At what angle with the direction of motion of the ship must the gun be pointed in order to hit the target?

Submitted by Jade Nopre Mijares on

paano po sagutan to?

A ship is traveling at a speed of 20 knots. (A knot is a nautical mile per hour, a nautical mile being approximately 1.1516 statute mile of 5280 feet each.) When directly opposite a target it fires a gun whose projectile has a velocity of 2000 feet a second. At what angle with the direction of motion of the ship must the gun be pointed in order to hit the target?

differential equation: Show that if f and f' are continuous on a ≤ x ≤ b then f and f' are linearly independent on a ≤ x ≤ b

Submitted by Dutsky Kamdon on

Show that if f and f' are continuous on a ≤ x ≤ b and f(x) is not zero for all x on a ≤ x ≤ b,
then f and xf are linearly independent on a ≤ x ≤ b.

The Intuition Behind Integration by Parts (Proof & Example)

Submitted by Kevin rain on

Many students simply memorize the Integration by Parts formula: ∫ u dv = uv - ∫ v du, but understanding where it comes from makes it much easier to remember and apply during exams.

1. The Intuitive Proof (Reverse Product Rule)

The entire concept is actually just the Product Rule for differentiation in reverse.
From the product rule for two differentiable functions, u and v: (uv)' = u'v + uv'

Centroids and Centers of Gravity; Moments of Inertia

Submitted by Rafael Christi… on

Modified True or False:
1. The intersection of the vertical lines at various single support and orientation of a rigid body may approximate the center of gravity of the body.
2. The vertical and horizontal coordinates of the intersection at any reference frame is the centroid of the body.
3. It is assumed that the body is laminar and non-homogenous to determine the centroid.