Answer:
Step-by-step explanation:
hello :
cot x + 2cot x sin x = 0 0≤ x≤ 180
cotx(1+2sinx) =0 means : cotx=0 or 1+2sinx=0
1) cotx=0 so : cosx=0 and sinx ≠ 0 because cotx = cosx/sinx
when : 0≤ x≤ 180 : x=90°
2) 1+2sinx=0 means : sinx = -1/2
when : 0≤ x≤ 180 : no solutions because : sinx ≥ 0
conclusion : one solution : x=90°
The area of the surface is 144.708
The equation of the given surface is,
z=g(x,y)=xy
Solving the partial derivatives,
∂g∂x=y,∂g∂y=x
Substituting to the formula
S=∬√1+( ∂g∂x)2+(∂g∂y)2dA
Thus,
S=∬√1+(y)2+(x)2dAS=∬√1+x2+y2dA
The region in the XY-plane is defined by the intervals 0≤θ≤2π,0≤r≤4
Converting the integral into polar coordinates,
S=∫2π0∫40√1+r2rdrdθ
Integrating with respect to r
S=∫2π0[13(1+r2)32]40dθ
S=∫2π0(17√173−13)dθ
Integrating with respect to θ
S=(17√173−13)[θ]2π0
S≈144.708
For more information about areas, visit
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If there are fractions, eliminate them using the right methods. Then gather x and y terms on one side, and the rest on the other side. Simplify.
Aloha~! My name is Zalgo and I am here to provide a bit more knowledge to you today. The following Improper Fractions have been changed into Mixed Numbers (and also into decimals because I like Math :3):
- 9/4 - 2.25 - 2 4/1
- 8/3 - 2.67 - 2 2/3
- 23/6 - 3.83 - 3 5/6
- 11/2 - 5.5 - 5 1/2
- 17/5 - 3.4 - 3 2/5
- 15/8 - 1.875 - 1 7/8
- 33/10 - 3.3 - 3 3/10
- 29/12 - 2.416 - 2 5/12
I hope that this info helps! :D
"Stay Brainly and stay proud!" - Zalgo
(By the way, can you mark me as Brainliest? I'd greatly appreciate it! Mahalo~! XP)
Answer:
2.
Step-by-step explanation:
1+1=2