The equation r(t) = (2t + 4) i + (t2 - 7) j + (t) is the position of a particular in space at time t. Find the particle's velocity and acceleration vectors. Then write the particle's velocity at t = 1 as a product speed and direction. What is the velocity vector? What is the acceleration vector? Write the velocity vector at t = 1 as a product of the speed and direction. (Type exact answers, using radicals as needed.) The equation r(t) = (6 cos t) i + (2 sin t) j + (t) k is the position of a particle in space at time t. Find the particle's velocity and acceleration vectors. Then write the particle's velocity at t = 0 as a product of its speed and direction. The velocity vector is The acceleration vector is velocity vector at t = 0 written as a product of the speed and direction is (Type exact answers, using radicals as needed.) The equation k is the position of a particle in space at time t. Find the angle between the velocity and acceleration vectors at time t = 0. What is the angle? (Type an exact answer, using n as needed.)

What is the volume of a rectangular prism if the length is 10.4 mm the width is 5 mm in the height is 8 mm

Adj has a total of 1075 dance and rock songs on her system. the dance selection is 4 times the size of the rock selection. write a system of equations to represent the situation.

For this option, you will work individually. the pythagorean theorem can be used in many real-world scenarios. part 1 write your own real-world scenario where the pythagorean theorem can be applied to find a missing piece. you may choose to write a problem that is two- or three-dimensional in nature. be sure that you will be able to draw a diagram of your scenario. write out your problem and submit it for part 1. be sure to end your scenario with a question. part 2 draw a diagram of the scenario you created in part 1. you may draw by hand and scan and upload your drawing or create a computer-generated drawing for submission. be sure to label all parts and dimensions of the drawing. part 3 solve the question that you posed in part 1. show all of your steps in answering the question. for this option, you will need to submit all three parts for full credit—your real-world problem and question, the diagram that you created, and your work solving the problem, showing all steps. * note that your instructor is looking for your own original idea. while it is acceptable to use the internet for research and inspiration, academic integrity policies apply.