Find all critical points of the given plane autonomous system. (Enter your answers as a comma-separated list.) x′ = x 12 − x − 1 2 y y′ = y(20 − y − x)

Answer:

the critical points are (0,0) , (0, 20), (12, 0) , (4,16)

Step-by-step explanation:

To consider the autonomous system

[tex]x' =x (12 -x - \dfrac{1}{2})[/tex]

[tex]y' = y( 20 -y - x)[/tex]

The critical points of the above system can be derived by replacing x' = o and y' = 0.

i.e.

[tex]x' =x (12 -x - \dfrac{y}{2}) = 0[/tex]

[tex]\dfrac{x}{2} (24 -2x - y) = 0[/tex]

x = 0 or 24 - 2x - y = 0     ----- (1)

Also

[tex]y' = y( 20-y-x) = 0[/tex]

y( 20 -y - x) = 0

y = 0 or 20 - y - x = 0  -----   (2)

By solving (1) and (2);

we get x = 4 and y = 16

Suppose x = 0 from (2)

y = 20

Also;

if y = 0 from (1)

x = 12

Thus, the critical points are (0,0) , (0, 20), (12, 0) , (4,16)

Please answer this is my last assignment for the semester

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"Good-bye, Mom," Tino cried as he rushed out the door. Tino had his new fishing pole with him and was anxious to try it out.

Tino Kanaha (kan' ah hah) was a Hawaiian boy. He had just turned twelve the day before and had received the fishing pole as a gift from his father.

Tino's house was about a half mile from the cliff overlooking the leeward side of Maui. Many times Tino had climbed down to the rocks below and looked for seashells while his father fished for aku.

"Now it's my turn," thought Tino as he scurried out onto one of the rocks, "and I get to do it all by myself!"

"Aku, here I come!" yelled Tino excitedly as he cast his bait into the surf.

An hour later, Tino heard someone call his name. He looked up and saw his good friend, Kona. "Have you caught anything?" Kona yelled.

"Oh, hi, Kona," Tino said disappointedly. "Wait for me, and I'll be right up."

As Tino reeled in his line, he noticed the waves were much bigger than they had been before. "The wind is stronger, too, " thought Tino as he glanced at the darkening sky.

"We'd better hurry home," Tino said to Kona as he reached the top of the hill. The two boys ran as quickly as they could. They even took the short cut through the sugar cane field to save time.

Kona raced into his yard and, without stopping, he yelled, "Good-bye, Tino! I'll see you tomorrow!"

The first big drops of rain began to fall as Tino reached the front door of his house.

"Oh, I'm glad you're home!" Mrs. Kanaha said. "It is beginning to rain very hard!"

"The storm must be the reason the fish weren't biting," Tino said as he put his fishing pole into the rack on the porch, "but I'll try again tomorrow."



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No bother to find or locateNope not found nope

Need help please
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