There are many different sources of income. Usually, most of an adult's income comes from ____

sertanlavr [38]

X= 2.5
just move the terms collect the terms calculate it, divide both sides !!

6 0

3 years ago

Evaluate the integral Integral ∫ from (1,2,3 ) to (5, 7,-2 ) y dx + x dy + 4 dz by finding parametric equations for the line seg

n200080 [17]

$\vec F(x,y,z)=y\,\vec\imath+x\,\vec\jmath+3\,\vec k$

is conservative if there is a scalar function $f(x,y,z)$ such that $\nabla f=\vec F$ . This would require

$\dfrac{\partial f}{\partial x}=y$

$\dfrac{\partial f}{\partial y}=x$

$\dfrac{\partial f}{\partial z}=3$

(or perhaps the last partial derivative should be 4 to match up with the integral?)

From these equations we find

$f(x,y,z)=xy+g(y,z)$

$\dfrac{\partial f}{\partial y}=x=x+\dfrac{\partial g}{\partial y}\implies\dfrac{\partial g}{\partial y}=0\implies g(y,z)=h(z)$

$f(x,y,z)=xy+h(z)$

$\dfrac{\partial f}{\partial z}=3=\dfrac{\mathrm dh}{\mathrm dz}\implies h(z)=3z+C$

$f(x,y,z)=xy+3z+C$

so $\vec F$ is indeed conservative, and the gradient theorem (a.k.a. fundamental theorem of calculus for line integrals) applies. The value of the line integral depends only the endpoints:

$\displaystyle\int_{(1,2,3)}^{(5,7,-2)}y\,\mathrm dx+x\,\mathrm dy+3\,\mathrm dz=\int_{(1,2,3)}^{(5,7,-2)}\nabla f(x,y,z)\cdot\mathrm d\vec r$

$=f(5,7,-2)-f(1,2,3)=\boxed{18}$

8 0

3 years ago

Which function has a vertex at the origin?

Elenna [48]

answer D

Step-by-step explanation:

Hello,

we can check the graph of the functions as attached or compute the vertex analytically

from the graph you can see that D is the correct answer

8 0

3 years ago

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A line with a slope of 4 passes through the point (2, 1). What is the equation of this line?

olasank [31]

Answer:

point slope form: y - 1 = 4 (x -2)

slope intercept form: y = 4x -7

Step-by-step explanation:

If you want it in point slope form it would be: y - 1 = 4 (x -2)

but if you want it in slope intercept form, you solve this equation

y -1 = 4 (x-2)

y-1 = 4x -8

+1 +1

y = 4x -7 in slope intercept form

7 0

2 years ago

A cell phone company charges a monthly fee of $50 for 300 minutes. Each addition minute costs $0.05. Determine if the function i

Ymorist [56]

Answer:

linear

Step-by-step explanation:

The graph would be linear since it's .05 every minute, which would mean that every minute it would cost .05 --> adding up minutes. The flat fee at the beginning is trying to trick you up, don't get fooled ;)

3 0

2 years ago

Read 2 more answers

There are many different sources of income. Usually, most of an adult's income comes from _____.