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labwork [276]
3 years ago
13

Is this right. If it is thanks

Mathematics
1 answer:
Natali [406]3 years ago
4 0

Answer:

yes

Step-by-step explanation:

yes

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26 percent of 200 is 52 :)
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3 years ago
Suppose F⃗ (x,y)=(x+3)i⃗ +(6y+3)j⃗ . Use the fundamental theorem of line integrals to calculate the following.
Scorpion4ik [409]

In order to use the fundamental theorem of line integrals, you need to find a scalar potential function - that is, a scalar function <em>f(x, y)</em> for which

grad <em>f(x, y)</em> = <em>F</em><em>(x, y)</em>

This amounts to solving for <em>f</em> such that

∂<em>f</em>/d<em>x</em> = <em>x</em> + 3

∂<em>f</em>/∂<em>y</em> = 6<em>y</em> + 3

Integrating both sides of the first equation with respect to <em>x</em> gives

<em>f</em> = 1/2 <em>x</em> ^2 + 3<em>x</em> + <em>g(y)</em>

Differentiating with respect to <em>y</em> gives

∂<em>f</em>/∂<em>y</em> = d<em>g</em>/d<em>y</em> = 6<em>y</em> + 3

Solving for <em>g</em> gives

<em>g</em> = ∫ (6<em>y</em> + 3) d<em>y</em> = 3<em>y</em> ^2 + 3<em>y</em> + <em>C</em>

and hence

<em>f(x, y)</em> = 1/2 <em>x</em> ^2 + 3<em>x</em> + 3<em>y</em> ^2 + 3<em>y</em> + <em>C</em>

<em />

(a) By the fundamental theorem, the integral of <em>F</em> along any path starting at the point <em>P</em> (1, 0) and ending at <em>Q</em> (3, 3) is

∫ <em>F</em><em>(x, y)</em> • d<em>r</em> = <em>f</em> (3, 3) - <em>f</em> (1, 0) = 99/2 - 7/2 = 46

(b) Now we're talking about a closed path, so the integral is simply 0. We can verify this by checking the integral over the origin-containing paths:

• From the origin to <em>P</em> :

∫ <em>F</em><em>(x, y)</em> • d<em>r</em> = <em>f</em> (1, 0) - <em>f</em> (0, 0) = 7/2 - 0 = 7/2

• From <em>Q</em> back to the origin:

∫ <em>F</em><em>(x, y)</em> • d<em>r</em> = <em>f</em> (0, 0) - <em>f</em> (3, 3) = 0 - 99/2 = -99/2

Then the total integral is 7/2 + 46 - 99/2 = 0, as expected.

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3 years ago
Will mark brainliest first correct answer asap
Flura [38]

Answer is in the file below

tinyurl.com/wpazsebu

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3 years ago
Since f is parallel to line g, use the diagram to the right right to answer the following question (I need help with problem D a
Snezhnost [94]

Given,

The line f and g are parallel lines.

a)The measure of angle 2 is 117 degree.

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\begin{gathered} \angle2=\angle7 \\ \angle7=117^{\circ} \end{gathered}

The measure of angle 7 is 117 degree.

b)The measure of angle 4 is 68 degree.

By sum of adjacent angle between two parallel lines property,

\begin{gathered} \angle4+\angle6=180^{\circ} \\ \angle6=180^{\circ}-68^{\circ} \\ \angle6=112^{\circ} \end{gathered}

The measure of angle 6 is 112 degree.

c)The measure of angle 5 is 32 degree.

By alternate interior angle property,

\begin{gathered} \angle4=\angle5^{} \\ \angle4=32^{\circ} \end{gathered}

The measure of angle 4 is 32 degree.

d)The measure of angle 7 is 121 degree.

By corresponding angle property,

\begin{gathered} \angle7=\angle3^{} \\ \angle3=121^{\circ} \end{gathered}

The measure of angle 3 is 121 degree.

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