### Algebraic Expressions

**Module 05 Content: Algebraic Expressions**

**Scenario**

The height, in feet, of an object shot upwards into the air with an initial velocity, in feet per second, of *vi*, after *t *seconds is given by the formula:

Use the equation above to answer questions about a model rocket launched from the ground into the air with an initial velocity of 352 feet per second. Use the graph below to help answer the questions.

### Assessment Instructions

Show and explain all steps in your responses to the following parts of the assignment. All mathematical steps must be formatted using the equation editor.

**Part 1**: Create the equation for the height of the rocket after *t *seconds.

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

**Part 3**: Find the time it takes to reach the top of its trajectory.

**Part 4**: Find the maximum height.

**Part 5**: Find the time it takes to reach a height of 968 feet. Round your answer to the nearest tenth.

2) **Module 06 Assignment – Glazed Icing Rational Algebraic Expressions**

### Scenario

Your donut shop has perfected a method for the perfect glazed icing by slowly mixing whole milk with the confectioner’s sugar while exposed to low heat. Your mixing tank starts with 10 fluid ounces of milk and 10 ounces of sugar. You continue adding sugar at a rate of 10 ounces per minute and milk at 1 ounce per minute, as depicted by the two equations below:

Where *S* represents the number of ounces of sugar, *M* represents the ounces of milk, and *t* represents the time in minutes. The ideal icing will have a ratio of 8 ounces of sugar per ounce of milk.

### Assessment Instructions

Show and explain all steps in your responses to the following parts of the assignment. All mathematical steps must be formatted using the equation editor.

**Part 1**: Create a rational equation to represent the concentration (*C*) in ounces of sugar per ounce of milk.

**Part 2**: Find the domain of the concentration equation.

**Part 3**: Will we ever encounter a time when the rational equation is undefined? Explain your reasoning.

**Part 4**: Calculate the concentration after five minutes.

**Part 5**: How long does it take to reach a concentration of 8 ounces of sugar per ounce of milk?