For the following exercises, graph the inequality. 1/4 x2 + y2 < 4

For the following exercises, graph the inequality.

1/4 x2 + y2 < 4

Expert Solution

Consider the following inequality

1/4x2 + y2 < 4

First, graph the corresponding equation 1/4x2 + y2 < 4. Since 1/4x2 + y2 < 4 has a less than symbol, draw the graph with a dashed line. Then choose points to test both inside and outside the parabola. Let’s test the points (-7, 1) and (1, 2). One point is clearly inside the parabola and the other point is clearly outside as shown in the following graph of inequality:

Nabeel answered 1 year ago

For the following exercises, graph the inequality. y > x2 − 1

If C is the part of the circle (x2)2+(y2)2=1(x2)2+(y2)2=1 in the first quadrant, find the following...

If C is the part of the circle (x2)2+(y2)2=1(x2)2+(y2)2=1 in the first quadrant, find the following line integral with respect to arc length. ∫C(8x−6y)ds

Consider the unit sphere x2 +y2 +z2 = 1 and the cone (z+√2)2 = x2 +y2....

Consider the unit sphere x2 +y2 +z2 = 1 and the cone (z+√2)2 = x2 +y2. Show that these surfaces are tangent where they intersect, that is, for a point on the intersection, these surfaces have the same tangent plane

For Exercises 1-4 below, (a) verify that y1 and y2 satisfy the given second-order equation, and...

For Exercises 1-4 below, (a) verify that y1 and y2 satisfy the given second-order equation, and (b) find the solution satisfying the given initial conditions (I.C.). 2. y′′−3y′+2y=0; y1(x)=e^x,y2(x)=e^2x. I.C.y(0)=0,y′(0)=−1. 3. y′′−2y′+y=0; y1(x)=e^x,y2(x)=xe^x. I.C.y(0)=1,y′(0)=3.

Solve: y' = (y2-6y-16)x2 y(4) = 3

Si U=(x2+y2+z2)-1/2 , demuestre que ∂2U/∂x2+∂2U/∂y2+∂2U/∂z2=0

Evaluate or solve the following A) dy/dx= -(2x2+y2)/(2xy+3y2) B)dy/dx=(1+y2)/(1+x2)xy C) (x2+1)dy/dx+2xy=4x2 given that when x=3,y=4 Already...

Evaluate or solve the following A) dy/dx= -(2x2+y2)/(2xy+3y2) B)dy/dx=(1+y2)/(1+x2)xy C) (x2+1)dy/dx+2xy=4x2 given that when x=3,y=4 Already rated.Best chegg expert

1. Let ρ: R2 ×R2 →R be given by ρ((x1,y1),(x2,y2)) = |x1 −x2|+|y1 −y2|. (a) Prove...

1. Let ρ: R2 ×R2 →R be given by ρ((x1,y1),(x2,y2)) = |x1 −x2|+|y1 −y2|. (a) Prove that (R2,ρ) is a metric space. (b) In (R2,ρ), sketch the open ball with center (0,0) and radius 1. 2. Let {xn} be a sequence in a metric space (X,ρ). Prove that if xn → a and xn → b for some a,b ∈ X, then a = b. 3. (Optional) Let (C[a,b],ρ) be the metric space discussed in example 10.6 on page 344...

Solve the following equations in non-negative integers. 1. x2 - y2 = 221 2. a +...

Solve the following equations in non-negative integers. 1. x2 - y2 = 221 2. a + b = ab 3. gcd(a,b)lcm(a,b) = b + 9 4. x4 + 2x3 - y2(1+2x) + x2(1-y2) = 2299

Show that the number of solution to x2 - y2 ≡ a (p) is p-1 if...

Show that the number of solution to x2 - y2 ≡ a (p) is p-1 if p not divides a and 2p -1 if p divides a, Use u = x+y and v= x-y Then show that summation y=0 to p-1 ((y^2 +a)/p) = -1 if p not divides a and = p-1 if p divides a

Question