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3 years ago

Can you help me please with this proof ? thank you!!

Mathematics

1 answer:

Alika [10]3 years ago

4 0

Answer:

what subject is this? or what

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Consider the following.x = t − 2 sin(t), y = 1 − 2 cos(t), 0 ≤ t ≤ 8πSet up an integral that represents the length of the curve.

sweet [91]

The length of the parametric curve (call it <em>C </em>) is given by

$\displaystyle\int_C\mathrm ds=\int_0^{8\pi}\sqrt{\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2}\,\mathrm dt$

We have

$x=t-2\sin t\implies\dfrac{\mathrm dx}{\mathrm dt}=1-2\cos t$

$y=1-2\cos t\implies\dfrac{\mathrm dy}{\mathrm dt}=2\sin t$

Now,

$\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2=5-4\cos t$

so that the arc length integral reduces to

$\displaystyle\int_0^{8\pi}\sqrt{5-4\cos t}\,\mathrm dt$

which has an approximate value of 53.4596.

8 0

3 years ago

The function f(x)=2x+1 is defined over the interval [2, 5]. If the interval is divided into n equal parts, what is the value of

vodomira [7]

Answer:

D. 5 +6k/n

Step-by-step explanation:

The width of the interval is (5 -2) = 3. The width of one of n parts of it will be ...

3/n

Then the difference between the left end point of the interval and the value of x at the right end of the k-th rectangle will be ...

k·(3/n) = 3k/n

So, the value of x at that point is that difference added to the interval's left end:

2 + 3k/n

The value of the function for this value of x is ...

f(2 +3k/n) = 2(2 +3k/n) +1 = (4 +6k/n) +1

= 5 +6k/n

4 0

3 years ago

On his way to work, a man notices that 9 of the 16 traffic lights are green. Is there statistical significance to say that these

olasank [31]

Yes because the results are unlikely to occur by chance, is what I think .

6 0

3 years ago

Read 2 more answers

map of a city uses the scale 1 cm equals 50 m. On the map, South Street is 25 cm long. If there is a traffic cone at the start

aivan3 [116]

Answer:

125 traffic cones

Step-by-step explanation:

In order to find the total number of meters, we can set up a proportion to find based on the ration of cm to m:

$\frac{centimeters}{meters}=\frac{1}{50}=\frac{25}{x}$ , where 'x' is the number of meters

cross-multiply: x = 25(50) or x = 1250 m

Since there is a cone every 10 m, we can divide the total number of meters by 10:

1250/10 = 125 cones

4 0

3 years ago

The hypotenuse of a right triangle is 25 cm, and the shorter leg is 15 cm. Find the length of the other leg.

nataly862011 [7]

Use the Pythagorean theorem

a^2 + b^2 = c^2

a^2 + 15^2 = 25^2

a^2 + 225 = 625

a^2 = 400

a = 20

Answer: 20 cm

Hope this helps!!

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5 0

3 years ago

Can you help me please with this proof ? thank you!!​

Can you help me please with this proof ? thank you!!