4/5
Find common fractions of 12/15
12 / 15. each part divided by 3
15 / 3 = 5...12 / 3 = 4...12/15 = 4/5
Answer:
Linearly independent, x = 0
Step-by-step explanation:
- We are given three functions as follows:
![f ( x ) = e^4^x\\\\g ( x ) = xe^4^x\\\\h( x ) = x^2e^4^x](https://tex.z-dn.net/?f=f%20%28%20x%20%29%20%3D%20e%5E4%5Ex%5C%5C%5C%5Cg%20%28%20x%20%29%20%3D%20xe%5E4%5Ex%5C%5C%5C%5Ch%28%20x%20%29%20%3D%20x%5E2e%5E4%5Ex)
- We are to determine the linear - independence of the given functions. We will use the theorem of linear independence which states that:
![c_1*f(x) + c_2*g(x) + c_3*h(x) = 0](https://tex.z-dn.net/?f=c_1%2Af%28x%29%20%2B%20c_2%2Ag%28x%29%20%2B%20c_3%2Ah%28x%29%20%3D%200)
Where,
c1 , c2 , c3 are all zeroes then for all values of (x),
- The system of function is said to be linearly independent
- We will express are system of equations as such:
- To express our system of linear equations we will choose three arbitrary values of ( x ). We will choose, x = 0. then we have:
![c_1*( 1 ) + c_2*(0) + c_3*(0 ) = 0\\\\c_1 = 0](https://tex.z-dn.net/?f=c_1%2A%28%201%20%29%20%2B%20c_2%2A%280%29%20%2B%20c_3%2A%280%20%29%20%3D%200%5C%5C%5C%5Cc_1%20%3D%200)
- Next choose x = 1:
![c_2*e^4 + c_3*e^4 = 0\\\\c_2 + c_3 = 0](https://tex.z-dn.net/?f=c_2%2Ae%5E4%20%2B%20c_3%2Ae%5E4%20%3D%200%5C%5C%5C%5Cc_2%20%2B%20c_3%20%3D%200)
- Next choose x = 2:
![2*c_2*e^8 + 4*c_3*e^8 = 0\\\\c_2 + 2c_3 = 0](https://tex.z-dn.net/?f=2%2Ac_2%2Ae%5E8%20%2B%204%2Ac_3%2Ae%5E8%20%3D%200%5C%5C%5C%5Cc_2%20%2B%202c_3%20%3D%200)
- Solve the last two equations simultaneously we have:
.... ( Only trivial solution exist )
Answer: The functions are linearly independent
- The only zero exist is x = 0.
Find the total capacity of 25 containers of cranberry juice is each bottle holds 5/4 one pant 60Z
The equation to your question would be P =10(c)+20. meaning 10 pencils in each box multiplied by the number of boxes (c) plus the 20 pencils the teacher gives her will equal the number of pencils (P) she has altogether. (C stands for the number of boxes and P stands for pencils)
so lets say she has 3 boxes. well, c stands for boxes soooo...... all you have to do is plug in 3 were c is. giving you this equation P = 10(3)+20. then all you have to do is solve. P = 10(3)+20
10 times 3 = 30 so P = 30+20
then add 30 and 20 P = 50 she has 50 pencils altogether
(remember this is just an example, 50 pencils is NOT the answer to your question. but you can use the equation i gave you to find your own answer!) :) Hope this helps!!
Answer:
You first identify the variable.