Question

A seal dives below the ice in search of fish. Its path can be modelled by d=81²-vt where d is the depth in decameters and t the

V
time in minutes. Use the equation above to answer questions about the seal's journey into the deep sea with an initial velocity of 24
decameters per minute. Use the graph below to help answer the questions.
-0.5
-10
depth (dam)
015
10 15 2.0
time (min)
3,5
4/0


Assessment Instructions
Show and explain all steps in your responses to the following parts of the assignment using the Algebra concepts discussed within the course. All mathematical steps and explanations must be typed up and formatted using the equation editor.
Part 1: Create the equation for the path of the seal after t minutes.

Part 2: Find the time it takes for the seal to reach a height of 0. Interpret both solutions.

Part 3: Find the time it takes to reach the bottom of its trajectory. (You must use Algebra concepts learned in this course. Any.
Calculus shown is an automatic zero).

Part 4: Find the maximum height.

Part 5: Using the quadratic equation,
find the time it takes to reach a height of -14 decameters. Round your answer to the nearest tenth. Interpret both answers.

Answer 1

The answers are matched based on geometric principles: isosceles triangles (8-A and 9-D), angle-side-angle inequality (10-B), and parallelograms (11-C) properties.

The image presents a set of geometric problems, requiring matching of given information with appropriate conclusions.

For problem 8, "AB = BC, m∠1 = m∠2," option A is correct because if two sides and their included angles are equal, the opposite angles will also be equal due to the properties of an isosceles triangle.

In problem 9, "AD ≅ EC, AD = CD," option D matches as it implies that triangle AED is an isosceles triangle and thus AE cannot be equal to EC.

For problem 10, "m∠9 < m∠10, BE = ED," option B fits as angle-side-angle inequality indicates that side AD will be greater than AB.

Lastly for problem 11, "AB = BC; AD ≅ CD," option C aligns since if two pairs of sides are equal in length respectively then their opposite angles will also be congruent due to the properties of a parallelogram.