Select the correct answer from the choices given

Determine whether or not the vector field is conservative. if it is, find a function f such that f = ∇f. if the vector field is

amm1812

$\dfrac{\partial f}{\partial x}=3y^2z^3\implies f(x,y,z)=3xy^2z^3+g(y,z)$

$\dfrac{\partial f}{\partial y}=6xyz^3+\dfrac{\partial g}{\partial y}=6xyz^3$
$\implies\dfrac{\partial g}{\partial y}=0\implies g(y,z)=h(z)$

$\dfrac{\partial f}{\partial z}=9xy^2z^2+\dfrac{\mathrm dh}{\mathrm dz}=9xy^2z^2$
$\implies\dfrac{\mathrm dh}{\mathrm dz}=0\implies h(z)=C$

$\implies f(x,y,z)=3xy^2z^3+C$

The potential function exists, so $\mathbf f$ is indeed conservative.

7 0

3 years ago

How many significant figures are in 0.0624000?

Dafna11 [192]

Answer:

Use notes and youll get an answer

Step-by-step explanation:

4 0

2 years ago

Write the equation you would use to find x, then solve for x.

goldfiish [28.3K]

Answer:

x + 6x+10 + x+2 = 180

x = 21

Step-by-step explanation:

The sum of the angles of a triangle add to 180 degrees

x + 6x+10 + x+2 = 180

Combine like terms

8x + 12 = 180

Subtract 12 from each side

8x+12-12 = 180-12

8x =168

Divide each side by 8

8x/8 = 168/8

x =21

6 0

2 years ago

Read 2 more answers

I need to know if it’s A B C OR D

Liula [17]

SOLUTION

Consider the property, opposite angle of a cyclic quadrilateral are supplementary

hence

$\angle NMP+\angle NOP=180^0$

Recall that

$\begin{gathered} \angle NMP=\angle M=(8x-24)^0 \\ \text{and } \\ \angle NOP=\angle O=(4x)^0 \end{gathered}$

Hnece, we have that

$\begin{gathered} \angle M+\angle O=180^0(opposite\text{ angles of a cyclic quadrilateral)} \\ (8x-24)^0+4x^0=180^0 \end{gathered}$

Then

$\begin{gathered} 8x-24+4x=180 \\ 8x+4x-24=180 \\ 12x-24=180 \\ \text{Add 24 t o both sides } \\ 12x-24+24=180+24 \\ 12x=204 \\ \text{divide both sides by 12} \\ \frac{12x}{12}=\frac{204}{12} \\ \text{Then} \\ x=17 \end{gathered}$

Hence

x=17

Since

$\begin{gathered} \angle NOP=(4x)^0 \\ \text{substitute the value of x, we have } \\ \angle NOP=4\times17=68^0 \\ \text{Hence } \\ \angle NOP=68^0 \end{gathered}$

Therefore

The measure of angle NOP is 68⁰

Answer; 68⁰ (The fourth Option )

5 0

1 year ago

A standard roll of toilet paper is 304 feet long. If Bob walks at a steady rate of five feet per second, how much time does it t

PtichkaEL [24]

Answer:

1.01 minutes

Step-by-step explanation:

The length of the roll is given to be 304 ft, and Bob's velocity is 5ft/s.

Velocity is defined as the rate of change of displacement over time t:

$v=d/t\\$

The function can be expressed to make t the subject to calculate time taken by Bob;

$v=d/t\\\therefore t=d/v, d=304, v=5\\\\t=\frac{304}{5}\times \frac{1}{60}\ min\\\\t=1.01 \ min$

Hence, it takes Bob 1.01 minutes to walk the length of the roll.

6 0

2 years ago