which figures do not have lateral area?

Use Simpson's Rule with n = 10 to estimate the arc length of the curve. Compare your answer with the value of the integral produ

SOVA2 [1]

$y=\ln(6+x^3)\implies y'=\dfrac{3x^2}{6+x^3}$

The arc length of the curve is

$\displaystyle\int_0^5\sqrt{1+\frac{9x^4}{(6+x^3)^2}}\,\mathrm dx$

which has a value of about 5.99086.

Let $f(x)=\sqrt{1+\frac{9x^4}{(6+x^3)^2}}$ . Split up the interval of integration into 10 subintervals,

[0, 1/2], [1/2, 1], [1, 3/2], ..., [9/2, 5]

The left and right endpoints are given respectively by the sequences,

$\ell_i=\dfrac{i-1}2$

$r_i=\dfrac i2$

with $1\le i\le10$ .

These subintervals have midpoints given by

$m_i=\dfrac{\ell_i+r_i}2=\dfrac{2i-1}4$

Over each subinterval, we approximate $f(x)$ with the quadratic polynomial

$p_i(x)=f(\ell_i)\dfrac{(x-m_i)(x-r_i)}{(\ell_i-m_i)(\ell_i-r_i)}+f(m_i)\dfrac{(x-\ell_i)(x-r_i)}{(m_i-\ell_i)(m_i-r_i)}+f(r_i)\dfrac{(x-\ell_i)(x-m_i)}{(r_i-\ell_i)(r_i-m_i)}$

so that the integral we want to find can be estimated as

$\displaystyle\sum_{i=1}^{10}\int_{\ell_i}^{r_i}p_i(x)\,\mathrm dx$

It turns out that

$\displaystyle\int_{\ell_i}^{r_i}p_i(x)\,\mathrm dx=\frac{f(\ell_i)+4f(m_i)+f(r_i)}6$

so that the arc length is approximately

$\displaystyle\sum_{i=1}^{10}\frac{f(\ell_i)+4f(m_i)+f(r_i)}6\approx5.99086$

5 0

2 years ago

A clinical test on humans of a new drug is normally done in three phases. Phase I is conducted with a relatively small number of

navik [9.2K]

Answer:

A clinical test on humans of a new drug is normally done in three phases. Phase I is conducted with a relatively small number of healthy volunteers. For example, a phase I test of a specific drug involved only 7 subjects.

Step-by-step explanation:

6 0

2 years ago

Shari walks 5 blocks to school each morning.The walk takes 10 minutes

olga2289 [7]

Answer:
If she walks 5 blocks and it takes 10 minutes each block takes 2 minutes to walk.

10
— = 2 So 2 minutes per block
5

4 0

2 years ago

I set a goal to drink 64 ounces of water day.If i drink 10 1/3 ounces in the morning,15 1/2 ounces at noon,and 20 5/6 at dinner

Vedmedyk [2.9K]

First find how much you've had. Make the fractions with similar denominaters: 1/3(2)=2/6, 1/2(3)=3/6, 5/6(1)=5/6. Now add the fractions: 2/6+3/6+5/6=10/6 or 1 4/6 or 1 2/3. Then add the whole numbers: 10+15+20+1=46. So you've had 46 2/3 oz now subtract that from how much you need: 64-46 2/3= 63 3/3-46 2/3=17 1/3. You still need 17 1/3 water :)

6 0

1 year ago

If x is the midpoint of ZW, then ZX=XW

sasho [114]

Answer:

True.

Step-by-step explanation:

By definition of a mid point, it is located in the middle of two connected points. This means that the split is equal on both sides.

IF X is the midpoint of ZW, then ZX = XW.

~

4 0

2 years ago

￼which figures do not have lateral area?

which figures do not have lateral area?