Find the x- and y- intercepts of the line 6x-2y=24 write your answers as ordered pairs

Mathematics

1 answer:

MrRissso [65]2 years ago

7 0

Answer:

(4,0),(0,-12)

Step-by-step explanation:

You might be interested in

Find the values of x on the interval [−π, π] where the tangent line to the graph of y = sin(x) cos(x) is horizontal. (Enter your

Lady_Fox [76]

A trig identity is asinucosu=a/2sin(2u)So you can write your equation asy=sin(x)cos(x)=1/2sin(2x)Use the crain rule herey′=d/dx1/2sin(2x)=1/2cos(2x)d/dx2x=cos(2x)The curve will have horizontal tangents when y' = 0.y′=0=cos(2x)On the interval [-pi, pi], solution to that isx=±π4,±3π4

6 0

2 years ago

Read 2 more answers

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

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