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schepotkina [342]
3 years ago
15

What is the value of the expression All of 3.9 multiplied by 10 to the power 5 over all of 1.3 multiplied by 10 to the power 2?

Mathematics
1 answer:
Dima020 [189]3 years ago
4 0
So first write out the expression:
\frac{3.9*10^{5}}{1.3*10^{2}}
take two 10's from the top to cancel with the two 10's on the bottom.
3.9/1.3 is 3.
The answer is 3*10^3
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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
Given the following table, determine the missing value.
sergeinik [125]
We know that
Based on the table
Percent%=[1-Decay factor]*100%
so

for decay factor=0.98
Percent%=[1-0.98]*100%----> 2%

for decay factor=0.50
Percent%=[1-0.50]*100%---->50 %

for decay factor=0.64
Percent%=[1-0.64]*100%----> 36%

for decay factor=0.23
Percent%=[1-0.23]*100%----> 77%

therefore

the answer is
36%

6 0
2 years ago
Jill is trying to find the area of football field with the track around it at her high school. It is composed of a rectangular m
Vaselesa [24]
I am pretty sure it is B or C I think B
7 0
3 years ago
Read 2 more answers
I only need help with #10 :) offering 10 pts
Semenov [28]

Answer:

The length of one side of the square is 3.

Step-by-step explanation:

The perimeter of any given shape is all of the sides added together. So, the perimeter of the triangle is 5x + 4x + 3x. Added together, 12x.

The perimeter of the square is (x + 2)*4. Distributed, it's 4x + 8. Since we know they're equal, set it up like this:

12x = 4x + 8

You then find that x = 1. Plug that into one side of the square, x + 2, to get 3.

8 0
3 years ago
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telo118 [61]

Answer:

i cant see

Step-by-step explanation:

5 0
3 years ago
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