Choose the sentence that might be found in a personal narrative that correctly uses both a gerund and an infinitive.
a. acting became my door to a world of adventure and excitement.
b. although i had participated in school plays since i was in first grade, my parents did not appreciate my acting.
c. if only they had realized that to act was the focus of my dreaming.
d. i knew i had to show them how i felt by saving all my money to attend drama camp.

Let's start with an infinitive: it has a form "to..." - only sentences C and D have a phrase like this, so we can exclude other options.

Among those, C does not have a gerund, which is a verbal form: "dreaming" has a function of a noun there.

So the correct answer is the remaining one, D.

    m₁v₁ + m₂v₂ = (m₁ + m₂)vmomentum is conserved.the left-hand side of the equation represents the momentum in the system before the collision.the right-hand side represents the momentum in the system after the collisionm₁ and v₁ represents the mass and the velocity of the physics blockm₂ and v₂ represents the mass and velocity of the ball of puttyv represents the final velocity of the combined mass.the question states the two masses stick together. they combined mass has its own velocity with the body mass the sum of the two objects' massestheir combined momentum is (m₁ + m₂)vto find the magitude of (m₁ + m₂)v, we need to add the vectors on the left-hand side of the equation: m₁v₁ + m₂v₂.note the diagram. i have positioned the vectors in accordance with their directions.the magnitude of the resultant can be calculated using the pythagorean theorem since this is a right triangle situation (north and west are perpendicular)|(m₁ + m₂)v| =  √[ (m₁v₁)² + (m₂v₂)² ]|(m₁ + m₂)v| =  √[ (1.5kg·8.0m/s)² + (0.40kg·20m/s)² ]|(m₁ + m₂)v| =  14.4 kg m/sfor two significant figures (assuming that 20m/s is two), this rounds to 14 kg m/s

When is this