What is the length of the hypotenuse
2 answers:
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Answer:
2 ( e^3 + 1 )
Step-by-step explanation:
The path of the attached Rectangle is anti-clockwise
and the Integrand: P( x, y ) dx + q ( x , y ) dy
P( x, y ) = ye^x
q ( x , y ) = 2ex
hence : dq/dx - dp/dy = 2e^x - e^x = e^x
attached below is the remaining solution
using Green's theorem
Answer:
Step-by-step explanation:
<u>Regular Hexagon</u>
For the explanation of the answer, please refer to the image below. Let's analyze the triangle shown inside of the hexagon. It's a right triangle with sides x,y, and z.
We know that x is half the length of the side length of the hexagon. Thus
Note that this triangle repeats itself 12 times into the shape of the hexagon. The internal angle of the triangle is one-twelfth of the complete rotation angle, i.e.
Now we have , the height of the triangle y is easily found by
Solving for y
The value of z can be found by using
The area of the triangle is
The area of the hexagon is 12 times the area of the triangle, thus
