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Vinil7 [7]
2 years ago
14

9. Shawn wants to make the perimeter of the

Mathematics
1 answer:
Vesna [10]2 years ago
7 0

Answer:

Scale factor of 2.5

Step-by-step explanation:

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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
Evaluate the expression when x = 9.<br>x + 5(x + 2)​
jasenka [17]

Answer:

64

Step-by-step explanation:

x + 5(x + 2)​

Distribute

x + 5x+10

Combine like terms

6x+10

Let x = 9

6(9) +10

54+10

64

8 0
3 years ago
Read 2 more answers
Mary's weight went from 80kg to 68kg. express her weight loss as a % of her original weight
Ratling [72]

80-68=12

12/80=0.12


12% is the answer

6 0
3 years ago
Marcy had 567 earmuffs in stock. If she can put 18 earmuffs on each shelf, about how many shelves does she need for all the earm
spin [16.1K]

567 / 18 = 31.5

But because she can't make half a shelf, the answer would be 32 shelves

5 0
3 years ago
Three moons are in the same circular orbit around a planet. The moons are each 115,000 kilometers from the surface of the planet
marshall27 [118]
275,000 km
The moons A, B, C form a right triangle with AC forming a hypotenuse with the diameter of the planet and the distance of both moons from the surface. So add A to the surface, plus the diameter of the planet, plus surface to c.
115000+45000+115000 = 275000
7 0
3 years ago
Read 2 more answers
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