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3 years ago

12

A cross section of a rectangular pyramid is made perpendicular to the base and through the vertex as shown. What is the area of

the cross section?

1 answer:

Dima020 [189]3 years ago

5 0

Answer:

20 cm²

Step-by-step explanation:

1/2 ( 5 x 8 ) = 1/2 ( 40 ) = 20

If my answer is incorrect, pls correct me!

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-Chetan K

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Now, lets evaluate the same integral using power series. first, find the power series for the function f(x = \frac{32}{x^2+4}. t

BlackZzzverrR [31]

No idea what the previous part of the problem is, but you have

$f(x)=\dfrac{32}{x^2+4}=\dfrac8{1-\left(-\frac{x^2}4\right)}=\displaystyle8\sum_{n\ge0}\left(-\frac{x^2}4\right)^n$
$f(x)=\displaystyle8\sum_{n\ge0}\left(-\dfrac14\right)^nx^{2n}$

which is valid for $\left|-\dfrac{x^2}4\right|$ , or $|x|$ . So the integral from 0 to 2 is

$\displaystyle\int_0^2f(x)\,\mathrm dx=\int_0^28\sum_{n\ge0}\left(-\frac14\right)^nx^{2n}\,\mathrm dx$
$=\displaystyle8\sum_{n\ge0}\left(-\frac14\right)^n\int_0^2x^{2n}\,\mathrm dx$

Note that since the power series only converges on the interval if $x$ is strictly less than 2, which means we have to treat this as an improper integral.

$=\displaystyle8\sum_{n\ge0}\left(-\frac14\right)^n\lim_{t\to2^-}\int_0^tx^{2n}\,\mathrm dx$ [/tex]
$=\displaystyle8\sum_{n\ge0}\left(-\frac14\right)^n\lim_{t\to2^-}\frac{x^{2n+1}}{2n+1}\bigg|_{x=0}^{x=t}$
$=\displaystyle8\sum_{n\ge0}\frac{(-1)^n}{2^{2n}(2n+1)}\lim_{t\to2^-}t^{2n+1}$
$=\displaystyle16\sum_{n\ge0}\frac{(-1)^n}{2n+1}$
$=16-\dfrac{16}3+\dfrac{16}5-\dfrac{16}7+\dfrac{16}9+\cdots$

6 0

3 years ago

Hi doe s anyone know the answer

Svetlanka [38]

Answer:

<u>Regular Polygon:</u>

<em>C, E </em>(All sides and angles are equal)

<u>Irregular Polygon:</u>

<em>A, B, </em>(Not all sides or angles are equal)

<u>Not a Polygon</u>

<em>E, F </em>(There are curves and not a closed shape)

Hope this helps! Comment if you have any questions :)

<em />

5 0

3 years ago

Read 2 more answers

Write 0.2 as a fraction in simplest form.

vredina [299]

Answer:

1/5

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Janette has 386 pennies. 58 nickels and 19 dimes If Janette exchanges her coins for dollars, how many dollars will she have? Ho

svet-max [94.6K]

Answer:

$8 ; 66 cents

Step-by-step explanation:

Given that:

Worth of penny, dimes and Nickel in cents and dollars

Nickel, n = 5 cents = $0.05

Dimes, d = 10 cent = $0.1

Penny, p = 1 cent = $0.01

Multiplying the number of each coin with its respective value ;

386(0.01) + 58(0.05) + 19(0.1)

$3.86 + $2.9 + $1.9

= $8.66

Changing it to dollar ,

$8.66 dollars = 8 dollars ;

$0.66 = 66 cents

6 0

3 years ago

In a quadrilateral ABCD, AB ∥ DC and AD ∥ BC . Find the perimeter of ΔCOD if the diagonals of the quadrilateral intersect each o

SVEN [57.7K]

Answer Perimeter = 33in

Step-by-step explanation:

AC = 20

BD = 20

AB = 13

O is the midpoint

OD = OC = 20/2 = 10

AB = DC = 13 in

P = DC + OD + OC = 13+10+10 = 33in

5 0

3 years ago