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marissa [1.9K]
3 years ago
9

3 1/2 x 1 2/3 Step by step explanation

Mathematics
1 answer:
Blababa [14]3 years ago
4 0

Answer:

5.83333333333

Step-by-step explanation:

i looked it up

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An electron at rest at P = (5,3,7) moves along a path ending at Q = (1, 1, 1) under the influence of the electric field (in newt
EastWind [94]

Answer:

a) \bf f(x,y,z)=200ln(x^2+z^2)

b) \bf 3.9819*10^{16}\;m/seg

Step-by-step explanation:

The electric field can be written as

\bf F(x,y,z)=(\displaystyle\frac{400x}{x^2+z^2},0,\displaystyle\frac{400z}{x^2+z^2})

a)Find a potential function for F

A potential function for F would be a function f such that

\bf \nabla f = F

That is, the gradient of f equals F.

If such a function exists then

\bf \displaystyle\frac{\partial f}{\partial x}=\displaystyle\frac{400x}{x^2+z^2}\\\\\displaystyle\frac{\partial f}{\partial y}=0\\\\\displaystyle\frac{\partial f}{\partial z}=\displaystyle\frac{400z}{x^2+z^2}

Integrating the first equation with respect to x

\bf f(x,y,z)=\displaystyle\int\displaystyle\frac{\partial f}{\partial x}dx+h(y,z)

 

where h(y,z) is a function that does not depend on x. We have then

\bf f(x,y,z)=\displaystyle\int\displaystyle\frac{400x}{x^2+z^2}dx+h(y,z)=400\displaystyle\int\displaystyle\frac{x}{x^2+z^2}dx+h(y,z)=\\\\200ln(x^2+z^2)+h(y,z)

By taking the partial derivatives with respect y and z we can notice that h(z,y)=0.

Therefore, a potential function for F is

\bf \boxed{f(x,y,z)=200ln(x^2+z^2)}

b) What is the electron’s speed at the point Q?

Since F is conservative, the work done to move the particle from P to Q does not depend on the path, but only on the potential function f.

Let W be the work done when moving the particle from P to Q

W = f(Q) - f(P) = f(1,1,1) - f(5,3,7)

\bf W=200ln(1^2+1^2)-200ln(5^2+7^2)=-722.183583 joules

According to the law of conservation of energy, the work done to move the electron from P to Q equals the change in kinetic energy of the object.

Since the electron is at rest in P, the kinetic energy at P equals 0 and we have

\bf W=-\displaystyle\frac{m(v_Q)^2}{2}

where  

m = mass of an electron

\bf v_Q = speed at point Q

Replacing in the equation

\bf  -722.183583=-\displaystyle\frac{9.10938356*10^{-31}(v_Q)^2}{2}\Rightarrow\\\\\Rightarrow v_Q=\sqrt{\displaystyle\frac{2*722.183583}{9.10938356*10^{-31}}}=3.9819*10^{16}\;m/seg

4 0
3 years ago
Teri ran 8 kilometers. One mile is approximately equal to 1.6 kilometers. Which measurement is closest to the number of miles Te
balandron [24]

Answer:

12.8

Step-by-step explanation:

8 x 1.6 = 12.8

That should be the answer

6 0
3 years ago
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Please can I have some help with these?
LenaWriter [7]
I hope this helps you

4 0
3 years ago
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Find the first four terms of the sequence an = 4n-6
natulia [17]

Answer:

The first four terms of the sequence are-6, -2, 2 and 6

Step-by-step explanation:

The given sequence is a_n=4n-6

In order to find the first four term of the sequence we put n =0, 1, 2 and 3.

For n =0

a_0=4(0)-6=-6

For n =1

a_1=4(1)-6=-2

For n =2

a_2=4(2)-6=2

For n =3

a_3=4(3)-6=6

Therefore, the first four terms of the sequence are

-6, -2, 2 and 6

5 0
3 years ago
Which relationship describes angles 1 and 2?
tamaranim1 [39]
Angles 1 and 2 are adjacent, we know this because they are side by side. Meaning they are adjacent.

Angles 1 and 2 are also complementary because they add up to 90°
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3 years ago
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