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

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

Stephanie wants to buy 6 pencils case at a cost of $0.99 each.How many will the 6 pencils cases cost altogether

levacccp [35]

6 pencil cases would cost $5.94.

You can create an expression to represent the scenario.

6×$0.99

=$5.94 for 6 pencil cases

6 0

3 years ago

Read 2 more answers

Please help me with the screenshot question

crimeas [40]

Answer:

owner withdrawal

1.225000

2.3300

4 0

2 years ago

5. Lines p and q are parallel, and line w is a transversal. Which angle is not congruent to angle 1?

Tamiku [17]

Answer:

∠2, ∠4, ∠6 and ∠8 are not congruent to ∠1.

Step-by-step explanation:

From the picture attached,

p and q are the parallel lines and w is a transversal.

∠1 ≅ ∠3 [Vertically opposite angles]

∠1 ≅ ∠5 [Corresponding angles]

∠1 ≅ ∠7 [Alternate exterior angles]

Therefore, ∠2, ∠4, ∠6 and ∠8 are not congruent to ∠1.

3 0

3 years ago