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NARA [144]
4 years ago
15

(1 point) In this problem we consider an equation in differential form M dx + N dy = 0. (8x + 8y)dx + (8x + 4y)dy = 0 Find My =

8 Nx = 8 If the problem is exact find a function F(x, y) whose differential, dF(x, y) is the left hand side of the differential equation. That is, level curves F(x, y) = C, give implicit general solutions to the differential equation. If the equation is not exact, enter NE otherwise find F(x, y) (note you are not asked to enter C) F(x, y) =
Mathematics
1 answer:
OLga [1]4 years ago
3 0

The ODE is exact because M_y=N_x. Then

F_x=8x+8y\implies F(x,y)=4x^2+8xy+g(y)

F_y=8x+g'(y)=8x+4y\implies g'(y)=4y\implies g(y)=2y^2+C

So we have

F(x,y)=4x^2+8xy+2y^2=C

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(a) x > 4   (b) y < -2

Step-by-step explanation:

Domain is referring to the x-values while the range is referring to the y-values.

Since the function (the line) has a circle at the point (4, -2), the function will be exclusive at that coordinate.

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7 0
3 years ago
Please help me if you can with this math problem
Viefleur [7K]

Answer:

m<BAC = 34

Step-by-step explanation:

It is given that (<BOC) is a central angle with a degree measure of (68). A central angle is an angle whose vertex is the center of the circle. (<BAC) is an inscribed angle, an angle whose vertex is on the circumference (perimeter) of the circle. Arc (BC) connects the ends of both of these angles.

The central angle theorem states that the measure of the central angle is equivalent to its surrounding arc. Using this theorem, one can state the following,

m<BOC = BC = 68

The inscribe angle theorem states that the measure of the arc surrounding the inscribed angle is twice the measure of the inscribed angle. Applying this theorem, one can state the following,

2(m<BAC) = (BC)

2 (m<BAC) = 68

m<BAC = 34

8 0
3 years ago
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