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Anettt [7]
3 years ago
8

Find S15 for the geometric series 72 + 12 + 2 + 1/3 +…

Mathematics
1 answer:
Gemiola [76]3 years ago
5 0
S1 = 72
S2 = 12 = 72*(1/6)
S3 = 2 = 72*(1/6)^2
.
.
.
S15 = 72*(1/6)^14 = 9.18*10^(-10)
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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

We conclude that the line integral is 1/2

4 0
3 years ago
How do you convert 7/6 into a mixed number
Natali [406]
Wel its kinda difficult to say but look on how much times 6 can fit into 7 which is 1 but that will be 6,so in order to become seven you need 1 which is our left over number,so in the end you will get 1 whole and 1/6 and you use the leftover number as your numerator and just leave the 6 as it was.Whoof that was long but its no nearly as long as i explain it.
6 0
3 years ago
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Zohar is using scissors to cut a rectangle with a length of 5x – 2 and a width of 3x + 1 out of a larger piece of paper. Which e
sweet-ann [11.9K]

Answer with Step-by-step explanation:

Zohar cut a rectangle with a length of 5x – 2

and a width of 3x + 1

We know that:

Perimeter of rectangle is:

Perimeter=2(length+width)

                =2(5x-2+3x+1)

                =2(8x-1)

                =16x-2

Hence, expression which can be used to find the perimeter of the rectangle is:

16x-2

Now, when x=4

16x-2=16×4-2

        =62

Hence, when x=4 ,Perimeter=62

4 0
3 years ago
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I put an answer but I’m unsure of it, any help would be much appreciated!!
Darya [45]
First you need to change 45 feet to 540 inches.

Now you can compare the two ratios:
1 : 25 and 25 : 540

We now need to change the second ratio to a unit rate:
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8 0
3 years ago
-3[2-(y-5)]-4[3(y+1)-(6-y)(-2)]
Natalka [10]

Answer:

−y−81

Step-by-step explanation:

8 0
3 years ago
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