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horsena [70]
3 years ago
12

For each of the following vector fields F, decide whether it is conservative or not by computing curl F. Type in a potential fun

ction f (that is, ∇f=F). Assume the potential function has a value of zero at the origin. If the vector field is not conservative, type N.1. F(x,y)=(-6x+5y)i+(5x+10y)j
2. F(x,y,z)=-3xi-2yj+k
3. F(x,y)=(-siny)i+(10y-3xcosy)j
4. F(x,y,z)=-3x^2i+5y^2j+5z^2k
Mathematics
1 answer:
Burka [1]3 years ago
5 0

Answer:

1,2 and 4 are conservatives

3 is not conservative

Step-by-step explanation:

We calculate  the Curl F

Remember that:

        Curl F = <\frac{dFz}{dy} - \frac{dFy}{dz}, \frac{dFz}{dx} - \frac{dFx}{dz}, \frac{dFy}{dx} - \frac{dFx}{dy}>

1. Curl F = <0,0,5-5> = <0,0,0>

  The potential function f so that  ∇f=F

  f(x,y,z) = -3x^{2} +5xy + 5y^{2}

  Then F is conservative

2. Curl F = < 0, 0 ,0>

  The potential function f so that  ∇f=F

  f(x,y,z) = -3/2x^{2} -y^{2}+z

  Then F is conservative

3. Curl F = <0 ,0, 10+3xsin(y) - (-cos(y))>

              = <0 ,0 , 10 +3xsin(y) + cos(y)<

 How the field's divergence is not zero the vector field is not conservative

4. Curl F = <0, 0, 0>  

  The potential function f so that  ∇f=F

  f(x,y,z) = x^{3}+(5/3)y^{3}+(5/3)z^{3}    

   Then F is conservative

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guajiro [1.7K]

Answer:

If the time passed is only 3 months, then it is $2040

Step-by-step explanation:

We can use the quarterly compounded interest equation for this problem: P(1 + r/n)^nt

Step 1: Find out how much 3 months is in a year

<em>In this case, 3/12 which is 1/4</em>

Step 2: Plug in known variables into equation

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Step 3: Solve/Plug in calc

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If the time passed in the problem is 1 year, then we can be able to solve how much money he earned per quarter. However, since only 3 months have elapsed, then he has only earned $2040.

7 0
3 years ago
A bill from a plumber was $306 The plumber charged $150 for parts and $52 per hour for labor. How long did ths plumber work at h
ludmilkaskok [199]
We can make an equation from this.
Our intial value is 150 for parts, and he works for 52 dollars an hour.
We can define <em /><em>h</em> for hours and <em /><em>c</em> for total cost.
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We can set this equal to 306 dollars, as that's the given total cost:
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3 years ago
Two triangular roofs are similar. The ratio of the corresponding sides of these roofs is 2:3. If the altitude of the smaller roo
schepotkina [342]

Answer:  6.75 feet

Step-by-step explanation:

Since, the ratio of the side of the similar triangle = 2 : 3

Thus, by the property of similar triangle,

The ratio of the altitudes of the triangle = 2 : 3

Let the altitude of smaller triangle = 2 x

And, the altitude of larger triangle = 3 x

Where x is any number.

According to the question,

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