Pls help I will give brainliest​

Since F is apparently a vector field, I assume you mean

[tex]\vec F = \nabla(x^3+y^3+z^3+3xyz)[/tex]

with ∇ = gradient, whereas ∆ is often used to denote the Laplacian, ∆ = ∂²/∂x² + ∂²/∂y² + ∂²/∂z².

Let [tex]f(x,y,z)=x^3+y^3+z^3+3xyz[/tex]. Compute the gradient of f :

[tex]\vec F = \nabla f(x,y,z) = \dfrac{\partial f}{\partial x} \, \vec\imath + \dfrac{\partial f}{\partial y} \, \vec\jmath + \dfrac{\partial f}{\partial z} \, \vec k[/tex]

[tex]\vec F = (3x^2+3yz) \,\vec\imath + (3y^2 + 3xz) \,\vec\jmath + (3z^2+3xy) \,\vec k[/tex]

Now compute the divergence of F (incidentally, divergence of a gradient field is the Laplacian of the f):

[tex]\mathrm{div} \, \vec F = \dfrac{\partial(3x^2+3yz)}{\partial x} + \dfrac{\partial(3y^2+3xz)}{\partial y} + \dfrac{\partial(3z^2+3xy)}{\partial z}[/tex]

[tex]\boxed{\mathrm{div} \, \vec F = 6x + 6y + 6z}[/tex]

and the curl: (the following is overkill, since any gradient field has curl zero, but it doesn't hurt to verify that)

[tex]\mathrm{curl}\, \vec F = \left(\dfrac{\partial(3z^2+3xy)}{\partial y} - \dfrac{\partial(3y^2+3xz)}{\partial z}\right) \,\vec\imath - \left(\dfrac{\partial(3z^2+3xy)}{\partial x} - \dfrac{\partial(3x^2+3yz)}{\partial z}\right) \, \vec\jmath \\ ~~~~~~~~~~~~ + \left(\dfrac{\partial(3y^2+3xz)}{\partial x} - \dfrac{\partial(3x^2+3yz)}{\partial y}\right) \,\vec k[/tex]

[tex]\boxed{\mathrm{curl} \,\vec F = \vec 0}[/tex]

Answer:

3 and 4

Step-by-step explanation:

30/8=3.75

3.75 lies between 3 and 4

Hey there!

30/8

= 30 ÷ 2 / 8 ÷ 2

= 15 / 4

≈ 3 3/4

≈ 3.75

It falls in between three (3) and four (4). But, fun fact it rounds to up to four (4)

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Step-by-step explanation:

Using BODMAS rule

[3x+12+x] = [4(3+x)]

[4x+12] = [12+4x]

Parentheses 1 = Parentheses 2

LHS = RHS

HENCE PROVED

Answer:

F = ma

m = F/a

m = 88/4

m = 22 kg

Step-by-step explanation:

Answer:

See below.

Step-by-step explanation:

A(1, 4)

B(3, 0)

C(-3, -2)

We find the coordinates of he midpoints using the midpioint formula.

D([1 + 3]/2, [4 + 0]/2) = D(2, 2)

E([1 + (-3)]/2, [4 + (-2)]/2) = E(-1, 1)

We find the slopes using the slope formula.

slope of BC:

m_BC = (-2 - 0)/(-3 - 3) = -2/(-6) = 1/3

slope of DE:

m_DE = (1 - 2)/(-1 - 2) = -1/(-3) = 1/3

Since the slopes of BC and DE are equal, the lines are parallel.

Answer:

832.5²

Step-by-step explanation:

Base x height ÷ 2 is the formula to find a triangles area.

45 x 37= 1665 then 1665 ÷ 2 = 832.5 dont forget to add the ²

Answer:

832.5²

Step-by-step explanation:

Answer: 4

Step-by-step explanation:

The length of QR(x) from the given figure is 4 units.

The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

From the given figure, QR=x, RS=2√3 units and ∠STR=60°.

We know that, sinθ= Opposite/Hypotenuse

sin60°=2√3/RT

√3/2=2√3/RT

RT=4 units

As we know, tanθ= Opposite/Adjacent

tan45°= x/4

1= x/4

x=4 units

Therefore, the length of QR(x) from the given figure is 4 units.

Learn more about the trigonometric ratios here:

brainly.com/question/25122825.

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Answer:

i cant see the grid

Step-by-step explanation:

show the grid please

Answer:

1620

Step-by-step explanation:

(-18)×(-10)×9= 1620

Answer:

The origin is at (0,0) its where the x and y coordinate intersect.

Step-by-step explanation:

what was the question here?

standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{-2})\qquad \qquad \stackrel{slope}{m}\implies -\cfrac{5}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-2)}=\stackrel{m}{-\cfrac{5}{4}}(x-\stackrel{x_1}{4})[/tex]

[tex]y+2=-\cfrac{5}{4}x+5\implies \stackrel{\textit{multplying both sides by }\stackrel{LCD}{4}}{4(y+2)=4\left( -\cfrac{5}{4}x+5 \right)}\implies 4y+8=-5x+20 \\\\\\ 5x+4y+8=20\implies 5x+4y=12[/tex]

Answer:

x+2 - and x+6

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

2/3 * 2/3 = 4/9

2/3 * 3/2 = 1

2/3 * 3/4 = 1/2

2/3 * 4/4 = 2/3

For the mean serum cholesterol level for U.S. adults was 198, with a standard deviation of 39,  the probability   is mathematically given as

x=0.1379

Generally, the equation for the probability  is mathematically given as

P(\=x>210)

Therefore

P=(z>\frac{204-198}{39/\sqrt{106}})

P=(z>1.583)

In conclusion, from cumulative table

x=1-p(z>1.583)

x=1-0.8621

x=0.1379

Read more about probability

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Answer:

1. x=4

2. x=14

3. x=3

Step-by-step explanation:

x is just a symbol they use as a temporary symbol to tell the person reading the problem that there is number that you do not know yet. if the x in the problem is next to a number then it needs to be multiplied with the number it's next to. in this case we know that 4 times 3=12 and if you take two away from 12 you get 10 so because 3 works in the equation it's the answer for 4x-2=10. this applies to every problem like this another way to solve it is if you add 2 to the left side it cancels out but you need to add 2 to the other side which would look like 4x=10+2 which equals 4x=12 and 4 times three equals 12. it doesn't matter how the equation changes as long as you find out whatx equals then that is the answer.

Answer:

1. x = 2

2. x = 14

3. x = 3

Step-by-step explanation:

1. 12 + 2x = 16

First, I did 16 - 12 which is 4. I did this because you want to know how much 2x is supposed to be fully, and you always want to do the opposite. like in this case it was addition so the opposite is subtracting. Next, the 2x is supposed to equal 4, and when you see 2x that means you have to multiply. So, 2 x 2 = 4. You can also do 4 divided by 2 equal 4. Finally, the answer for x is 2.

________________________________________________________

2. 12 + x = 26

So, you have to do 26 - 12 which is 14. I turned the addition problem to a subtraction problem because you always want to do the opposite. and you should already know that x will equal 14. you can double check if you want and change it back to addition which will be 12 + 14 = what ? 26 . so 14 is the answer for x !

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3. 4x - 2 = 10

First, you want to do 10 + 2 which is 12. You should know by now if you read above for the other equations that you have to do the opposite. Next, 4x is going to have to be equal to 12. So, 4 x 3 = 12 or you can do 12 divided by 4 which will still equal 3. Finally the answer for x is 3.

________________________________________________________

Hope this helps !

here a fun quote

"Happiness is the secret to all beauty. There is no beauty without happiness." - Chirstian Dior

Answer:

Option C, [tex]36x^2 + 60x + 25[/tex]

Step-by-step explanation:

Step 1:  Determine the perfect square

According to online, "When an expression has the general form a²+2ab+b², then we can factor it as (a+b)². For example, x²+10x+25 can be factored as (x+5)². This method is based on the pattern (a+b)²=a²+2ab+b², which can be verified by expanding the parentheses in (a+b)(a+b)"

The only one that seems to work is Option C so lets factor it.

[tex]36x^2 + 60x + 25[/tex]

[tex](6x + 5)(6x + 5)[/tex]

[tex](6x + 5)^2[/tex]

Yup!  We can see that Option C would give us a perfect square

Answer:  Option C, [tex]36x^2 + 60x + 25[/tex]

Answer:

the answer is B <3

Step-by-step explanation:

have a good day!

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Answer:

b

Step-by-step explanation:

Answer:

Option A is correct. (light blue color in the triangle choices)

Step-by-step explanation:

Or with the same dimensions as my screenshot

Answer:

25.2

Step-by-step explanation:

To calculate hydronium concentration from pH, type on you calculator

10 to the power of negative pH value

10^-5.5 = 3•10^6 mol/L

Since there are 3 hydrogens in every hydronium molecule,

There are 9 • 10^6 hydrogens in that liter of acid.

Answer:

Area of a triangle is 1/2 x base x height.

area of triangle = 1/2 x 20 x 17 = 170 square feet.

the image shows 4 triangles, total area = 170 x 4 = 680 square feet.

the answer is A. 680 sq. ft.

Hope this helps you!!

Please Mark me as Brainleast!!!!!!!!!!!!!

Answer:

56

Step-by-step explanation:

two of the angles are the same meaning the bottom two are 62. angles in a triangle add up to 180° so you just do 62 + 62 and then take the answer away from 180

62+62=124

180-124=56

Answer:

Discriminant

[tex]b^2-4ac\quad\textsf{when}\:ax^2+bx+c=0[/tex]

[tex]\textsf{when }\:b^2-4ac > 0 \implies \textsf{two real roots}[/tex]

[tex]\textsf{when }\:b^2-4ac=0 \implies \textsf{one real root}[/tex]

[tex]\textsf{when }\:b^2-4ac < 0 \implies \textsf{no real roots}[/tex]

Given equation: [tex]kx^2+2x+(1-k)=0[/tex]

[tex]\implies a=k,\:b=2,\:c=(1-k)[/tex]

[tex]\begin{aligned}\implies b^2-4ac & =(2)^2-4(k)(1-k)\\ & =4-4k(1-k)\\ & =4-4k+4k^2\\ & = 4k^2-4k+4 \end{aligned}[/tex]

Complete the square:

[tex]\begin{aligned}\implies 4k^2-4k+4 & =4(k^2-k+1)\\ & = 4\left[k^2-k+\left(\dfrac{-1}{2}\right)^2+1-\left(\dfrac{-1}{2}\right)^2\right]\\ & = 4\left[\left(k-\dfrac12\right)^2+\dfrac34\right]\\ & = 4\left(k-\dfrac12\right)^2+3\end{aligned}[/tex]

[tex]\textsf{As }\left(k-\dfrac12 \right)^2 \geq 0 \implies 4\left(k-\dfrac12 \right)^2+3\geq 3[/tex]

Therefore, the roots are always real.

Probability helps us to know the chances of an event occurring. The probability of a family owning a cat or a dog is 0.22.

Probability helps us to know the chances of an event occurring.

[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

As it is given that the probability of a family owning a cat is 0.10, the probability of owning a dog is 0.20, and the probability of owning a cat and a dog is 0.08. Therefore, the probability of a family owning a cat or a dog can be written as,

Probability (family owning a cat or a dog)

= Probability (Cat) + Probability (Dog) - Probability (Cat And Dog)

[tex]\text{Probability (family owning a cat or a dog)} = 0.10+0.20-0.08 = 0.22[/tex]

Hence, the probability of a family owning a cat or a dog is 0.22.

Learn more about Probability:

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Answer:

72

Step-by-step explanation:

84/7 = 12

12 × 6 = 72

84 to 72

Answer:

72

Step-by-step explanation:

divide 84 by 7, and then multiply 12(what you got from the division) by 6 and you get 72

Answer:

parallel: 1, perpendicular: -1

Step-by-step explanation:

slope of a parallel line is the same

slope of a perpendicular line is a negative recipricol

slope of y=x+9 is 1

parallel: 1

perpendicular: -1

since there are 36 inches in 1 yard, 12 yards will have 12(36) = 432 inches.

Answer:

[tex]\tt 1)\: \boxed{\tt 4y+10}[/tex]

[tex]\tt 2)\:\boxed{\tt 0.5x^4+10.5}[/tex]

Step-by-step explanation:

1) y + 4 + 3(y + 2)

Expand:-

[tex]\tt y+4+3y+6[/tex]

Combine like terms:-

[tex]\tt y+3y+4+6[/tex]

[tex]\boxed{\tt 4y+10}[/tex]

__

2) 0.5(x⁴ - 3) + 12

Expand:-

[tex]\tt 0.5x^4-1.5+12[/tex]

Add/Subtract Numbers:-

[tex]\boxed{\tt 0.5x^4+10.5}[/tex]

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