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aleksklad [387]
3 years ago
7

What is the value of x?

Mathematics
1 answer:
melisa1 [442]3 years ago
3 0

Answer:

x=71

Step-by-step explanation:

38+x+x=180

x+x=142

2x=142

x=71

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F=(2xy +z³)i + x³j + 3xz²k find a scalar potential and work done in moving an object in the field from (1,-2,1) to (3,1,4)​
Alex73 [517]

Step-by-step explanation:

Given:

\textbf{F} = (2xy + z^3)\hat{\textbf{i}} + x^3\hat{\textbf{j}} + 3xz^2\hat{\textbf{k}}

This field will have a scalar potential \varphi if it satisfies the condition \nabla \times \textbf{F}=0. While the first x- and y- components of \nabla \times \textbf{F} are satisfied, the z-component doesn't.

(\nabla \times \textbf{F})_z = \left(\dfrac{\partial F_y}{\partial x} - \dfrac{\partial F_x}{\partial y} \right)

\:\:\:\:\:\:\:\:\: = 3x^2 - 2x \ne 0

Therefore the field is nonconservative so it has no scalar potential. We can still calculate the work done by defining the position vector \vec{\textbf{r}} as

\vec{\textbf{r}} = x \hat{\textbf{i}} + y \hat{\textbf{j}} + z \hat{\textbf{k}}

and its differential is

\textbf{d} \vec{\textbf{r}} = dx \hat{\textbf{i}} + dy \hat{\textbf{j}} + dz \hat{\textbf{k}}

The work done then is given by

\displaystyle \oint_c \vec{\textbf{F}} • \textbf{d} \vec{\textbf{r}} = \int ((2xy + z^3)\hat{\textbf{i}} + x^3\hat{\textbf{j}} + 3xz^2\hat{\textbf{k}}) • (dx \hat{\textbf{i}} + dy \hat{\textbf{j}} + dz \hat{\textbf{k}})

\displaystyle = (x^2y + xz^3) + x^3y + xz^3|_{(1, -2, 1)}^{(3, 1, 4)}

= 422

5 0
3 years ago
49 / 80 Marks
Sergio039 [100]

Answer:

What is this...?

Step-by-step explanation:

3 0
3 years ago
Find the slope and reduce.<br> P=(-3, 3) Q=(1, 3)<br> Slope =
Sindrei [870]

Answer:

Slope is 0.

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8 0
1 year ago
I need help asap! <br> What is <br> -3^6-2<br> -3^6-1<br> -3^6-0<br> -3^6+1<br> -3^6+2
MakcuM [25]

Answer:

3^6-2  = 727

3^6-1  = 728

3^6-0  = 729

3^6+1  = 730

3^6+2 = 731

Step-by-step explanation:

4 0
3 years ago
Does doubling the radius of a sphere double the surface area? Explain your reasoning using an example.
Annette [7]

Answer:

yes

Step-by-step explanation:

because area of sphere equals =

4\pi \: r{2}

so if we doubled the radius the surface area will be doubled

5 0
3 years ago
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