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In-s [12.5K]
3 years ago
13

Somebody helppppp !!!

Mathematics
1 answer:
Serga [27]3 years ago
8 0
The first one!! it should be correct
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Rationalize the denominator and simplify. 6 /5-3
sattari [20]

Answer:

-9/5

Step-by-step explanation:

Step 1: Take the LCM in the denominator

6/5-3

multiply the numerator and denominator by 5 to make the denominator 5.

<u>6</u>-<u>3</u> (x5)

5  1 (x5)

=<u>6-15</u>  

   5

= <u>-9</u>

   5

!!

6 0
3 years ago
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
One serving of milk has 120 Calories. If one serving is equal to 1 cup, how many Calories are in 1 fluid ounce? (1 cup = 8 fluid
aleksandrvk [35]

Answer:

15

Step-by-step explanation:

the answer should be 15 because, if one cup is 120 calories or 8 fluid ounces is 120 calories,  divide 120 by 8 so you can find how many calories one fluid ounce is.

8 0
3 years ago
Simplify (6 + 8i) (4 - 7i)
erica [24]
The answer is 80-10i
8 0
3 years ago
Read 2 more answers
Delia measured her bathtub to be 2 meters long. Which of these is an equivalent measurement?
snow_lady [41]
The answer would be D) 78.7 inches is equivalent to 2 meters. 
6 0
3 years ago
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