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11Alexandr11 [23.1K]
3 years ago
6

Please help me :) i will give you brainliest :)

Mathematics
1 answer:
Sophie [7]3 years ago
5 0

Answer:

answer is last number....

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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
3 years ago
A rectangular picture has dimensions 2½ by 1½. It is to be enlarged so that it is still similar to the original rectangle. If th
S_A_V [24]
Original Perimeter = 2.5 + 2.5 + 1.5 + 1.5 = 8
The longer dimension is 2.5 as 2.5 > 1.5To make 2.5 into 10, we must multiply by 4For the smaller length, we must also multiply by 41.5 x 4 = 6
New Perimeter = 10 + 10 + 6 + 6 = 32
Now find the difference between the old and the new perimeter32 - 8 = 24

<em>*No units were specified - if included, remember to put them in your answer.</em>
4 0
3 years ago
Read 2 more answers
Which numerical descriptive measure shows whether two numerical variables have a linear relationship
Brrunno [24]

Answer:

Correlation Coefficient

Step-by-step explanation:

Correlation Coefficient: The correlation coefficient is a numerical measure that measures the strength and direction of a linear relationship between two quantitative variables.

3 0
2 years ago
Camille uses 7.9 pints of blue paint and white paint to paint her bedroom walls. 1/4 of this amount is blue paint, and the rest
Mila [183]
First you do 7.9/ 1/4, that gets you 1.975. that is how much blue paint there is. Then you do 7.9-1.975= 5.925, which is how much white paint she used. So in total she used 1.975 pints of blue paint, and 5.925 pints of white paint.
7 0
3 years ago
What is 8/10 divided by 1 5/6
yulyashka [42]
The answer is <span>0.43 that is what i got</span>
7 0
3 years ago
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