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Pascal sells fruit from a fruit stand. He starts the day with 80 pounds of fruit. In the morning, 5 customers each buy w pounds

kifflom [539]

An algebraic expression that represents the weight of the fruit that Pascal still has after feeding the birds is 26.7 - 1.7w.

The total pounds of fruit that Pascal has after feeding the birds can be determined by subtracting the sum of the pounds of fruits he sold and the pounds of fruits he uses to feed the birds from the total pounds of fruit he had at the beginning of the day.

Pounds of fruit left = pounds of fruit he had at the beginning of the day - (pounds of fruit he sold + pounds of fruits he used to feed the birds)

Pounds of fruit he sold = 5 x w = 5w pounds

Pounds of fruits he used to feed the birds = $\frac{2}{3}$ × $(80 - 5w)$ = 53.3 - 3.3w

Pounds of fruit left = 80 - (5w + 53.3 - 3.3w)

After combining similar terms, the expression is:

26.7 - 1.7w

A similar question was answered here: brainly.com/question/24007639?referrer=searchResults

5 0

2 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 home alarm system randomly assigns a five-character code for each customer. The code will not repeat a character. The characte

ahrayia [7]

Answer:

The total number of codes which can be assigned is, 55440 .

Step-by-step explanation:

According to the question, the home alarm system randomly assigns a five-character code for each customer.The code will not repeat a character and there are 11 distinct characters.

So, the total number of codes that can be randomly assigned is given by,

$^{11}{P}_{5}$