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ryzh [129]
3 years ago
6

Suppose you solved a second-order equation by rewriting it as a system and found two scalar solutions: y = e^5x and z = e^2x. Th

ink of the corresponding vector solutions y1 and y2 and use the Wronskian to show that the solutions are linearly independent Wronskian = det [ ] = These solutions are linearly independent because the Wronskian is [ ] Choose for all x.
Mathematics
1 answer:
xenn [34]3 years ago
3 0

Answer:

The solutions are linearly independent because the Wronskian is not equal to 0 for all x.

The value of the Wronskian is \bold{W=-3e^{7x}}

Step-by-step explanation:

We can calculate the Wronskian using the fundamental solutions that we are provided and their corresponding the derivatives, since the Wroskian is defined as the following determinant.

W = \left|\begin{array}{cc}y&z\\y'&z'\end{array}\right|

Thus replacing the functions of the exercise we get:

W = \left|\begin{array}{cc}e^{5x}&e^{2x}\\5e^{5x}&2e^{2x}\end{array}\right|

Working with the determinant we get

W = 2e^{7x}-5e^{7x}\\W=-3e^{7x}

Thus we have found that the Wronskian is not 0, so the solutions are linearly independent.

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Arte-miy333 [17]

Answer:

-16

Step-by-step explanation:

Represent the number by n.

Then:

8(n + 18) = 16

Performing the indicated multiplication, we get:

8n + 144 = 16

Subtracting 144 from both sides results in 8n = -128.

Dividing both sides by 8:  n = -128/8  =  -16

The number was -16.

4 0
3 years ago
Use the triangle below to find cos V.
Semenov [28]

Answer:

cos\ V = \frac{2\sqrt{29}}{29}

Step-by-step explanation:

Given

The attached triangle

Required

Find cos V

In trigonometry:

cos\theta = \frac{Adjacent}{Hypotenuse}

In this case:

cos V= \frac{TV}{UV}

Where

TV = 6

and

UV^2 = TV^2 + TU^2 -- Pythagoras

UV^2 = 6^2 + 15^2

UV^2 = 261

Take square roots

UV = \sqrt{261

UV = \sqrt{9*29

UV = \sqrt{9} *\sqrt{29

UV = 3\sqrt{29

So:

cos V= \frac{TV}{UV}

cos\ V = \frac{6}{3\sqrt{29}}

cos\ V = \frac{2}{\sqrt{29}}

Rationalize:

cos\ V = \frac{2}{\sqrt{29}}*\frac{\sqrt{29}}{\sqrt{29}}

cos\ V = \frac{2\sqrt{29}}{29}

8 0
2 years ago
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Vikentia [17]

Answer:

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Step-by-step explanation:

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8 0
3 years ago
Tamika makes a 5.5% commision selling electronics how much commission doesshe make if she sells a flat screen for 10000
sergey [27]

Answer:

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Step-by-step explanation:

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3 years ago
What is the solution to the inequality -4 x < 8?
alekssr [168]

<u>Answer:</u>

  • The solution of the inequality is x < -2.

<u>Step-by-step explanation:</u>

<u>Let's simplify the inequality first.</u>

  • => -4x < 8
  • => -4x/4 < 8/4
  • => -x < 2
  • => x < -2

Hence, <u>the solution of the inequality is</u><u> x < -2.</u>

Hoped this helped.

BrainiacUser1357

6 0
2 years ago
Read 2 more answers
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