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3 years ago

Monthly salary is 1848 plus a sales commission of 5.2% of the total sales for the month. what is the equation

1 answer:

4 0

There can be a couple of answers for this..

(1) 1848 + 0.052(1848) <== thats one equation
(2) 1848 (1.052) <== there is the other one

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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

2 years ago

Determine which of the values is a solution of 4t + 6 less thank or equal to 10.

Afina-wow [57]

Answer:

Can you put the screen more closer to the values

Step-by-step explanation:

Or you could type in the values so i can see.

4 0

1 year ago

Hurry ASAP need help please !!!!!!

lara [203]

Answer:

100y^4x^2

Step-by-step explanation:

^ means that's where an exponent is, so 100y exponent 4 x exponent 2.

8 0

3 years ago

Read 2 more answers

What is a definition of a scale on a graph

babunello [35]

Answer:

A scale on the graph shows the way the numbers or pictures are used in data. Let us now move on to a bar graph. We use the same data of “Favorite Musical Instrument” to plot a Bar graph

Step-by-step explanation:

3 0

2 years ago

When you run, your average step length is 42 inches. How many steps would you have to take to run 1 mile (5,280 feet)? Round to

bezimeni [28]

First convert 5,280 ft. into inches.
$5280 \times 12 = 63360$
5280 ft. equals 63360 inches.

Then you divide that by 42
$63360 \div 42 = 1508.57$
If you're rounding to the nearest step then it would take 1509 steps to run 1 mile.

6 0

3 years ago