How do i find the intercepts of the equation -5x-4y=10

Mathematics

1 answer:

Y_Kistochka [10]3 years ago

8 0

Answer:

To find the x intercept, let y=0. To find the y-intercept, let x=0. Hence, the x-intercept of the given equation is -2 and the y-intercept is -5/2.

Step-by-step explanation:

Let - 5x - 4y = 10 be the given equation.

Simplify the whole equation by dividing both sides by -1 :

5x + 4y = -10

To get the x-intercept, simply let y=0 :

5x + 4(0) = -10 (substitution)
5x = -10 (evaluate)
x = -2 (simplify by dividing both sides of the equation by 5)

To get the y-intercept, simply let x=0 :

5(0) +4y = -10 (substitution)
4y = -10 (evaluate)
y = -10/4 (simplify by dividing both sides of the equation by 4)
y = -5/2 (simplify the fraction)

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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

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