3

Mathematics

1 answer:

Alecsey [184]3 years ago

7 0

Answer:

O y-x+4

O y=-3x+1 O y=-x-2

Step-by-step explanation:

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I will mark brainliestand 40 points! :)

frosja888 [35]

Answer is D) take 5 blocks away from the left side.

There are 8 blocks on the left and only 3 on the right, 8 - 3 = 5

7 0

3 years ago

Read 2 more answers

Find the range of f(x)=x+3 <br> when the domain (2,4,6)

jarptica [38.1K]

<u>f(x) = x + 3</u>
f(2) = 2 + 3
f(2) = 5

f(4) = 4 + 5
f(4) = 9

f(6) = 6 + 5
f(6) = 11

{(2, 5), (4, 9), (6, 11)}

5 0

3 years ago

Let C be the positively oriented square with vertices (0,0), (1,0), (1,1), (0,1). Use Green's Theorem to evaluate the line integ

liq [111]

Answer:

1/2

Step-by-step explanation:

The interior of the square is the region D = { (x,y) : 0 ≤ x,y ≤1 }. We call L(x,y) = 7y²x, M(x,y) = 8x²y. Since C is positively oriented, Green Theorem states that

$\int\limits_C {L(x,y)} \, dx + {M(x,y)} \, dy = \int\limits^1_0\int\limits^1_0 {(Mx - Ly)} \, dxdy$

Lets calculate the partial derivates of M and L, Mx and Ly. They can be computed by taking the derivate of the respective value, treating the other variable as a constant.

Mx(x,y) = d/dx 8x²y = 16xy
Ly(x,y) = d/dy 7y²x = 14xy

Thus, Mx(x,y) - Ly(x,y) = 2xy, and therefore, the line ntegral is equal to the double integral

$\int\limits^1_0\int\limits^1_0 {2xy} \, dxdy$

We can compute the double integral by applying the Barrow's Rule, a primitive of 2xy under the variable x is x²y, thus the double integral can be computed as follows

$\int\limits^1_0\int\limits^1_0 {2xy} \, dxdy = \int\limits^1_0 {x^2y} |^1_0 \,dy = \int\limits^1_0 {y} \, dy = \frac{y^2}{2} \, |^1_0 = 1/2$