Round the number. Write the result as the product of a single digit and a power of 10. 0.0000001801

Thanks for the update. "Irrotational" means curl = zero, so we compute the curl, set it equal to zero, and solve for the constants.

[tex]\vec f(x,y,z) = (axy+z^3) \, \vec\imath + (3x^2-z) \, \vec\jmath + (bz^2-y) \, \vec k[/tex]

[tex]\nabla \times \vec f(x,y,z) = \left(\dfrac{\partial(bz^2-y)}{\partial y} - \dfrac{\partial(3x^2-z)}{\partial z}\right) \, \vec\imath - \left(\dfrac{\partial(bz^2-y)}{\partial x} - \dfrac{\partial(axy+z^3)}{\partial z}\right) \, \vec\jmath \\ ~~~~~~~~~~~~ + \left(\dfrac{\partial(3x^2-z)}{\partial x} - \dfrac{\partial(axy+z^3)}{\partial y}\right) \, \vec k[/tex]

[tex]\nabla \times \vec f(x,y,z) = 3z^2 \, \vec\jmath + (6-a)x \, \vec k[/tex]

At this point, all we can conclude is that a = 6 to make the k-component vanish. Unfortunately there's no zeroing out the j-component, so the field as given is *not* irrotational.

As I mentioned in comments, if the i-component had instead been [tex]axy+bz^3[/tex], we would have ended up with

[tex]\nabla \times \vec f(x,y,z) = 3bz^2 \, \vec\jmath + (6-a)x \, \vec k[/tex]

in which case we would have b = 0.

I'll continue working with this "fixed" field to find Φ, if only to give you an idea of how to proceed. We want a scalar function Φ(x, y, z) such that the given vector field is the gradient of f. This would entail solving the partial differential equations,

[tex]\dfrac{\partial\Phi}{\partial x} = axy+bz^3 = 6xy[/tex]

[tex]\dfrac{\partial\Phi}{\partial y} = 3x^2 - z[/tex]

[tex]\dfrac{\partial\Phi}{\partial z} = bz^2-y = -y[/tex]

Let's start with the last equation. Integrating both sides with respect to z yields

[tex]\Phi(x,y,z) = \displaystyle \int (-y) \, dz = -yz + g(x,y)[/tex]

Now differentiate both sides with respect to y :

[tex]\dfrac{\partial\Phi}{\partial y} = -z + \dfrac{\partial g}{\partial y} = 3x^2 - z \implies \dfrac{\partial g}{\partial y} = 3x^2[/tex]

Integrate both sides of the latter PDE with respect to y to solve for g :

[tex]g(x,y) = \displaystyle \int 3x^2 \, dy = 3x^2y + h(x)[/tex]

Now we differentiate Φ with respect to x :

[tex]\Phi(x,y,z) = -yz + 3x^2y + h(x) \\\\ \dfrac{\partial\Phi}{\partial x} = 6xy + \dfrac{dh}{dx} = 6xy \implies \dfrac{dh}{dx} = 0[/tex]

Integrate to solve for h :

[tex]h(x) = \displaystyle \int 0 \, dx = C[/tex]

where C is an arbitrary constant.

So the scalar function whose gradient is our "fixed" field f is

[tex]\Phi(x,y,z) = -yz + 3x^2y + C[/tex]

Answer:

20

Step-by-step explanation:

36/9 = 4

4x5= 20

Answer:

16

Step-by-step explanation:

well, if you remember P.E.M.D.A.S, which is the order for doing equations, the first two dont matter, but from M for Multiplication, D for Division, A for addition, and finally S for Subtraction, those are the ones that you need here. So you divide the 9s first giving you 9-1+9-1=8+8=16.

Answer:

2/9

Step-by-step explanation:

12,14,16,18 are all greater than 10, which is 4/18 numbers, simplified as 2/9

Answer: 13/18

Step-by-step explanation:

First you add up the amount of even numbers and the amount of numbers greater than 10

2,4,6,8,10 make 5 then add 8 more for 11-18, leaving you with 13 then take 13 and divide it by the total (18) and you will get 0.72 or 13/18

Based on the variable costs and contribution margin, the unit sales price is $80 and the unit contribution margin is $32.

The sales volume in units needed to earn $600,000 is 43,750 units and the amount in dollar sales needed is $3,500,000.

The unit sales price can be found as:

= Variable cost / (1 - contribution margin ratio)

= 48 / (1 - 40%)

= $80

Unit contribution margin is:
= Selling price x Contribution margin ratio

= 80 x 40%
= $32

In units, this amount is:
= (Fixed cost + income required) / Contribution margin

= (800,000 + 600,000) / 32

= 43,750 units

In dollar terms the amount needed is:

= Units needed x selling price

= 43,750 x 80

= $3,500,000

Find out more on contribution margin at https://brainly.com/question/24039258.

Answer:

C. 9

Step-by-step explanation:

This is the answer because of how the math works...Its really hard to explain how it works.

Answer:

44

Step-by-step explanation:

double both 13 and 9 then add the awnser together to get 44

Answer:

point form: (3,2), equation form: x=3, y=2

Step-by-step explanation:

Answer:

Step-by-step explanation:

Probability of drawing 1st red marble

Probability of drawing 2nd red marble

Probability

Using the combination formula, it is found that the number of possible outcomes are given by:

1. 3150

2. 700.

3. 3920.

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

Item 1:

We have combinations of 2 from 6, 5 from 7 and 3 from 5, all independent, hence we multiply them:

[tex]T = C_{6,2}C_{7,5}C_{5,3} = 15 \times 21 \times 10 = 3150[/tex]

3150 different choices are possible.

Item 2:

1 from 5, 1 from 4 and 4 from 7, hence:

[tex]T = C_{5,1}C_{4,1}C_{7,4} = 5 \times 4 \times 35 = 700[/tex]

700 different combinations are possible.

Item 3:

3 men from a set of 8, 4 women from a set of 8, hence:

[tex]T = C_{8,3}C_{8,4} = 56 \times 70 = 3920[/tex]

3920 ways to select the team of 7.

More can be learned about the combination formula at https://brainly.com/question/25821700

Comparing the measurement needed for the batch and the measurement of the scale, Robert does not have enough noodles.

A fraction is a non-integer. It is made up of numerators and denominators. A decimal is a non-integer where the integers are differeniated from a non-integer by a decimal point.

In order to determine the answer, convert the fraction to a decimal by dividing the numerator by the denominator.

4 1/6 = 4. 17

To learn more about fractions, please check: brainly.com/question/1114498

Answer: 6

Step-by-step explanation: simplify is basically solving........

Answer:

y= -4x

Step-by-step explanation:

it will be more helpful to answer this question if the equations were provided.

Answer:

Thus, 12+14+16=42.

Step-by-step explanation:

Hope this helps.

Answer:

4

Step-by-step explanation:

if you have 2 apples and you get 2 more apples how many do you have.

Answer:

x = 4

Step-by-step explanation:

I don't know I tried i just divided 3 by 3x and 12

Answer:

15x^2 6y^2 5z^6

Step-by-step explanation:

area = length x width

area =  5x3y5z^2   *   3x2yz^4

One of the biggest downsides for businesses (besides government regulation) is taxes.

The tax is a term to refer to a tribute that must be paid by an individual or group of people associated with a state without direct consideration.

Taxes affect companies because the state establishes some special taxes for companies to export or import their products. In some cases, they are also assigned a tax for receiving large amounts of money as profit for their services.

Learn more about taxes in: https://brainly.com/question/1362871

Answer:taxes

Step-by-step explanation:

Answer:

27 cm.

Step-by-step explanation:

As there are 3 sides in a triangle and this is regular , the length of one side

= 81/3

= 27 cm

Answer:

y = -x +0

Step-by-step explanation:

y = mx + b

y= slope * x + y-intercept

To find slope, use any x and y pair from the table, for example (x= 5, y= -5)

slope = y/x = -5/5 = -1

y=  -x + b

To find b the y-intercept, substitute any x and y pair from the table, for example (x= 5, y= -5)

-5 = -5 +b

 b = 0

The linear equation that gives the rule for this table is

y = -x + 0 or just y = -x

Answer:

There are two rectangular prisms and two right triangular prisms

Step-by-step explanation:

The two right-angle triangular prisms can be found on the right and left. One rectangular prism can be found in the middle between those two triangular prims, and the other can be found at the top. Voila.

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill &\$3000\\ P=\textit{original amount deposited}\dotfill &\$2000\\ r=rate\to 9.5\%\to \frac{9.5}{100}\dotfill &0.095\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus twice} \end{array}\dotfill &2\\ t=years \end{cases}[/tex]

[tex]3000=2000\left(1+\frac{0.095}{2}\right)^{2\cdot t} \implies \cfrac{3000}{2000}=1.0475^{2t}\implies \cfrac{3}{2}=1.0475^{2t} \\\\\\ \log\left( \cfrac{3}{2} \right)=\log(1.0475^{2t})\implies \log\left( \cfrac{3}{2} \right)=t\log(1.0475^{2}) \\\\\\ \cfrac{\log\left( \frac{3}{2} \right)}{\log(1.0475^{2})}=t\implies 4.37\approx t\qquad \textit{about 4 years and 4 months and a half}[/tex]

Answer:

it will move from (3,5) to (1,3)

When Matthew noticed that the container was one fourth full of sand, the remaining volume quantity needed is 432 inches³.

The container has the following dimensions. 12 in. by 8in. by 6in. Therefore, the volume will be:

= 12 × 8 × 6

= 576 inches.

Since Matthew noticed that the container was one fourth full of sand, the remaining quantity needed will be:

= 576 - (1/4 × 576)

= 576 - 144

= 432 inches³.

Learn more about volume on:

https://brainly.com/question/12410983

Step-by-step explanation:

the side lengths of the base (the ground triangle) are equal. that means every ground side length is 8 in.

and that also makes the 3 triangles of the side areas of the pyramid equal.

so, for the surface area of the pyramid we need to calculate the area of one side area triangle, multiply it by 3 (as we have 3 side areas) and add the area of the ground triangle.

the area of a triangle is

baseline × height / 2

so, for a side area triangle we get

8 × 14 / 2 = 8×7 = 56 in²

all 3 side areas together are then

3×56 = 168 in²

the ground area triangle is then

8 × 6.9 / 2 = 4 × 6.9 = 27.6 in²

so, the total surface area of the pyramid is

168 + 27.6 = 195.6 in²

Answer:

b

Step-by-step explanation:

This a very difficult question but im pretty sure its b

Check the picture below.