A boat is pulled into a dock by a rope with one end attached to the front of the boat and the other end passing through a ring attached to the dock at a point 5 feet higher than the front of the boat. The rope is being pulled through the ring at the rate of 0.6 feet per second. How fast is the boat approaching the dock when 13 feet of rope are out?

Answers

Answer 1

Answer:

0.65 ft/s

Explanation:

Let l be the length of the rope and x the distance from the boat to the dock, this forms a right triangle, hence:

l² = x² + 5²

substituting l = 13 ft, to get x gives:

13² = x² + 5²

x² = 13² - 5²

x² = 144

x = √144 = 12 ft

But, l² = x² + 5²; differentiating both sides with respect to time (t):

2l(dl/dt) = 2x(dx/dt)

dx/dt = l(dl / dt)/x

but dl / dt = 0.6 ft/s, hence:

dx/dt = 13 ft * 0.6 ft/s / 12 ft

dx/dt = 0.65 ft/s

The boat is approaching the dock at 0.65 ft/s

Answer 2

When 13 ft of rope is out, the boat will be approaching the dock at the rate of; 0.65 ft/sec.

Let x be the horizontal distance of the boat from the dock at time t

Let y be the length of rope at time t

We are given;

Rate at which rope is being pulled through the ring; dy/dt = -0.6 ft/s

We want to find dx/dt when y = 13

We are told that a ring attached to the dock at a point 5 feet higher than the front of the boat. Thus by Pythagorean Theorem, we can say;

x² + 5² = y²

Differentiating each term with respect to t gives;

2x(dx/dt) = 2y(dy/dt)

Now, When y = 13, it means that;

x² + 5² = 13²

x² + 25 = 169

x² = 169 - 25

x = √144 x = 12

We have 2x(dx/dt) = 2y(dy/dt)

Thus;

2(12)(dx/dt) = 2(13)(-0.6)

dx/dt = -(7.8/12)

dx/dt = -0.65 ft/s

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Does industrialization lead to high energy consult rates? Why or why not

Answers

Answer:

The results indicate that income increases energy consumption in both the long run and the short run. In the long run, urbanization decreases energy consumption, while industrialization increases it. ... Economic growth policies designed to increase income and industrialization will increase energy consumption

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Explain Sigmund Freud’s view of personality. In your response, discuss the conscious mind, the subconscious mind, the id, the ego, the superego, and the reality principle. What assumptions did Freud make about people based on their personalities?

Answers

Answer:

According to Sigmund Freud, human personality is complex and has more than a single component. In his famous psychoanalytic theory, Freud states that personality is composed of three elements known as the id, the ego, and the superego. These elements work together to create complex human behaviors. Freud believed that the id, ego, and superego are in constant conflict and that adult personality and behavior are rooted in the results of these internal struggles throughout childhood.

Hope this helps:)

The conscious mind, the subconscious mind, and the unconscious mind are three distinct parts of the human mind, according to Sigmund Freud's theory of personality.

Who was Sigmund Freud?

Sigmund Freud was an Austrian neurologist and the founder of psychoanalysis, a clinical method for evaluating and treating pathologies thought to be the result of psyche conflicts, through dialogue between patient and psychoanalyst, and the distinct theory of mind and human agency derived from it.

The unconscious mind, according to Freud, is the most important part of our psyche because it contains hidden feelings, memories, and desires that influence our behavior. The unconscious mind includes the id, ego, and superego.

The importance of the unconscious mind and the complex interplay between our basic instincts, societal norms, and personal experiences was emphasized in Freud's view of personality.

Thus, this is the Sigmund Freud’s view of personality.

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explain one development in the period before 1930 that would support duara's claim that japan had "amply demonstrated its leadership abilities" as stated in the first paragraph

Answers

Answer:

One piece of evidence that Duara uses in the passage to support his claim regarding Western racial attitudes and Japanese militarism in the second paragraph is where he says that Japan was allotted a lower quota of ships than the British and Americans.

Duara provides evidence in the first paragraph when he claims that Japan was given a smaller ship allotment than the British and Americans.

Japan army and Americans:

Discrimination was evident in international conventions such as the Washington Naval Conference (1922), the London Naval Conference (1930), and everywhere else when Japan was given a smaller ship quota than the British and Americans.

It was the escalation of exclusionary practices in the United States, culminating in the 1924 Exclusion Laws restricting Japanese immigration, that enraged Japanese nationalists the most.

These rooted civilizational divisions would have to be battled out in last, holy war of the East versus the West, according to extremists.

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The half-life of carbon-14 is about 5700 years. If you left those 100 carbon-14 atoms to sit around for 5700 years, how many would you expect to decay during that time?

Answers

Answer:

50 atoms have decayed during that time

Explanation:

The radioactive decay is represented as

[tex]N = N_0 * \frac{1}{2}^X\\[/tex]

Where N is the amount of radioactive element after a certain time period

N0 is the amount of radioactive element during the initial time period

X is the half life of the radioactive element

Substituting the given  values in above equation,  we get:

[tex]N = 100 * \frac{1}{2}^1\\N = 50[/tex]atoms

So, 50 atoms of carbon-14 remain are left after decaying for 5700 years.

Hence,  atoms of carbon-14 that decay during 5700 years are 100-50 - 50

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