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larisa86 [58]
3 years ago
10

Let c be the curve which is the union of two line segments, the first going from (0, 0) to (4, 4) and the second going from (4,

4) to (8, 0). computer the line integral ∫c4dy−4dx
Mathematics
1 answer:
victus00 [196]3 years ago
4 0
First of all we need to find a representation of C, so this is shown in the figure below.

So the integral we need to compute is this:

I=\int_c 4dy-4dx

So, as shown in the figure, C = C1 + C2, so:

I=\int_{c_{1}} (4dy-4dx)+\int_{c_{2}} (4dy-4dx)=I_{1}+I_{2}

Computing first integral:

c_{1}: y-y_{0}=m(x-x_{0}) \rightarrow y=x

Applying derivative:

dy=dx

Substituting this value into I_{1}

I_{1}=\int_{c_{1}} (4dx-4dx)=\int_{c_{1}} 0 \rightarrow \boxed{I_{1}=0}

Computing second integral:

c_{2}: y-y_{0}=m(x-x_{0}) \rightarrow y-0=-(x-8) \rightarrow y=-x+8

Applying derivative:

dy=-dx

Substituting this differential into I_{2}

I_{2}=\int_{c_{2}} 4(-dx)-4dx=\int_{c_{2}} -8dx=-8\int_{c_{2}}dx

We need to know the limits of our integral, so given that the variable we are using in this integral is x, then the limits are the x coordinates of the extreme points of the straight line C2, so:

 I_{2}= -8\int_{4}^{8}}dx=-8[x]\right|_4 ^{8}=-8(8-4) \rightarrow \boxed{I_{2}=-32}

Finally:

I=\int_c 4dy-4dx=0-32 \rightarrow \boxed{I=-32}
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Please help me with this
Zanzabum

Answer:

x=

−4y+32

9

Step-by-step explanation:

Let's solve for x.

y=

−9

4

x+8

Step 1: Flip the equation.

−9

4

x+8=y

Step 2: Add -8 to both sides.

−9

4

x+8+−8=y+−8

−9

4

x=y−8

Step 3: Divide both sides by (-9)/4.

−9

4

x

−9

4

=

y−8

−9

4

x=

−4y+32

9

I think this is the right answer.

6 0
3 years ago
The probability that a fair coin tossed 10 tines will land heads up on all ten tosses is 1 out of
Sidana [21]
1/10 because you will do it 10 times
6 0
3 years ago
i need help on math
dolphi86 [110]
X=2
2x-3=-x+3

add three to both sides
add 1x to each side
should be left with 3x=6
divide both sides by 3 to get x alone
your answer then is x=2
7 0
3 years ago
EMERGENCY PLEASE HELP STRUGGLING! The triangles in each pair are similar.
Ludmilka [50]

Answer: The missing length is 120 {option C}

Step-by-step explanation: What we have in the question is a triangle placed on top of another triangle and as shown in the attached diagram we can separate them into triangles BFC and GFH.

A close observation shows that line BC is parallel to line GH. Hence we have two similar triangles, and we can determine their similarity ratios as follows;

BF/FC = GF/FH

Similarly BF/BC = GF/GH

We can also express the following ratio

FC/FH = BC/GH

Therefore to calculate the missing side, which is GF, we can use the ratio

FC/FH = FB/FG

30/100 = 36/FG

By cross multiplication we now have 30 (FG) = 100 (36)

30FG = 3600

Divide both sides of the equation by 30

FG = 120

5 0
2 years ago
THE SUM OF TWO INTEGERS WITH DIFFERENT SIGNS IS 8.GIVE TWO POSSIBLE INTEGERS THAT FIT THIS DESCRIPTION.
marusya05 [52]
Sum of two integers with different signs is equal to 8.

There are several answers:

+12 and -4
+10 and -2
+11 and -3

ETC.
6 0
3 years ago
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