Which r-value suggests a strong negative correlation? A. r=0.97351 B. r= -0.27331 C. r= -0.97351 D. r= 0.27331

Find the work done by F= (x^2+y)i + (y^2+x)j +(ze^z)k over the following path from (4,0,0) to (4,0,4)

babunello [35]

$\vec F(x,y,z)=(x^2+y)\,\vec\imath+(y^2+x)\,\vec\jmath+ze^z\,\vec k$

We want to find $f(x,y,z)$ such that $\nabla f=\vec F$ . This means

$\dfrac{\partial f}{\partial x}=x^2+y$

$\dfrac{\partial f}{\partial y}=y^2+x$

$\dfrac{\partial f}{\partial z}=ze^z$

Integrating both sides of the latter equation with respect to $z$ tells us

$f(x,y,z)=e^z(z-1)+g(x,y)$

and differentiating with respect to $x$ gives

$x^2+y=\dfrac{\partial g}{\partial x}$

Integrating both sides with respect to $x$ gives

$g(x,y)=\dfrac{x^3}3+xy+h(y)$

Then

$f(x,y,z)=e^z(z-1)+\dfrac{x^3}3+xy+h(y)$

and differentiating both sides with respect to $y$ gives

$y^2+x=x+\dfrac{\mathrm dh}{\mathrm dy}\implies\dfrac{\mathrm dh}{\mathrm dy}=y^2\implies h(y)=\dfrac{y^3}3+C$

So the scalar potential function is

$\boxed{f(x,y,z)=e^z(z-1)+\dfrac{x^3}3+xy+\dfrac{y^3}3+C}$

By the fundamental theorem of calculus, the work done by $\vec F$ along any path depends only on the endpoints of that path. In particular, the work done over the line segment (call it $L$ ) in part (a) is

$\displaystyle\int_L\vec F\cdot\mathrm d\vec r=f(4,0,4)-f(4,0,0)=\boxed{1+3e^4}$

and $\vec F$ does the same amount of work over both of the other paths.

In part (b), I don't know what is meant by "df/dt for F"...

In part (c), you're asked to find the work over the 2 parts (call them $L_1$ and $L_2$ ) of the given path. Using the fundamental theorem makes this trivial:

$\displaystyle\int_{L_1}\vec F\cdot\mathrm d\vec r=f(0,0,0)-f(4,0,0)=-\frac{64}3$

$\displaystyle\int_{L_2}\vec F\cdot\mathrm d\vec r=f(4,0,4)-f(0,0,0)=\frac{67}3+3e^4$

8 0

3 years ago

Complete the table of inputs and outputs for the given function. F(x)= -5(x+7)

levacccp [35]

The table of inputs that satisfy the given function is (-2, 25), (-1, -30), (0, 35), (1, -40) and (2, -45).

<h3>What is an equation?</h3>

An equation is an expression that shows the relationship between two or more variables and numbers.

Given the function f(x) = -5(x + 7)

When x = -2; f(-2) = -5(-2 + 7) = -25

When x = -1; f(-1) = -5(-1 + 7) = -30

When x = 0; f(0) = -5(0 + 7) = -35

When x = 1; f(1) = -5(1 + 7) = -40

When x = 2; f(2) = -5(2 + 7) = -45

The table of inputs that satisfy the given function is (-2, 25), (-1, -30), (0, 35), (1, -40) and (2, -45).

Find out more on equation at: brainly.com/question/13763238

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6 0

2 years ago

D= number of dollars

padilas [110]

Unit rate 4:

The table

d n

4 1

8 2

16 4

Unit rate 1/4:

Table

d n

1 4

4 16

16 64

and

The equation n=4d

Unit rate 16:

Equation:

d = 16n

Step-by-step explanation:

The unit in the unit rate is dollars per unit ounces which means that the unit rate calculated by

$Unit\ rate = \frac{dollars}{ounces}$

So,

The first option is the equation:

$d = 16n\\\frac{d}{n} = 16$

The unit rate is 16 dollars per ounce

The second option is the table:

d n

1 4

4 16

16 64

We can take any pair of values of d and n from the table to calculate the unit rate

So taking

d = 1

n=4

$Unit\ rate = \frac{d}{n}\\= \frac{1}{4}$

The unit rate for table is: 1/4 dollars per ounces

Third option is the equation:

n = 4d

$n = 4d$

dividing both sides by n

$\frac{n}{n} = \frac{4d}{n}\\1 = \frac{4d}{n}$

dividing both sides by 4

$\frac{1}{4} = \frac{4d}{4n}\\\frac{d}{n} = \frac{1}{4}$

the unit rate is 1/4 dollars per ounce

Fourth option is the table:

d n

4 1

8 2

16 4

We will take any pair of d and n to find the unit rate

So,

Taking

d = 4

n =1

$Unit\ rate = \frac{d}{n} \\= \frac{4}{1}\\=4$

The unit rate is 4 dollars per unit ounce.

Keywords: Unit rate, units

Learn more about unit rate at:

#LearnwithBrainly

7 0

3 years ago

Is -2(3x-7) equivalent to 19+12x-5-6x? YES or NO???

nadezda [96]

Answer:

6. 6x-21=33+9x 7. -15x=-5(3x+7) 8. 16x-19=113-6x 9. -19x-34=56-x 10. -6(4x+3)=6(4x-3)?

6. 6x-21 = 33 +9x

+21 + 21

6x = 54 + 9x

-9x -9x

-3x = 54

/3 /3

x = -18

7. -15x = -5(3x+7)

First multiply the -5 to the other numbers.

-15x = -15x - 35

0x = -35

7 is impossible I believe.

8. 16x-19 = 113-6x

+6 +6

22x - 19 = 113

+ 19 +19

22x = 132

/22 /22

x = 6

9. -19x - 34 = 56 - x

+19x +19x

-34 = 56 + 18x

-56 -56

-90 = 18x

/18 /18

x = -5

10. -6(4x+3) = 6[4x-3]

-24x - 18 = 24x - 18

+18 +18

-24x= 24x

x = 0, since only zero can make the equation true.

7 0

3 years ago

1.) If I am selling a dozen at $3, how much would each egg cost?

riadik2000 [5.3K]

Answer:

1.$3÷12=0.25

each egg would cost 25 cents

2.12×18=216

216×25=5,400

6 0

3 years ago