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3 years ago

9

You hand in 2 homework pages to your teacher. Your teacher now has 32 homework pages to grade. Find the number of homework pages

that your teacher originally had to grade.

2 answers:

vredina [299]3 years ago

8 0

Answer:

i am guessing she originally had to gade 30 but you decided to turn work in

natulia [17]3 years ago

8 0

Answer:

30

Step-by-step explanation:

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Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n.

Otrada [13]

I guess the "5" is supposed to represent the integral sign?

$I=\displaystyle\int_1^4\ln t\,\mathrm dt$

With $n=10$ subintervals, we split up the domain of integration as

[1, 13/10], [13/10, 8/5], [8/5, 19/10], ... , [37/10, 4]

For each rule, it will help to have a sequence that determines the end points of each subinterval. This is easily, since they form arithmetic sequences. Left endpoints are generated according to

$\ell_i=1+\dfrac{3(i-1)}{10}$

and right endpoints are given by

$r_i=1+\dfrac{3i}{10}$

where $1\le i\le10$ .

a. For the trapezoidal rule, we approximate the area under the curve over each subinterval with the area of a trapezoid with "height" equal to the length of each subinterval, $\dfrac{4-1}{10}=\dfrac3{10}$ , and "bases" equal to the values of $\ln t$ at both endpoints of each subinterval. The area of the trapezoid over the $i$ -th subinterval is

$\dfrac{\ln\ell_i+\ln r_i}2\dfrac3{10}=\dfrac3{20}\ln(ell_ir_i)$

Then the integral is approximately

$I\approx\displaystyle\sum_{i=1}^{10}\frac3{20}\ln(\ell_ir_i)\approx\boxed{2.540}$

b. For the midpoint rule, we take the rectangle over each subinterval with base length equal to the length of each subinterval and height equal to the value of $\ln t$ at the average of the subinterval's endpoints, $\dfrac{\ell_i+r_i}2$ . The area of the rectangle over the $i$ -th subinterval is then

$\ln\left(\dfrac{\ell_i+r_i}2\right)\dfrac3{10}$

so the integral is approximately

$I\approx\displaystyle\sum_{i=1}^{10}\frac3{10}\ln\left(\dfrac{\ell_i+r_i}2\right)\approx\boxed{2.548}$

c. For Simpson's rule, we find a quadratic interpolation of $\ln t$ over each subinterval given by

$P(t_i)=\ln\ell_i\dfrac{(t-m_i)(t-r_i)}{(\ell_i-m_i)(\ell_i-r_i)}+\ln m_i\dfrac{(t-\ell_i)(t-r_i)}{(m_i-\ell_i)(m_i-r_i)}+\ln r_i\dfrac{(t-\ell_i)(t-m_i)}{(r_i-\ell_i)(r_i-m_i)}$

where $m_i$ is the midpoint of the $i$ -th subinterval,

$m_i=\dfrac{\ell_i+r_i}2$

Then the integral $I$ is equal to the sum of the integrals of each interpolation over the corresponding $i$ -th subinterval.

$I\approx\displaystyle\sum_{i=1}^{10}\int_{\ell_i}^{r_i}P(t_i)\,\mathrm dt$

It's easy to show that

$\displaystyle\int_{\ell_i}^{r_i}P(t_i)\,\mathrm dt=\frac{r_i-\ell_i}6(\ln\ell_i+4\ln m_i+\ln r_i)$

so that the value of the overall integral is approximately

$I\approx\displaystyle\sum_{i=1}^{10}\frac{r_i-\ell_i}6(\ln\ell_i+4\ln m_i+\ln r_i)\approx\boxed{2.545}$

4 0

3 years ago

Determine the slope of the table

AURORKA [14]

Answer:

The slope is -1/2 or -0.5

Hope this helps!

5 0

2 years ago

Read 2 more answers

The current of a river is 4 miles per hour. A boat travels to a point 30 miles upstream and back in 4 hours. What is the speed o

Maurinko [17]

16 mph is the answer I found after doing the work

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2 years ago

Un estanque tiene 13/2 litros de leche y se le agregan 87/10. ¿Cuánta leche quedó en el estanque? ¿Sí en el estanque caben 65/4

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2 years ago

Compare the doubling times found with the approximate and exact doubling time formulas. Then use the exact doubling time formula

g100num [7]

The population after 15 years become according to the doubling time is 470000000.

According to the statement

We have given that the nation of 200 million people is growing at a rate of 9% per year.And we have to find that the What will its population be in 15 years.

So, For this purpose, we know that the

The doubling time is the time it takes for a population to double in size/value. It is applied to population growth etc.

So,

Population of nation is 200 million and growing at a rate of 9% per year.

So, 9% of the population is

Percentage population = 9/100*200,000,000

Percentage population = 9* 200,000,0

Percentage population = 1800,000,0.

It means 18000000 number of population is increased per year.

So, The total population increased in 15 years is 15*18000000

The total population increased in 15 years is 270000000.

The population after 15 years is 270000000 + 200,000,000

The population after 15 years is 470000000.

So, The population after 15 years become according to the doubling time is 470000000.

Learn more about doubling time here

brainly.com/question/16407547

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6 0

1 year ago