least one solution. The…

Q: Let a and b be positive integers with ged(a, b) = 1. Show that if d > ab, then as + tb = d has a…

A: 4. Given that a and b be positive integers with gcd(a, b)=1.     To prove that if then has a…

Q: Suppose you want to have $800,000 for retirement in 35 years. Your account earns 5% interest. a) How…

A:

Q: 2. (a) Sketch the finite planar region D which is bounded by the four curves y = x², Show that the…

A:

Q: 25. Vector A points in the positive x direction and has a magnitude of 75 m. The vector C = A + B…

A:

Q: You have $500,000 saved for retirement. Your account earns 5% interest. How much will you be able to…

A:

Q: (d) Suppose f and g are continuous on an open interval (a, b), and let y₁ be any nontrivial solution…

A:

Q: c. y' + 2y = x³ with y(1) = 2 Yo (x) = e Yp (x) = y (x) = y (x) = -2x 1½ e ²x³ - 2/ ( 10²x² -…

A:

Q: Let Z denote the centre of a group G. Then show that z € Z iff N(a) = G. Also show that if G is…

A: Let Z denote the centre of a group G,  we have to show that a∈Z iff N(a)=G. ,also show that if G is…

Q: Is λ = 5 an eigenvalue of 40-3 44 -2 3 9? If so, find one corresponding eigenvector. 8

A: We first calculate the characteristic polynomial and then find the eigenvalue and eigenvector