15. Solve by factoring: 3x? - 15x + 12 = 0

Mathematics

1 answer:

Lostsunrise [7]3 years ago

3 0

The solution for that proplem is X=4,1

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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

The area of a rectangular parking lot is 7031m? If the with of the parking lot is 79m, what is its length?

serg [7]

The length of the parking lot is 89m.

To find the length, we can abide by the following formula:

L = A/W

where L is the length, A is the area, and W is the width.

Given this formula, we can set up an equation:

7,031 / 79 = 89

The length of the parking lot is 89 meters.

7 0

1 year ago

Read 2 more answers

C/2 - 3 + 6/d when c=14 d=3

Nataliya [291]

Answer:

Step-by-step explanation:

14/2 - 3 + 6/3

Divide 14 by 2 to get 7.

7−3+6/3

Subtract 3 from 7 to get 4.

4+6/3