Arithmetic Sequences Worksheets Grade 12

1. A civil engineer is designing a parabolic arch bridge that spans 80 meters. The arch follows the equation h(x) = -0.02x² + 1.6x, where h is the height in meters and x is the horizontal distance from the left support. To determine the maximum clearance for boats passing under the bridge, the engineer needs to find the maximum height of the arch. What is the maximum height of the bridge arch?
2. A civil engineer is designing a parabolic arch bridge that spans 80 meters. The arch follows the equation y = -0.02x² + 1.6x, where y is the height in meters and x is the horizontal distance from the left support. To determine the maximum clearance for boats passing under the bridge, the engineer needs to find the maximum height of the arch. What is the maximum height of the bridge arch?
3. Kaia is a construction manager overseeing the laying of a new pipeline. The first section of pipe laid is 12 meters long. Each subsequent section must be 9 meters longer than the previous one to account for the increasing elevation gradient. If the project requires a total of 24 sections to complete the pipeline, what is the length of the 24th section, and what is the total length of the entire pipeline?

…and 3 more problems

1. Sequence: 9, 18, 27, 36... Find a₁₇ and sum of first 17 terms.
2. Sequence: 2, 8, 14, 20... Find a₁₈ and sum of first 18 terms.
3. A civil engineer is designing a suspension bridge where the main cable follows the curve y = 2x² - 8x + 10 meters above the water level, where x is the horizontal distance from the left tower in meters. To determine the minimum clearance between the cable and the water, the engineer needs to find the vertex of this parabola. What is the minimum height of the cable above the water?

…and 4 more problems

1. A biomedical researcher is modeling the concentration of a new drug in a patient's bloodstream over time. The concentration function is given by C(t) = 80e^(-0.15t) + 20e^(-0.03t) mg/L, where t is time in hours. The researcher needs to calculate the total drug exposure over the first 24 hours, which is represented by the area under the concentration curve. Find the definite integral of C(t) from t=0 to t=24 to determine the total drug exposure.
2. Mere is training for a marathon and records her weekly running distances. In week 1, she runs 12 km. Each subsequent week, she increases her distance by a constant amount. By week 16, she is running 87 km per week. What is the total distance Mere runs over the first 16 weeks?
3. Sequence: 3, 9, 15, 21... Find a₁₉ and sum of first 19 terms.

…and 4 more problems