Please help me with this

An area is approximated to be 14 in 2 using a left-endpoint rectangle approximation method. A right- endpoint approximation of t

USPshnik [31]

The trapezoidal approximation will be the average of the left- and right-endpoint approximations.

Let's consider a simple example of estimating the value of a general definite integral,

$\displaystyle\int_a^bf(x)\,\mathrm dx$

Split up the interval $[a,b]$ into $n$ equal subintervals,

$[x_0,x_1]\cup[x_1,x_2]\cup\cdots\cup[x_{n-2},x_{n-1}]\cup[x_{n-1},x_n]$

where $a=x_0$ and $b=x_n$ . Each subinterval has measure (width) $\dfrac{a-b}n$ .

Now denote the left- and right-endpoint approximations by $L$ and $R$ , respectively. The left-endpoint approximation consists of rectangles whose heights are determined by the left-endpoints of each subinterval. These are $\{x_0,x_1,\cdots,x_{n-1}\}$ . Meanwhile, the right-endpoint approximation involves rectangles with heights determined by the right endpoints, $\{x_1,x_2,\cdots,x_n\}$ .

So, you have

$L=\dfrac{b-a}n\left(f(x_0)+f(x_1)+\cdots+f(x_{n-2})+f(x_{n-1})\right)$
$R=\dfrac{b-a}n\left(f(x_1)+f(x_2)+\cdots+f(x_{n-1})+f(x_n)\right)$

Now let $T$ denote the trapezoidal approximation. The area of each trapezoidal subdivision is given by the product of each subinterval's width and the average of the heights given by the endpoints of each subinterval. That is,

$T=\dfrac{b-a}n\left(\dfrac{f(x_0)+f(x_1)}2+\dfrac{f(x_1)+f(x_2)}2+\cdots+\dfrac{f(x_{n-2})+f(x_{n-1})}2+\dfrac{f(x_{n-1})+f(x_n)}2\right)$

Factoring out $\dfrac12$ and regrouping the terms, you have

$T=\dfrac{b-a}{2n}\left((f(x_0)+f(x_1)+\cdots+f(x_{n-2})+f(x_{n-1}))+(f(x_1)+f(x_2)+\cdots+f(x_{n-1})+f(x_n))\right)$

which is equivalent to

$T=\dfrac12\left(L+R)$

and is the average of $L$ and $R$ .

So the trapezoidal approximation for your problem should be $\dfrac{14+21}2=\dfrac{35}2=17.5\text{ in}^2$

4 0

2 years ago

Which of the following statements best describes the graph of −5x + 2y = 1?

Nina [5.8K]

First, we determine that the given equation in this item is a linear equation. Thus, it should be a straight line. With this, we are left with the third and fourth choice. Then, we substitute the given data points to the equation and see if the points satisfy the given.

Choice 3:

(1,3) : (-5)(1) + (2)(3) = 1 TRUE

(3,8) : (-5)(3) + 2(8) = 1 TRUE

(-3,-7) : (-5)(-3) + (2)(-7) = 1 TRUE

Choice 4:

(4,-3) : (-5)(4) + (2)(-3) ≠ 1 FALSE

(-1,2) : (-5)(-1) + (2)(2) ≠ 1 FALSE

(-4,5) : (-5)(-4) + (2)(5) ≠ 1 FALSE

Thus, the answer is the third choice.

5 0

2 years ago

Read 2 more answers

42 is 64% of what number

steposvetlana [31]

Answer: x = 65.63
Explanation:
We have, 64% × x = 42 or, 64/100 × x = 42
Multiplying both sides by 100 and dividing both sides by 64, we have x = 42 × 100 64
x = 65.63

4 0

2 years ago

Read 2 more answers

Can somebody help me with this plz?!?

fomenos

Answer:

Step-by-step explanation:

The angle is 60 degrees and a whole circle has a total of 360 degrees, of that makes sense. So if you do 360/60, you get 6. This tells you that 6 of those particular arcs fit into this particular circle.

Find the circumference of the circle. You are given the radius, 3. Use the circumference formula, 2(pi)(r). You get 6pi.

6/6 = 1, so the length of that one arc is just p

Hope this helps!.

3 0

2 years ago

3(x + 4) = 27 what is x

Alla [95]

Answer:

x = 5

Step-by-step explanation:

This is a simple equation if you look at it right and don't get scared by the "x."

All we need to do is figure out what times 3 = 27. We can do this easily by diving 27 by 3.

27 ÷ 3 = 9

Since our "equation" is 3(x + 4) = 27 we know whatever is in the parenthesis () has to equal to 9. We already get 4 so:

5 + 4 = 9.

3 times 9 = 27.

5 is your answer.

Hope this helps and have a nice day!

PS if you could mark brainliest that'd be great! I'm very close the "expert" rank. Haha, sorry I usually don't ask.

6 0

2 years ago