Are the functions linearly dependent on the interval (0,1)? y1=sintcost, y2=4sin2ty1=sin⁡tcos⁡t, y2=4sin⁡2t hint: recall that function are linearly dependent on a given interval if one is a constant multiple of the other.

hello your question is poorly written attached below is the complete question

since y1 = 1/2 y2 on ( 0,1 ) the function are linearly dependent on ( 0,1 ) ( B )

Step-by-step explanation:

First step : Determine if y1 and y2  are linearly dependent

interval = ( 0,1 )

Functions: y1 = sin t cost t ,   y2 = 4 sin t

We can verify if these functions are linearly independent or linearly dependent by using the determinate form

attached below is the detailed solution

From the attached solution we can conclude that

y1, y2 is linearly dependent on ( 0,1 )

hence ; since y1 = 1/2 y2 on ( 0,1 ) the function are linearly dependent on ( 0,1 )

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)

x = 23.78

step-by-step explanation: