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Fantom [35]
3 years ago
7

Determine if the given vectors are linearly independent. u = −4 0 −3 , v = −2 −1 4 , w = −8 2 −17

Mathematics
1 answer:
lesya [120]3 years ago
6 0

These three vectors are linearly <u>dependent</u> (details are in the attachment).

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The equation of motion for a weight suspended from a particular spring is given by p(t)=2sint3+5cost3p(t)=2sin⁡t3+5cos⁡t3, where
daser333 [38]
The given displacement at time, t, is
p(t) = 2 sin(t³) + 5 cos(t³)

The initial equilibrium position is
p(0) = 5

To determine future equilibrium postions, define
f(t) = p(t) - 5 = 2 sin(t³) + 5 cos(t³ - 5
The derivative of f(t) is
f'(t) = (3t²)[2 cos(t³) - 5sin(t³)]

Equilibrium is established when f(t) = 0.
To solve this equation numerically, we shall use the Newton-Raphson method, given by.
t(n+1) = t(n) - f[t(n)]/f'[(t(n)], n=0,1,2, ...,

As a guess, let (0) = 1.
The iterative solution for t is shown below.

  n         t(n)
 ---   -----------
   0   1.0000
   1    0.9344
   2   0.9147
   3   0.9130
   4   0.9130

The solution converges rapidly to t = 0.913 s.
The graphical solution (shown below) confirms the numerical solution.

Answer:
The weight first reaches the equilibrium position in 0.913 sec.

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Step-by-step explanation:

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2 years ago
There are slips of paper that are numbered from 1 to 15 in a hat. What is the theoretical probability that a slip of paper that
lesya [120]

Okay! Let's write out all the numbers:

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

Now, let's bold (or you can circle them... or do really anything to them as long as they are standing out to you) the even numbers (remember all even numbers are divisible by 2)

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

Now let's list all the ones we highlighted:

2

4

6

8

10

12

14

Count up how many numbers that is.

You should get 7.

So, our answer is 7 out of 15 numbers.

Or as a fraction:

7/15 is our answer.

Note: A probability is the number of chances something has to happen out of the total number of chances. So in this case the number of even numbers out of the total number of numbers. You can apply this to any probability problem. Hope this helps!

Read more on Brainly.com - brainly.com/question/2150566#readmore

5 0
3 years ago
Read 2 more answers
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