Diverse opinions are necessary becuase if you have a small group of people who agree on all of the same things, then you won't get different perspectives and typically things will go unchanged if they don't think of the problem as something that affects them.

Hope this helps!

3 0

2 years ago

Read 2 more answers

Use midpoints to approxiamte the area under the curve y=f(x) 5 sin(xx)!+ 2.5 cos(4xx) on the interval [0,1] using 10 equal subdi

alisha [4.7K]

Subdividing [0, 1] into 10 equally spaced intervals of length $\Delta x=\frac{1-0}{10}=\frac1{10}$ gives the partition

$[0,1] = \left[0,\dfrac1{10}\right] \cup \left[\dfrac1{10},\dfrac2{10}\right] \cup \cdots \cup \left[\dfrac9{10},1\right]$

The $i$ -th subinterval has left and right endpoints, respectively, given by

$\ell_i = \dfrac{i-1}{10} \text{ and } r_i = \dfrac i{10}$

where $i\in\{1,2,3,\ldots,10\}$ .

The midpoint of the $i$ -th interval is the average of these,

$m_i = \dfrac{\ell_i+r_i}2 = \dfrac{2i-1}{20} \in \left\{\dfrac1{20},\dfrac3{20},\dfrac5{20},\ldots,\dfrac{19}{20}\right\}$

We approximate the area under $f(x)$ over [0, 1] by the Riemann sum,

$\displaystyle \int_0^1 f(x) \, dx \approx \sum_{i=1}^{10} f(m_i) \Delta x \\\\ ~~~~~~~~ = \frac1{10} \sum_{i=1}^{10} \bigg(5\sin(\pi m_i) + 2.5 \cos(4\pi m_i)\bigg) \\\\ ~~~~~~~~ = \frac{\sin\left(\frac\pi{20}\right) + \sin\left(\frac{3\pi}{20}\right) + \cdots + \sin\left(\frac{19\pi}{20}\right)}2 \\\\ ~~~~~~~~~~~~ + \dfrac{\cos\left(\frac\pi5\right) + \cos\left(\frac{3\pi}5\right) + \cdots + \cos\left(\frac{19\pi}5\right)}4 \\\\ ~~~~~~~~ \approx 3.19623$

(D)

6 0

2 years ago

Links will be reported

MariettaO [177]

There are many different accents all over America. For instance, people that live in New York sound a lot different than those who live in California. Same goes to other states around the country.

6 0

2 years ago