The value of the given surface integral is 4.
The given plane intercepts the coordinate axes at (2, 0, 0), (0, 2, 0), and (4, 0, 0). These point are the coordinates of a triangular region that we can parameterize using.
<h3>What is the surface integral?</h3>
A surface integral is a generalization of multiple integrals to integration over surfaces. It can be thought of as the double integral analog of the line integral. Given a surface, one may integrate a scalar field over the surface or a vector field.
with 0≤u≤1 and 0≤v≤1. Then the surface element ds is equivalent to
The surface integral is then
Therefore the value of the given surface integral is 4.
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Answer:
C
Step-by-step explanation:
cot =cos/sin =a/b
cos=a/b*sin
(sin-cos)/(sin+cos) =(sin-sin*a/b)(sin+sin*a/b)
=(1-a/b)/(a+a/b)
=(b-a)/(a+b)
Answer:
Converges, 57.6
Step-by-step explanation:
48, 8, 4/3, 2/9...
ratio = 8/48 = 1/6
A sequence converged if the ratio is between -1 and 1.
So, this sequence converges
Limit = a/(1-r)
Where a is the first term, and r is the common ratio
Limit = 48/[1 - (1/6)]
= 48/[5/6]
= 48 × 6/5
= 57.6
Answer:
{- 11, - 1 }
Step-by-step explanation:
Since the coefficient of the x² term is 1 , to complete the square
add (half the coefficient of the x-term )² to both sides
x² + 2(6)x + 36 = - 11 + 36 ← complete the square on the left side
(x + 6)² = 25 ( take the square root of both sides
= ± 
x + 6 = ± 5 ( subtract 6 from both sides )
x = - 6 ± 5
x = - 6 + 5 = - 1 or x = - 6 - 5 = - 11
Answer:
Therefore the equation of the line through ( 4 , -8 ) and ( 8 , 5 ) is
13x - 4y = 84.
Step-by-step explanation:
Given:
Let,
point A( x₁ , y₁) ≡ ( 4 ,-8)
point B( x₂ , y₂) ≡ (8 , 5)
To Find:
Equation of Line AB =?
Solution:
Equation of a line passing through Two points A( x₁ , y₁) and B( x₂ , y₂)is given by the formula
Substituting the given values in a above equation we get
Therefore the equation of the line through ( 4 , -8 ) and ( 8 , 5 ) is
13x - 4y = 84.
