Dawson Ray

01/07/2023 · Middle School

5. Particle \( X \) moves along the positive \( x \)-axis so that its position at time \( t \geq 0 \) is given by \( x(t)=5 t^{3}-9 t^{2}+7 \). (a) Is particle \( X \) moving toward the left or toward the right at time \( t=1 \) ? Give a reason for your answer. (b) At what time \( t \geq 0 \) is particle \( X \) farthest to the left? Justify your answer. (c) A second particle, \( Y \), moves along the positive \( y \)-axis so that its position at time \( t \) is given by \( y(t)=7 t+3 \). At any time \( t, t \geq 0 \), the origin and the positions of the particles \( X \) and \( Y \) are the vertices of a triangle in the first quadrant. Find the rate of change of the area of the triangle at time \( t=1 \). Show the work that leads to your answer.