3. On (-∞, ∞), three functions y₁ (x) = cos 2x, y₂(x) = sin² x, y³(x) = cos² x are linearly independent linearly dependent

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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3. On (-∞, ∞), three functions y₁ (x) = cos 2x, y₂(x) = sin² x, y³(x) = cos² x are
linearly independent
linearly dependent
Transcribed Image Text:3. On (-∞, ∞), three functions y₁ (x) = cos 2x, y₂(x) = sin² x, y³(x) = cos² x are linearly independent linearly dependent
4. A cannonball of mass 1kg is shot vertically upward from the top of a building with an unknown velocity
vo(m/sec). After 2 seconds, the ball reaches its maximum height 30 meters from the ground. Neglecting the
air resistance and taking the gravitational acceleration g to be 10(m/sec²), find the height of the building.
6
10
12
14
Transcribed Image Text:4. A cannonball of mass 1kg is shot vertically upward from the top of a building with an unknown velocity vo(m/sec). After 2 seconds, the ball reaches its maximum height 30 meters from the ground. Neglecting the air resistance and taking the gravitational acceleration g to be 10(m/sec²), find the height of the building. 6 10 12 14
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