Careful; (dy/dx)^2 = x^2 cos^2(x) + 2x sin x cos x + sin^2(x).
<span>So, the arc length equals </span>
<span>∫(x = 0 to 2π) √[1 + (x^2 cos^2(x) + 2x sin x cos x + sin^2(x))] dx </span>
<span>= ∫(x = 0 to 2π) √[1 + x^2 cos^2(x) + x sin(2x) + sin^2(x)] dx, via double angle identity. </span>
<span>Let Δx = (2π - 0)/10 = π/5. </span>
<span>Using Simpson's Rule with n = 10, this integral approximately equals </span>
<span>((π/5)/3) * [f(0) + 4 f(π/5) + 2 f(2π/5) + 4 f(3π/5) + 2 f(4π/5) + 4 f(π) + 2 f(6π/5) + 4 f(7π/5) + 2 f(8π/5) + 4 f(9π/5) + f(2π)], </span>
<span>where f(x) = √[1 + x^2 cos^2(x) + x sin(2x) + sin^2(x)]. </span>
<span>------- </span>
<span>I hope this helps!</span>
3% = 3/100 = 0,03
When it's compount interest it's 1,03 because you gain 3% more from what you already have.
All you need to do
1,03•2000=2060$ for the first year
And then for the second year, you take the actual amount after one year of 3%
1,03•2060=2121,8
After two years, there will be 2121,8$
9514 1404 393
Answer:
(a) 5/6
Step-by-step explanation:
Positive numbers are greater than negative ones.
Fractions with the same denominator are greater if their numerator is greater.
All of these fractions have the same denominator. Because 5 > 1 > -1 > -5, the ordering of the fractions is ...
5/6 > 1/6 > -1/6 > -5/6
The fraction with the greatest value is 5/6.
Answer:
<em>7*6543=45801</em>
Step-by-step explanation:
We have the digits 34567 and must arrange them into a product with the largest possible value.
It's clear that we must place the largest digits to the left, so they represent larger numbers to multiply.
Let's try with:
7654*3=22962
765*43=32895
76*543=41268
7*6543=45801
This last combination definitely produces the largest product
Answer: 7*6543=45801
