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2 years ago

In Exercises 1–6, write the first five terms of the sequence whose th term is given.

Mathematics

1 answer:

Vadim26 [7]2 years ago

7 0

Answer:

Step-by-step explanation:

1. Un = 3^ n

U1 = 3, U2 = 9, U3 = 27, U4 = 81, U5 = 243

2. Un = (-2/5)^n

U1 = -2/5, U2 = 4/25, U3 = 8/125, U4 = 16/625, U5 = 32/3125

3. Un = sin npi/2

U1 = 1, U2 = 0, U3 = -1, U4 = 0, U5 = -1

4. Un = 3n/n+4

U1 = 3/5, U2 = 1, U3 = 9/7, U4 = 3/2, U5 = 5/3

5. Un = (-1)^n+1(2/n)

U1 = 1, U2 = 2, U3 = -1/3, U4 = 3/2, U5 = -3/5

6. Un = 2 + 2/n - 1/n^2

U1 = 3, U2 = 11/4, U3 = 23/9, U4 = 39/16, U5 = 59/25

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sukhopar [10]

Answer:

The lifeguard should run across the shore a distance of 48.074 m before jumpng into the water in order to minimize the time to reach the child.

Step-by-step explanation:

This is a problem of optimization.

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The time can be calculated by dividing the distance by the speed for each section.

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Then, the distance in the shore is d_b=x and the distance swimming can be calculated using the Pithagorean theorem:

$d_s^2=(60-x)^2+40^2=60^2-120x+x^2+40^2=x^2-120x+5200\\\\d_s=\sqrt{x^2-120x+5200}$

Then, the time (speed divided by distance) is:

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To optimize this function we have to derive and equal to zero:

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$x$

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