Are the functions f, g, and h given below linearly independent? f(x) = et – cos(5æ), g(x) = e* + cos(5æ), h(x) = cos(5x). they are independent, enter all zeroes. If they are not linearly independent, find a nontrivial olution to the equation below. Be sure you can justify your answer. (edz – cos(5x)) + (eta + cos(5x)) + COS - cos(5x)) = 0. help (numbers)

Q: Find a and d for the function f(x) = a cos(x) + d such that the graph of f matches the figure. a = d…

A: From the given graph, we see       f(0) = -10       f(π) = -2

Q: given y=f(x) and the function is linear, use this change equation to solve the problem.  Given that…

A: Given that f(4)=-5 We have to find what is the numeric value of f(0).

Q: The temperature of points on a plate x2 + xy + y? <1 is modeled by the function f(x, y) = 25(x² +…

A: Given: The temperature of point on a plate x2+xy+y2≤1 is model by the function is : f(x, y)=25 x2+y2…

Q: 2. (a) Define what it means by for y = f(x). %3D

A:

Q: c. _h(x) = e¯³(sin(x) + 2x); only quotient rule

A: To solve the following using quotient rule

Q: 6. If f(x) = x2 + 2x - 1 and g(x) = 2x-3, find each of the following functions. (a) f°g (b) g°f (c)…

A:

Q: 2. The function y = 2 sin (x +) has an x-intercept at A. (,0) B. (,0) C. (π, 0) D. (2π,0)

A:

Q: Find the value of C if f ′ (x) = 2x2 and f (4) = 5

A: Given,    f ′ (x) = 2x2 and f (4) = 5

Q: The equation of motion of a particle is s = t-5t, where s is in meters and t is in seconds. Assuming…

A: Please see the below picture for detailed solution.

Q: 1. Find the intercepts of the function. f(x)-x* +2 а.

A: Given data÷

Q: Express y as a function of x. The constant C is a positive number.; ln(y + 4) = 5x + ln C

A: We need to express y as a function of x. The constant C is a positive number.; ln(y + 4) = 5x + ln C

Q: ots.) Let f (x) = and g(x)= 2x+3. X-3 %3D a. Find (fog)(x) b. Find (gof)(x) C. Are f and g inverse…

A: a) Plug g(x)=2x+3 inside f(x) and then simplify.

Q: dy as a function of x. Write the following function in the form y = f(u) and u = g(x). Then find xp…

A:

Q: a. f(t) = cos(2t). Find F(s) b. g(t) = e²t sin(3t). Find G(s) c. H(s) = 3s +1 s² - 2s + 5* Find h(t)

A: We have to find the Laplace transform and inverse Laplace transform.

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.