Use the following expression to answer the questions below:
a. Simplify the expression down to one rational expression.
b. Explain the steps you used to do the simplification.
c. Are there any values cannot be? Explain.
d. Find the values of that make the expression equal to 0. Explain the steps you used to find these values.
To calculate the volume of a chemical produced in a day a chemical manufacturing company uses the following formula below:
where represents the number of units produced. This means two chemicals are added together to make a new chemical and the resulting chemical is multiplied by the expression for the holding container with respect to the number of units produced. The equations for the two chemicals added together with respect to the number of unit produced are given below:
The equation for the holding container with respect to the number of unit produced is given below:
a. What rational expression do you get when you combine the two chemicals?
b. What is the simplified equation of ?
c. What would the volume be if 50, 100, or 1000 units are produced in a day?
d. The company needs a volume of 3000 How many units would need to be produced in a day?
The following diagram represents all of the stages of a shrinking iceberg. The iceberg is circular, and when it started out, it had a radius of 100 feet. The iceberg shrank to a radius that was 75% of its original size every hour. Each circle in the drawing represents the size of the iceberg in each of the successive hours it was shrinking. Using this information, answer the questions below the image:
a. Is this a geometric series or an arithmetic series? Explain why you chose this answer.
b. Describe the steps you would use to calculate the radius of the 6th circle.
c. Assuming this pattern continued forever, what would be the total length if you added all of the circlesâ€™ radii* together? Explain your answer.
*The word is the plural of .
|A Venn diagram is a common way for teachers and students to organize information. Have you ever seen a three-circle Venn diagram?
a) Create a Venn diagram by writing equations for three circles. Your equations do not have to create a perfect replica of this image, but your circles must overlap in a similar way. It may help you to visualize your equations if you graph them! What are the equations to your circles?
Scientists have collected a sample of the bacteria responsible for an illness and determined the equation below:
a. Describe the graph of the exponential equation. Is it growth or decay? Does it have any asymptotes?
You are visiting a Redwood tree forest and want to verify the height of one of the trees. You measure its shadow along the ground and use trig to calculate the height.
a. What is the measure of the other acute angle?
The math teacher and cheerleading coach have teamed up to help the students do better on their math test. The cheer coach, using dance move names for the positioning of their arms, yells out polynomial functions with different degrees.
a1. Constant Function:
When it comes time to take the test not only do the students have to describe the shape of the polynomial function, you have to find the number of positive and negative real zeros, including complex. Use the equation below:
b. Identify all possible rational zeros.