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swat32
2 years ago
15

Use the Midpoint Rule with n = 10 to approximate the length of c(t) = (5 + sin(4t), 6 + sin(7t)) for 0 ≤ t ≤ 2π. (Round your ans

wer to two decimal places.)

Mathematics
1 answer:
sukhopar [10]2 years ago
8 0

Answer:

  34.43

Step-by-step explanation:

A differential of length in terms of t will be ...

  dL(t) = √(x'(t)^2 +y'(t)^2)

where ...

  x'(t) = 4cos(4t)

  y'(t) = 7cos(7t)

The length of c(t) will be the integral of this differential on the interval [0, 2π].

Dividing that interval into 10 equal pieces means each one has a width of (2π)/10 = π/5. The midpoint of pieces numbered 1 to 10 will be ...

  (π/5)(n -1/2), so the area of the piece will be ...

  sub-interval area ≈ (π/5)·dL((π/5)(n -1/2))

It is convenient to let a spreadsheet or graphing calculator do the function evaluation and summing of areas.

__

The attachment shows the curve c(t) whose length we are estimating (red), and the differential length function (blue) we are integrating. We use the function p(n) to compute the midpoint of the sub-interval. The sum of sub-interval areas is shown as 34.43.

The length of the curve is estimated to be 34.43.

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Natali [406]

Answer:

-3

Step-by-step explanation:

Note the right side of the equation. There is a negative sign outside of the parenthesis. Distribute the negative sign to all terms within the parenthesis:

x + 3 = - (-x + __)

x + 3 = x - ___

Note:

1) When multiplying a negative and positive together, the answer will be negative

2) When multiplying a negative and negative together, the answer will be positive:

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Note the equal sign, this means that the two side of the equation must equal. This means that the only answer choice is -3:

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~

6 0
2 years ago
Work out the volume of a cuboid 6cm by 4cm by 2.5cm
djverab [1.8K]
This should be a nice and simple answer to your question.

The formula for working out the volume of a cuboid is
Volume=Length×Width×Height

This can be shortened to
V=l×w×h
Or
V=lwh

So, now you know the formula, on to the question

Work out the volume of a cuboid 6cm by 4cm by 2.5cm

Find the relevant information

6cm 4cm and 2.5cm

Write out the formula

V=l×w×h

Substitute in the values

V=6×4×2.5

Solve the equation

V=60

Volume is always a cubed number so remember to add the cubed sign next to your answer (³)

So your final answer will be
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I hope that this has helped you.
6 0
3 years ago
Read 2 more answers
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marta [7]

Answer:

24 :)

Step-by-step explanation:

12 divided by 3 = 4

24 divided by 3 = 8

36 divided by 3 = 12

4 + 8 = 12

12 + 12 = 24

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2 years ago
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65  ÷ 1.5 = 43.333333...

Hope this helps you!

Always remember you are a Work Of Art!

-Nicole :) <3

5 0
2 years ago
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