What is the area of this quadrilateral? 2 ft 3 ft 8 ft 8 ft 3 ft 2 ft

Express your answer as a polynomial in a standard form.

Andrej [43]

Here you go! Hope this helps!

7 0

3 years ago

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

A manufacturer has cube shaped cardboard boxes with an exact volume of 12000 cubic inches. What is the volum of the largest sphe

vladimir1956 [14]

Answer:

6283 in³

Step-by-step explanation:

The largest sphere that can fit into the cardboard box must have its diameter, d equal to the length, L of the cardboard box.

Since the cardboard box is in the shape of a cube, its volume V = L³

So, L = ∛V

Since V = 12000 in³,

L = ∛(12000 in³)

L= 22.89 in

So, the volume of the sphere, V' = 4πr³/3 where r = radius of cube = L/2

So, V = 4π(L/2)³/3

= 4πL³/8 × 3

= πL³/2 × 3

= πL³/6

= πV/6

= π12000/6

= 2000π

= 6283.19 in³

≅ 6283.2 in³

= 6283 in³ to the nearest whole cubic inch

6 0

3 years ago

What is 4.409 rounded to the nearest penny

andre [41]

4.41 because .409 rounds up to .41,

8 0

3 years ago

Read 2 more answers

Will Mark Brainlest helppp plss

bearhunter [10]

Answer:

? hey your question is not full at all

7 0

3 years ago