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3 years ago

Name the vertex

Mathematics

1 answer:

Dvinal [7]3 years ago

8 0

I need something to work with. like a graph

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Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of

diamong [38]

Parameterize $S$ by

$\vec r(u,v)=u\,\vec\imath+v\,\vec\jmath+(4-u^2-v^2)\,\vec k$

with $0\le u\le1$ and $0\le v\le1$ . Then

$\vec r_u\times\vec r_v=2u\,\vec\imath+2v\,\vec\jmath+\vec k$

In the integral we get

$\displaystyle\iint_S\vec F\cdot\mathrm d\vec S$

$\displaystyle=\int_0^1\int_0^1(uv\,\vec\imath+v(4-u^2-v^2)\,\vec\jmath+u(4-u^2-v^2)\,\vec k)\cdot(2u\,\vec\imath+2v\,\vec\jmath+\vec k)\,\mathrm du\,\mathrm dv$

$\displaystyle=\int_0^1\int_0^1(4u-u^3+2u^2v+8v^2-uv^2-2u^2v^2-2v^4)\,\mathrm du\,\mathrm dv=\frac{713}{180}$

5 0

3 years ago

Solve for y 5(y 4)-7y=8

Naily [24]

The answer is y = - 3

8 0

3 years ago

Given 1+ cos x/ sin x + sin x/1+ cos x= 4, find a numerical value of one trigonometric function of x.

laiz [17]

Answer:

The numerical value of the trigonometric function is 30 °

Step-by-step explanation:

Given trigonometric function as :

$\frac{1 + cos x}{sin x}$ + $\frac{sin x}{1 + cos x}$ = 4

or, Taking LCM we get

$\frac{(1+cosx)^{2}+sin^{2}x}{(sinx)\times (1+cosx)}$ = 4

Or, ( 1 + cos x )² + sin² x = 4 × ( sin x ) × ( 1 + cos x )

1 + cos² x + 2 cox + sin² x = 4 sin x + 4 sin x × cos x

or, ( cos² x + sin² x ) + ( 1 + 2 cos x ) = 4 sin x ( 1 + cos x )

∵ cos² x + sin² x = 1

or, 1 + 1 + 2 cos x = 4 sin x ( 1 + cos x )

or, 2 + 2 cos x = 4 sin x ( 1 + cos x )

or, 2 ( 1 + cos x ) = 4 sin x ( 1 + cos x )

Or, $\frac{2 ( 1+ cos x )}{4 ( 1 + cos x )}$ = sin x

Or, sin x = $\frac{1}{2}$

∴ x = $sin^{-1}\frac{1}{2}$

∵ sin 30 ° = $\frac{1}{2}$

I.e x = 30 °

Hence The numerical value of the trigonometric function is 30 ° answer

3 0

3 years ago

Solve the equation. Then check your solution.

spin [16.1K]

Answer: C. -1 ............

7 0

4 years ago

The area of a square garden is 200 m^2. How long is the diagonal?

Sladkaya [172]

Answer:

b. 20 m

Step-by-step explanation:

Let A represent the area

Let d represent the diagonal

then

$A=\frac{d*d}{2} = \frac{d^{2} }{2}$

Then

d² = 2A

then

$d = \sqrt{2A} =\sqrt{2*200} =\sqrt{400} = 20$

8 0

3 years ago