Unit 07 Core Practice

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Core pathway

Physical, Engineering & Probability Applications

College-level fluency, interpretation, and verification.

1. A spring with k=20 N/m is stretched from 0.1 m to 0.3 m. Find work.

2. Which statement best describes the central reasoning in Work by a Variable Force & Hooke’s Law?

3. A cylindrical tank of radius 1 m and height 2 m is full of water; pump to the top. Set up work.

4. Which statement best describes the central reasoning in Pumping Fluids & Distributed Lifting?

5. A vertical 2 m by 3 m plate has its top at water surface. Find force.

6. Which statement best describes the central reasoning in Hydrostatic Force on Submerged Surfaces?

7. A rod on [0,2] has density ρ(x)=x+1. Find mass.

8. Which statement best describes the central reasoning in Moments, Centroids & Centers of Mass?

9. For f(x)=2x on [0,1], find P(X≤1/2).

10. Which statement best describes the central reasoning in Probability Density Functions?

11. For f(x)=2x on [0,1], find E[X].

12. Which statement best describes the central reasoning in Expected Value, Variance & Risk Interpretation?

β Beta Program