HELP ASAP PLEASE!!

Mathematics

1 answer:

Korolek [52]2 years ago

3 0

Answer:

you can check on a website called "desmos graphing."

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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 C ) 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

2 years ago

How do you answer this question.

Ipatiy [6.2K]

Lets write this out:-

$\frac{50}{100} + \frac{30}{100}$

To answer this we just need to add the numerators of both fractions because the denominator's are already common multiples.

$\frac{50}{100}+ \frac{30}{100} = \frac{80}{100}$

Now lets simplify $\frac{80}{100}$ .

$\frac{80/20}{100/20}= \frac{4}{5}$

So, $\frac{50}{100}+ \frac{30}{100} = \frac{80}{100}= \frac{4}{5}$

Hope I helped ya!! xD

8 0

2 years ago

Read 2 more answers

The inequality of the graph

fiasKO [112]

Answer:

$\displaystyle y > 4x - 2$

Step-by-step explanation:

Starting from the y-intercept of $\displaystyle [0, -2],$ you do $\displaystyle \frac{rise}{run}$ by either moving four blocks south over one block west or four blocks north over one block east [west and south are negatives]. Next, we have to determine the types of inequality symbols that are suitable for this graph, which will be less than and greater than since this is a dashed line graph. We then use the zero-interval test [test point (0, 0)] to ensure whether we shade the opposite portion [portion that does not contain the origin] or the portion that DOES contain the origin. At this step, we must verify the inequalities as false or true: