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3 years ago

Last week, Sarah worked for 13 hours at her part time job. If she earned $143.00 for the week, how much did she earn per hour?

Mathematics

1 answer:

bezimeni [28]3 years ago

8 0

Answer:

11 dollars an hour.

Step-by-step explanation:

143/13=11

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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

Question 7<br> Which is the quotient of 1/5 divided by 3??

blondinia [14]

Answer:

1/5 divided by 3 =1/15 because when dividing a fraction by a whole number, it is gonna end as a fraction so the answer is 1/15. All you do is just multiply the denominator times the whole number and you will get your answer. Have a nice day! If this helped then please mark as brainliest.

6 0

3 years ago

A few students conducted a study on how many peanuts it would take to completely fill a jar. They had the following data to help

Marizza181 [45]

Answer:

370 peanuts

Step-by-step explanation:

65/108 = 0.60185

90/150 = 0.6000

In each case, the number of peanuts is either exactly or very close to 60% of the volume.

A cylinder with radius 3.5 cm and height 16 cm has volume:

V = (pi)r^2h

V = (3.14159)(3.5 cm)^2(16 cm)

V = 615.752 cm^3

We take 60% of the volume to estimate the number of peanuts.

60% * 615.752 cm^3 = 369.451

Answer: 370 peanuts

8 0

3 years ago

What describes the slope and y-intercept of the line for this equation<br> x - 5 = 0

DanielleElmas [232]

Isn’t it 5 or no cuz 5-5=0 that’s easy

3 0

3 years ago

2/10 = 20%= 0.2<br> True or false

Shalnov [3]

Answer:

True

Step-by-step explanation:

8 0

3 years ago