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2 years ago

Evan is going to invest $2,800 and leave it in an account for 12 years. Assuming the

Mathematics

2 answers:

anyanavicka [17]2 years ago

8 0

Answer:

5000=2000/1 hshshsjsnndjskbdjs

Dominik [7]2 years ago

8 0

Answer:

r = 4.95046%

r ≈ 4.95%

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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

On average, Anna can drive 31 miles on every gallon of gasoline. If she fills up her tank for $2.19 per gallon, how much will it

Fantom [35]

Answer:

30.66

Step-by-step explanation:

5 0

2 years ago

Your backpack contains 3 blue pens and 2 black pens. You randomly choose one pen to give to a friend and then you randomly choos

Nadusha1986 [10]

Since there are 5 pens total, and three of those pens are blue, the probability for both pens being blue is 3/5.
(just like if the black pens were being chose the probability would be 2/5, since there are 5 pens total and 2 black pens.)

6 0

3 years ago

Shawn's Breakfast Goodies recently sold 3 blueberry muffins and 3 other muffins. What is the experimental probability that the n

katovenus [111]

Answer:

The experimental probability can be expressed in three ways:

Fraction Form: 3/6 or 1/2

Decimal Form: 0.5

Percent Form: 50%

Step-by-step explanation:

Experimental probability is expressed as:

(Favorable outcomes) / (Total outcomes)

The favorable outcome in this situation is blubbery muffins. There were 3 blueberry muffins sold, so this is the numerator of our fraction.

To find the total outcomes we add 3 + 3, which equals 6. This will be the denominator of our fraction.

The fraction used to express experimental probability will look like this: 3/6

We can further simplify this to 1/2.

3 ÷ 3 = 1

6 ÷ 3 = 2

To find a decimal, we divide 1 ÷ 2 = 0.5

Multiply this by 100 to get a percentage, 0.5 x 100 = 50%

3 0

3 years ago

A line's y-intercept is -10, and its slope is 1. What is its equation in slope-intercept form?

ratelena [41]

Answer:

$y=1x-10$

Step-by-step explanation:

$y=mx+b$

m(slope) = 1

b(y-intercept) = -10

$y=1x-10$

✨Hope this helps✨

5 0

2 years ago