The variable a is the length of the ladder. The variable h is the height of the ladder's top at time t, and x is the distance from the wall to the ladder's bottom. Suppose that the length of the ladder is 7.0 meters and the top is sliding down the wall at a rate of 0.4 m/s. Calculate dx/dt when h = 5.4. (Round your answer to three decimal places.)

  0.485 m/s

Step-by-step explanation:

The Pythagorean theorem tells you ...

  a² = h² +x²

Differentiating with respect to time, we find ...

  0 = 2h·h' +2x·x'

Solving for x', we get ...

  x' = -h'(h/x)

To evaluate this, we need to find the value of x when h=5.4. We can do this using the original Pythagorean relation.

  7.0² = 5.4² + x²

  x = √(49-29.16) ≈ 4.454

Then the desired rate of change is ...

  x' = -(-0.4 m/s)(5.4/4.454) ≈ 0.485 m/s

both equations and proportions are better.

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step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

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