Write the answer in simplest form

Given that

[tex]\vec A = xz^3 \, \vec\imath - 2x^2 y \, \vec\jmath + 2yz^4 \, \vec k[/tex]

its curl is

[tex]\displaystyle \nabla\times\vec A = \left(\frac{\partial\left(2yz^4\right)}{\partial y} - \frac{\partial\left(-2x^2y\right)}{\partial z}\right) \, \vec\imath - \left(\frac{\partial\left(2yz^4\right)}{\partial x} - \frac{\partial\left(xz^3\right)}{\partial z}\right) \, \vec\jmath \\ ~~~~~~~~~~~~ + \left(\frac{\partial\left(-2x^2y\right)}{\partial x} - \frac{\partial\left(xz^3\right)}{\partial y}\right) \, \vec k[/tex]

[tex]\nabla\times\vec A = 2z^4 \, \vec\imath + 3xz^2 \, \vec\jmath - 4xy \, \vec k[/tex]

so that at the point (1, -1, 1), the curl is

[tex]\nabla\times\vec A \bigg|_{(x,y,z)=(1,-1,1)} = \boxed{2 \, \vec\imath + 3 \, \vec\jmath + 4 \, \vec k}[/tex]

Answer:

[tex]\tan(X)=\dfrac{77}{36}[/tex]

Step-by-step explanation:

First we need to find the length of side WX.

To do this, use Pythagoras' Theorem:  [tex]a^2+b^2=c^2[/tex]

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

[tex]\implies WX^2+77^2=85^2[/tex]

[tex]\implies WX^2=85^2-77^2[/tex]

[tex]\implies WX=\sqrt{85^2-77^2}[/tex]

[tex]\implies WX=36[/tex]

Now use the Tan trig ratio:

[tex]\tan(x)=\sf \dfrac{O}{A}[/tex]

where:

From inspection of the triangle,

Substituting these values into the tan trig formula:

[tex]\implies \tan(X)=\dfrac{77}{36}[/tex]

Therefore, the tangent of ∠X is [tex]\dfrac{77}{36}[/tex]

Answer:

77 / 36

Step-by-step explanation:

Finding the adjacent side

Tangent of ∠X

Recall that

[tex]\dfrac{d}{dx}\left[\cot(x)\right] = -\csc^2(x)[/tex]

so that

[tex]\displaystyle \int \frac{dx}{\sin^2\left(\frac{x-2}3\right)} = \int \csc^2\left(\frac{x-2}3\right) \, dx = \boxed{-3 \cot\left(\frac{x-2}3\right) + C}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{Your \ exercise \ is \to\int\limits \frac{1}{sin^2\left(\dfrac{x-2}{3}\right) }dx } \end{gathered}$}[/tex]

             [tex]\boldsymbol{Replaces \ u=\dfrac{x-2}{3} \longmapsto \dfrac{du}{dx}=\dfrac{1}{3} \longmapsto \ dx=3 \ du }[/tex]

                                               [tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{=\int\limits \frac{3}{Sin^2(u) }du } \end{gathered}$}[/tex]

                                                    [tex]\boldsymbol{\sf{Simplify }}[/tex]

                                              [tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{=3\int\limits csc^2(u)du } \end{gathered}$}[/tex]

                                                    [tex]\boldsymbol{\sf{Solving \ now }}[/tex]

                                                    [tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\int\limits csc^2(u)du } \end{gathered}$}[/tex]

                                            [tex]\boldsymbol{\sf{This\:is\:a\:standard\:integral. }}[/tex]

                                                     [tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{=-cot(u)} \end{gathered}$}[/tex]

                                       [tex]\boldsymbol{\sf{We\:replace\:the\:integrals\:already\:solved. }}[/tex]

                                                   [tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{=\int\limits \frac{3}{Sin^2(u) }du } \end{gathered}$}[/tex]

                                                      [tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{=-cot(u)} \end{gathered}$}[/tex]

                                      [tex]\boldsymbol{The\:substitution\:is\:undone\: u=\dfrac{x-2}{3} ;}[/tex]

                                                      [tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{=-3cot\left(\frac{x-2}{3}\right) } \end{gathered}$}[/tex]

       [tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf Answer \longmapsto \bf{\int\limits \dfrac{1}{sin^2\left(\dfrac{x-2}{3}\right) }dx }=\boldsymbol{ -3cot\left(\frac{x-2}{3}\right)+C } \end{gathered}$}}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \underline{\bf{\green{I\:hope \ it \ helps \ you..... Regards }}} \end{gathered}$}[/tex]

Answer:

Step-by-step explanation:

The graph of the linear equation cuts the x-axis at (5,0)

Reason:

Triangles A, B and E all have the angles 68 and 79 with a 3 unit side sandwiched between them. We can use the angle side angle (ASA) congruence theorem to prove those three triangles are identical copies of each other. They are rotated, reflected and shifted versions of one another. These tranformations are known as rigid transformations or isometries.

On the other hand, we can rule out choice C because the side between the angles is not 3 units long (even though the angles do match up). The same goes for choice D.

Applying proportions, it is found that the discounted price of each console at store B is given by:

B. $210.80.

A proportion is a fraction of a total amount.

In this problem, at store B, 15 consoles sold for a total of $3,720, hence the price per console is of:

P = 3720/15 = $248.

A discount of 15% is applied, which means that the new price is 85% of the original price, hence:

P = 0.85 x 248 = $210.8.

Which means that option B is correct.

More can be learned about proportions at https://brainly.com/question/24372153

Answer:

[tex]1590.6cm {}^{3} [/tex]

Step-by-step explanation:

[tex]volume \: of \: a \: cone \: v = \frac{1}{3}\pi \: r {}^{2} h \\ radius = \frac{diameter}{2} = \frac{15}{2} = 7.5 \\ v = \frac{1}{3} \times 3.42 \times (7.5) {}^{2} \times 27 \\ v = \frac{3.142 \times 7.5 \times 7.5 \times 27}{3} \\ v = \frac{4771.9125}{3} = 1590.6375 \\ v = 1590.6cm {}^{3} (approximatly) \\ please \: rate \: and \: mark \: brainliest[/tex]

Answer:

360

Step-by-step explanation:

9x4=36 add the zero you didn't use

Answer:

10.6 oz

Step-by-step explanation:

X × 0.25 = 0.265

x= 2.65/0.25= 10.6 oz

Answer:

1.91, 1.92, 1.93

Step-by-step explanation:

They are all between 1.9 and 2

Answer:

10

Step-by-step explanation:

here it is

the explanation is in the photo

Answer:

4,000

Step-by-step explanation:

The value goes down by around 2,000 every year and 4,00 is the closest answer of any of them.

Answer:1) In Δ FGH,

FH=7 ft, FG=12 ft,

∠F=70 degrees

By "Law of cosines":

So,By applying Law of Sines , we get that

Hence, Option 'D' is correct.

2) In Δ XYZ,

XY=14, ∠Y=22°, and XZ=26

By using "Law of sines":

so, X = 147° , Y = 22° , Z = 11.6°

Step-by-step explanation:

The angle of fire in the standard position will be B. 120°; 2 pi over 3 radians.

It should be noted that the image shows the shooting angles arrangements. Also, π = 180°.

In this case, the value of the angle will be:

= 12π/18

= (12 × 180) / 18

= 12 × 10

= 120°

Therefore. the angle of fire in the standard position will be B. 120°; 2 pi over 3 radians.

Learn more about angles on:

https://brainly.com/question/25770607

Answer: 6cm.

Step-by-step explanation:

Strategy 1 (in-head thinking)

300 divided by 50 would be 6, multiply 6 by 1 and get 6cm.

Strategy 2 (proportions)

First, set up a proportion.

We know that 1cm = 50km, so we put them on a fraction (whichever is denominator/numerator doesn’t affect the process)

However, we don’t know how much cm equals 300km, so we turn that into a variable, in this case x.

1cm       x cm

———   ———

50km  300km

To solve a proportion, go diagonal to where the variables have already been filled in. You can’t so 50km and x cm, as you don’t know x. You can do 300km however. To start, multiply 1 and 300, to which you get 300. Then, multiply 300 by the 50km and you’ll get x. That’ll equal to 6.

So in conclusion, your answer is 6.

Answer:

1.28!

Step-by-step explanation:

hope this helps, let me know if you need an explination! :)

Answer:

Step-by-step explanation:

Answer:

x times square then subtract

We can represent the pattern by a general sequence:

u(n+1)=8n+2

u(1)=8(10)+2

u(1)=82

u(2)=8(82)+2

u(2)=658

....

Answer:

10:82:658:5266:42130

The expression that returns the probability that a data value in a normal distribution is between a z- score of -0.18 and a z-score of 1.99 is (d) normalcdf(-0.18, 1.99)

To calculate the probability between two z-scores is to calculate the area between the z-scores.

This is done using the following syntax:

normalcdf(lower bound, upper bound)

From the question, the lower and the upper z-scores are -0.18 and 1.99

So, the formula would be normalcdf(-0.18, 1.99)

Hence, the expression is (d)

Read more about normal distribution at:

https://brainly.com/question/25991460

Answer:

I hope it helps you

Answer:

Step-by-step explanation:

A number decreased by 16 is − 3

hope this helps.

mark me brainliest please.

Answer:

c. 1 1/2 hours

Step-by-step explanation:

6 hours / 4 games = 1 1/2 hours per game

Another way to think of it:

1 hour = 60 minutes

6 hours = 6 hours x 60 minutes per hour = 360 minutes

360 minutes / 4 games = 90 minutes per game

90 minutes per game / 60 minutes per hour = 1.5 hours

1.5 hours is the same as 1 1/2 hours

So, the answer is c. 1 1/2 hours

Answer:

1. 5/(2+2)= 5/4= 1.25

2. 5/(2x2)= 5/4= 1.25

Step-by-step explanation:

3x5/12= 15/12= 1.25

Answer:

B Building = 865 feet,   A Building = 665 feet.

Step-by-step explanation:

If you divide 1530 by 2 you get 765, if you add 100 to 765, and subtract 100 from 865, there is a 200 feet difference from each of the buildings.

[tex]v (total)= v(r \: p \: ) + v(c)[/tex]

[tex]v(t) = lwh + \pi {r}^{2} h[/tex]

[tex]v(t) =( 18 \times 10 \times 5 )+( 3.14 \times {5}^{2} \times 5) \\ [/tex]

[tex]v(t) = 900 + 392.50[/tex]

[tex]v(t) = 1292.50 \: \: \: {ft}^{3} [/tex]

Depth is also referred as height.

Volume of the rectangular part = l b h

= 18 × 10 × 5

= 900 ft³

Volume of two semi circular parts = 4 / 3 π r³

= 4 / 3 × 5 × 5 × 5 × π

= 523.8 ft³

Total Volume of the figure = 1423.8 ft³

Answer:

1,005cm²

Step-by-step explanation:

First, you need to know the area of a cylinder and also the value of pi.

Area = 2πrh

pi = π = 3.14

r = radius = 80cm

h = height of cylinder = 20

now let's substitute

[tex]2 \times 3.14 \times 80 \times 20 = 1004.9{cm}^{2} [/tex]

but to the nearest square centimetre is.

1005cm²

because the number after the point is more than 4 so we add one to the last number before the point.

Answer:

It shows a deficit of $261

Step-by-step explanation:

$32,508/12 = $2709 per month

$2709 - ($1860 + $860 + $259) = -$270

I'm assuming you put a typo somewhere, but the closest answer is the deficit of $261