Some can help me please to find the answer please

A video received -16 points and 33 points in one day how many members voted

Amanda [17]

That would be 33+ (-16) so 17 members

5 0

4 years ago

Evaluate the integral Integral from (5 comma 2 comma 4 )to (7 comma 9 comma negative 3 )y dx plus x dy plus 3 dz by finding para

padilas [110]

$\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\int_{(5,2,4)}^{(7,9,-3)}y\,\mathrm dx+x\,\mathrm dy+3\,\mathrm dz$

Parameterize the line segment (call it $C$ ) by

$\vec r(t)=(1-t)(5\,\vec\imath+2\,\vec\jmath+4\,\vec k)+t(7\,\vec\imath+9\,\vec\jmath-3\,\vec k)$

$\vec r(t)=(2t+5)\,\vec\imath+(7t+2)\,\vec\jmath+(4-7t)\,\vec k$

with $0\le t\le1$ . Then

$\vec r'(t)=2\,\vec\imath+7\,\vec\jmath-7\,\vec k$

and the line integral is

$\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\int_0^1((7t+2)\,\vec\imath+(2t+5)\,\vec\jmath+3\,\vec k)\cdot\vec r'(t)\,\mathrm dt$

$=\displaystyle\int_0^1((2t+5)+2(7t+2)-21)\,\mathrm dt$

$=\displaystyle\int_0^1(28t+18)\,\mathrm dt=\boxed{32}$

Alternatively, if we can show that $\vec F$ is conservative, then we can apply the fundamental theorem of calculus. We need to find $f$ such that $\nabla f=\vec F$ , which requires

$\dfrac{\partial f}{\partial x}=y$

$\dfrac{\partial f}{\partial y}=x$

$\dfrac{\partial f}{\partial z}=3$

Integrating both sides of the first equation with respect to $x$ gives

$f(x,y,z)=xy+g(y,z)$

Differentiating both sides wrt $y$ gives

$\dfrac{\partial f}{\partial y}=x=x+\dfrac{\partial g}{\partial y}$

$\implies\dfrac{\partial g}{\partial y}=0\implies g(y,z)=h(z)$

Differentiating wrt $z$ gives

$\dfrac{\partial f}{\partial z}=3=\dfrac{\mathrm dh}{\mathrm dz}$

$\implies h(z)=3z+C$

So we have

$f(x,y,z)=xy+3z+C$

and $\vec F$ is conservative. By the FTC, we find

$\displaystyle\int_C\vec F\cdot\mathrm d\vec r=f(7,9,-3)-f(5,2,4)=\boxed{32}$

5 0

3 years ago

Which of the following statements regarding Pascal's triangle are correct?

tia_tia [17]

Answer:

Option A, C and D are correct.

Step-by-step explanation:

Option A is correct because if we take example of $(x+y)^3$ we get:

1,2,1

1,3,3,1

1,4,6,4,1

So we can see that either we read left to right or right to left we are getting same row

Option B is not correct because When we take power zero it will occupy first row hence, $(x+y)^n$ is not given by nth row.

Option C is correct because adding adjacent terms on a will give us the term directly below look at the example in option A.

Option D is correct because nth row will give coefficients in the expansion of (x + y) n-1 since, zero will occupy first row hence, nth row will be n-1.

5 0

3 years ago

Read 2 more answers

What is the value of the expression 2.6 x 10 to the 9th power over 1.3 x 10 to the 2nd power?

yKpoI14uk [10]

2.6 * 10^9
-------------
1.3 * 10^2

2.6 / 1.3 = 2 and 10^9 / 10^2 = 10^7

so the answer is 2 * 10^7

4 0

4 years ago

I need to know if this is true or false

vlabodo [156]

The answer is "yes"

The expression 4x is the same as 4x^1. It is in the form ax^n where a = 4 is the coefficient and n = 1 is the exponent.

A polynomial can have exactly one term, which is what the case is here.

4 0

3 years ago