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hoa [83]
1 year ago
15

What is the area of a tringe with a base of 16cm and a height of 5ft plus the area of a rectangle with the height of 19cm and wi

dth of 23cm.​
Mathematics
1 answer:
slavikrds [6]1 year ago
6 0
Triangles area is 40 cm^2 and the rectangles area is 437 centimeters squared I assume you mean triangle by the phrase tringe
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Suppose integral [4th root(1/cos^2x - 1)]/sin(2x) dx = A<br>What is the value of the A^2?<br><br>​
Alla [95]

\large \mathbb{PROBLEM:}

\begin{array}{l} \textsf{Suppose }\displaystyle \sf \int \dfrac{\sqrt[4]{\frac{1}{\cos^2 x} - 1}}{\sin 2x}\ dx = A \\ \\ \textsf{What is the value of }\sf A^2? \end{array}

\large \mathbb{SOLUTION:}

\!\!\small \begin{array}{l} \displaystyle \sf A = \int \dfrac{\sqrt[4]{\frac{1}{\cos^2 x} - 1}}{\sin 2x}\ dx \\ \\ \textsf{Simplifying} \\ \\ \displaystyle \sf A = \int \dfrac{\sqrt[4]{\sec^2 x - 1}}{\sin 2x}\ dx \\ \\ \displaystyle \sf A = \int \dfrac{\sqrt[4]{\tan^2 x}}{\sin 2x}\ dx \\ \\ \displaystyle \sf A = \int \dfrac{\sqrt{\tan x}}{\sin 2x}\ dx \\ \\ \displaystyle \sf A = \int \dfrac{\sqrt{\tan x}}{\sin 2x}\cdot \dfrac{\sqrt{\tan x}}{\sqrt{\tan x}}\ dx \\ \\ \displaystyle \sf A = \int \dfrac{\tan x}{\sin 2x\ \sqrt{\tan x}}\ dx \\ \\ \displaystyle \sf A = \int \dfrac{\dfrac{\sin x}{\cos x}}{2\sin x \cos x \sqrt{\tan x}}\ dx\:\:\because {\scriptsize \begin{cases}\:\sf \tan x = \frac{\sin x}{\cos x} \\ \: \sf \sin 2x = 2\sin x \cos x \end{cases}} \\ \\ \displaystyle \sf A = \int \dfrac{\dfrac{1}{\cos^2 x}}{2\sqrt{\tan x}}\ dx \\ \\ \displaystyle \sf A = \int \dfrac{\sec^2 x}{2\sqrt{\tan x}}\ dx, \quad\begin{aligned}\sf let\ u &=\sf \tan x \\ \sf du &=\sf \sec^2 x\ dx \end{aligned} \\ \\ \textsf{The integral becomes} \\ \\ \displaystyle \sf A = \dfrac{1}{2}\int \dfrac{du}{\sqrt{u}} \\ \\ \sf A= \dfrac{1}{2}\cdot \dfrac{u^{-\frac{1}{2} + 1}}{-\frac{1}{2} + 1} + C = \sqrt{u} + C \\ \\ \sf A = \sqrt{\tan x} + C\ or\ \sqrt{|\tan x|} + C\textsf{ for restricted} \\ \qquad\qquad\qquad\qquad\qquad\qquad\quad \textsf{values of x} \\ \\ \therefore \boxed{\sf A^2 = (\sqrt{|\tan x|} + c)^2} \end{array}

\boxed{ \tt   \red{C}arry  \: \red{ O}n \:  \red{L}earning}  \:  \underline{\tt{5/13/22}}

4 0
2 years ago
Find the Mean from the line plot. Show your work and explain how you solved using First, Next, and Last.
Musya8 [376]

Answer:

mean is 5

Step-by-step explanation:

<h2>MEAN</h2>

mean is regarded as the average number of items

<h3>mean formula:</h3>

<em>(sum of terms) / (number of terms)</em>

<h3><u /></h3><h3><u>Firstly</u></h3>

the numbers in the data set are :

3,3,3,4,6,6,7,8

they are already arranged in order, so no need to rearrange.

<h3><u>Next </u></h3>

add the numbers together to find the total :

3 +3 +3 +4 +6+ 6+7 +8

= 40

ALSO,

find how many number of terms they are --- this is 8

Last

use the mean formula to solve :

<em>(sum of terms) / (number of terms)</em>

= 40/8

= 5

<h3><em><u>the mean is the 5 </u></em></h3>
8 0
3 years ago
How many ducks do you see?
tekilochka [14]

Answer:

13

Step-by-step explanation:

count the big ducks first

then go back and count the smaller ones

6 0
3 years ago
If you know how to solve this, Please answer it. Thank You
lara31 [8.8K]

y = ( x + 9 )^2 - 2

................................

................................

8 0
2 years ago
Evaluate the following expression for x = 4. <br><br><br> 1+3(x-1)-2x
xz_007 [3.2K]

Answer:

2

Step-by-step explanation:

1+3(x-1)-2x

Substitute the value of x into the equation:

1 + 3(4-1) -2 (4)

1 + 3(3)- 8

1 + 9 - 8

2

8 0
3 years ago
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