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Varvara68 [4.7K]3 years ago

7 0

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Evaluate ∫SF⃗ ⋅dA⃗ , where F⃗ =(bx/a)i⃗ +(ay/b)j⃗ and S is the elliptic cylinder oriented away from the z-axis, and given by x2/

Norma-Jean [14]

Answer:

Therefore surface integral is $\pi(a^2+b^2)c-0-0=\pi(a^2+b^2)c$ .

Step-by-step explanation:

Given function is,

$\vec{F}=\frac{bx}{a}\uvec{i}+\frac{ay}{b}\uvec{j}$

To find,

$\int\int_{S}\vec{F}dS$

where S=A=surfece of elliptic cylinder we have to apply Divergence theorem so that,

$\int\int_{S}\vec{F}dS$

$=\int\int\int_V\nabla.\vec{F}dV$

$=\int\int\int_V(\frac{b}{a}+\frac{a}{b})dV$

$=\frac{a^2+b^2}{ab}\int\int\int_VdV$

$=\frac{a^2+b^2}{ab}\times \textit{Volume of the elliptic cylinder}$

$=\frac{a^2+b^2}{ab}\times \pi ab\times 2c=\pi (a^2+b^2)c$

If unit vector $\cap{n}$ directed in positive (outward) direction then z=c and,

$\int\int_{S_1}\vex{F}.dS_1=\int\int_{S_1} . dA$

$=\int\int_{S_1}.dA=0$

If unit vector $\cap{n}$ directed in negative (inward) direction then z=-c and,

$\int\int_{S_2}\vex{F}.dS_2=\int\int_{S_2}. -dA$

$=\int\int_{S_2}. -dA=0$

Therefore surface integral without unit vector of the surface is,

$\pi(a^2+b^2)c-0-0=\pi(a^2+b^2)c$

5 0

4 years ago

Please help with this 7th grade math I need to pass this test

kari74 [83]

Area of triangle = (1/2) × Base × Height

Area of bigger triangle = (1/2) × 15 cm × 10 cm

Area of bigger triangle = (1/2) × 150 sq. cm

Area of bigger triangle = 75 sq. cm

Similarly,

Area of smaller triangle = (1/2) × 12 cm × 5 cm

Area of smaller triangle = (1/2) × 60 sq. cm

Area of smaller triangle = 30 sq. cm

Area of shaded region = Area of bigger triangle - Area of smaller triangle

Area of shaded region = 75 sq. cm - 30 sq. cm

Area of shaded region = 45 sq. cm

Answer :

Area of shaded region in sq. cm = 45

7 0

3 years ago

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Which relationship between x and y in the equation shows a proportional relationship?

Alecsey [184]

C is the answer hope I had enjoy doing boring homework like I did

Well I actually didn't :/

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3 years ago

In the diagram below,point O is the center of the given circle.

Minchanka [31]

Yeah you right, it is the center of the given circle

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3 years ago

“twenty-eight plus the product of five and a number”

svlad2 [7]

Answer: A

Step-by-step explanation:

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3 years ago