1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
inn [45]
2 years ago
7

1 point) Are the functions f,g, and h given below linearly independent? f(x)=e3x+cos(5x), g(x)=e3x−cos(5x), h(x)=cos(5x). If the

y are independent, enter all zeroes. If they are not linearly independent, find a nontrivial solution to the equation below. Be sure you can justify your answer. 1 (e3x+cos(5x))+ -1 (e3x−cos(5x))+ 0 (cos(5x))=0.
Mathematics
1 answer:
Fynjy0 [20]2 years ago
8 0

Answer:

Functions are linearly dependent (are not linearly independent.)

Step-by-step explanation:

Remember that two functions f(x), g(x) and h(x) are said linearly independent on an interval I if the <em>only solution</em> to the equation

\alpha f(x)+\beta g(x)+\omega h(x)=0, \ \text{for all } x\in I

is the trivial one: α = 0, β = 0, ω = 0. If they are not linearly independent, they are called linearly dependent.

Now, let f(x), g(x) and h(x) be the functions:

f(x)=e^{3x}+\cos(5x),

g(x)=e^{3x}-\cos(5x),

h(x)=\cos(5x).

Then, letting α = 1, β= -1 and ω = -2, we see that:

\alpha f(x)+\beta g(x)+ \omega h(x)=e^{3x}+\cos(5x)-e^{3x}+\cos(5x)+2\cos(5x)=0.

Hence, the functions f(x), g(x) and h(x) are not linearly independent, or equivalently, are linearly dependent.

You might be interested in
in the lab, Tammy has two solutions thta contain alcohol and is mixing them with each other. She use twice as much Solution A as
Dmitry_Shevchenko [17]

Answer:

She uses 200 milliliters of solution B

Step-by-step explanation:

Notice that there are two unknowns in this problem: 1) the amount of solution A that is being used, and 2) the amount of solution B being used. We can name such unknowns with letters to facilitate our work:

Amount of solution A to be used = A

Amount of solution B to be used = B

So, since we need to find two unknowns, we need to create a system of two equations to solve them.

Our first equation can be obtained from the sentence: "She uses twice as much Solution A as Solution B," which written in mathematical form is:

A = 2 B

The second equation we can build from the information of the amount of alcohol in each solution that combined will add up to 104 milliliters of alcohol in the mixture. Knowing the percent of alcohol in each solution, we can write an equation for the amount of alcohol:

0.19 A + 0.14 B = 104

Now we can use our first equation to substitute A in terms of B in the second equation:

0.19 (2 B) + 0.14 B = 104

0.38 B + 0.14 B = 104

0.52 B = 104

B = 104 / 0.52

B = 200 milliliters

4 0
3 years ago
School started at 8:05 a.m. and ended at 2:40 p.m. The work below shows Erica’s calculation of the length of the school day.
lisabon 2012 [21]
6 hours and 5 minut3s or so
8 0
2 years ago
How can you find the answer of 15 only using the numbee 4
Kryger [21]
(4 x 4) - (4/4)
= 16 - 1
= 15
8 0
3 years ago
Read 2 more answers
Describe how to find all the points on a baseball field that are equidistant from second base and third base.
Zielflug [23.3K]

From the given diagram, the following statements are true:

AB = BC

3y = 5y - 22

3y - 5y = -22

-2y = -22

y = 11

Similarly, m<DBE = 50 degrees

m<BED = 90 - m<DBE

m<BED = 90 - 50

m<BED = 40 degrees

Since BE = BC = 3y

BE = BC = 3(11) = 33

Also, 7x  - 2 = 40

7x = 40 + 2

7x = 42

x = 6

Get the measure of m<BEA

m<BEA = 7x - 2

m<BEA = 7(6) - 2

m<BEA = 40 degrees

Learn more on angles here: brainly.com/question/16281260

8 0
2 years ago
The expression below is scientific notation for what number?<br> 3.34.*10^-4
Stella [2.4K]
0.000334 is the scientific notation
7 0
2 years ago
Other questions:
  • Nina can paint two 10 ft. by 12 ft. walls in 3 hours. She has to paint her house, and it has 7 walls this size
    11·1 answer
  • Help plz my teacher won't help
    14·1 answer
  • A coin has heads on one side and tails on the other the coin is tossed 12 tossed 12 times and lands heads up 4 times which best
    6·1 answer
  • A 12 ft ladder leaning againist a house make a 64 degree angle with the ground will the ladder reach a window till that is 10.5
    15·1 answer
  • Combine to create an equivalent expression -n + (-4) - (-4n) +6
    13·1 answer
  • Plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz
    15·1 answer
  • A system of inequality, where x is the rate of a spaceship in a video game and y is where the ship travels on the screen in 3.5
    8·2 answers
  • The width of a rectangular field is 20 feet less than its length. The area of the field is 12,000 ft? What is the length of the
    8·2 answers
  • Which of the following expressions to 36x + 24y? choose all that apply.
    15·1 answer
  • Terry and Ed start a lawn mowing business and purchase the mowers and equipment for $800. They charge $20 for each lawn and use
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!