All categories

2 years ago

Is this true or false?

Mathematics

1 answer:

marusya05 [52]2 years ago

4 0

Answer:

TRUE

Step-by-step explanation:

You might be interested in

Use Stokes' Theorem to evaluate C F · dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = 2yi + xzj + (x

Lady_Fox [76]

By Stokes' theorem, the line integral of $\vec F$ over $C$ is given by the surface integral of the curl of $\vec F$ over $S$ , where $S$ is the region of intersection of the plane $z=y+6$ and the cylinder $x^2+y^2=1$ with $S$ having positive/upward orientation.

Parameterize $S$ by

$\vec s(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec\jmath+(u\sin v+6)\,\vec k$

with $0\le u\le1$ and $0\le v\le2\pi$ .

Take the normal vector to $S$ to be

$\vec s_u\times\vec s_v=-u\,\vec\jmath+u\,\vec k$

The curl of $\vec F$ is

$\nabla\times\vec F(x,y,z)=(1-x)\,\vec\imath-\vec\jmath+(z-2)\,\vec k$

Then the line integral is equivalent to

$\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\iint_S(\nabla\times\vec F)\cdot\mathrm d\vec S$

$=\displaystyle\int_0^{2\pi}\int_0^1\bigg((1-u\cos v)\,\vec\imath-\vec\jmath+(u\sin v+4)\,\vec k\bigg)\cdot\bigg(-u\,\vec\jmath+u\,\vec k\bigg)\,\mathrm du\,\mathrm dv$

$=\displaystyle\int_0^{2\pi}\int_0^1(5u+u^2\sin v)\,\mathrm du\,\mathrm dv=\boxed{5\pi}$

4 0

2 years ago

Solve this equation: 2s + s + 12 = 132. a. s = 9 B. s = –30 C. s = 120 D. s = 40

madam [21]

The equation given in the question is
2s + s + 12 = 132
3s + 12 = 132
3s = 132 - 12
3s = 120
s = 120/3
= 40
From the above deduction we can see that the value of the unknown variable comes out to be exactly 40. This is possible because there is a single unknown variable and a single equation to get the value of the variable from. So the correct option among all the options given in the question is option "D".

8 0

2 years ago

Read 2 more answers

5.Solve the quadratic equation.

Dafna1 [17]

Answer:

x=5 twice

Step-by-step explanation:

x^2-10x+25=0

multiply the coefficient of x^2 and the last term

1X25=25

find two numbers you can multiply to get 25 and add to get -10

-5 + (-5)=-10 the middle term

replace -10x with -5x -5x and solve the equation

x^2-5x-5x+25=0

factorise by grouping

x(x-5)-5(x-5)=0

(x-5)(x-5)=0

Either x-5=0,x=5 or x-5=0,x=5

Therefore x=5 twice.

5 0

3 years ago

What is the value of 3x² + 2y3 when x = -4 and y = -2

skad [1K]

Ummmmmmm -26 ......... in

7 0

2 years ago

Read 2 more answers

What are the greatest common factor of 20x76 and 8x92?

adelina 88 [10]

Gcf of 20 time 76 is 4

6 0

2 years ago