Answer: Find the discriminant
Check explanation
Step-by-step explanation:
b^2-4ac
if it is equal to 0 there is no solution
Greater then 0 there is 2 real solution
Less then 0 there is 1 real
3^2-4(2*-1)
9-4(-2)
9(8)
72 there is at least one real solution
Answer:
Step-by-step explanation:
Given:
x = 2cost,
t = (1/2)arccosx
y = 2sint
dy/dx = dy/dt . dt/dx
dy/dt = 2cost
dt/dx = -1/√(1 - x²)
dy/dx = -2cost/√(1 - x²)
Differentiate again to obtain d²y/dx²
d²y/dx² = 2sint/√(1 - x²) - 2xcost/(1 - x²)^(-3/2)
At t = π/4, we have
(√2)/√(1 - x²) - (√2)x(1 - x²)^(3/2)
26>-9
This states that 26 is greater than -9. Look at the > sign like it's an alligator's mouth - the alligator wants to eat the bigger side, and 26 is clearly bigger than -9, so the alligator wants to eat 26!
Answer:
D) a hyperbola
Step-by-step explanation:
IMO, the image is not helpful, as it suggests the ends of the curve are nearly parallel to each other. In fact, the ends of the curve asymptotically approach straight lines parallel to the sides of the cone. That is, there are asymptotes that form an X shape. This is a characteristic of a hyperbola.
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A parabola is formed when the plane cuts the cone parallel to one side. That cut plane only intersects one nap of the cone. At a shallower angle yet, one gets an ellipse. Parallel to a base, one gets a circle.
