Algebra Answers

Use a diagrams to present the following:

1. 1/2 -1/8

2. 3/4 - 1/2

3. 1/2 - 1/8

4. 1/4 - 1/8

Solve the following problems by providing the mathematical and pictorial representations:

1. Base problem (by G Lavery)

Baseballs are manufactured in groups of 4, sporting goods stores sell the baseballs in packages of 3. Therefore, 3/4 of a group from the factory are used to make a store package. How many store packages can be made from 3 factory groups of baseballs?

2. Cookies trays problem (by Pollino)

Exactly 7 cookies fit on each tray for baking four - sevenths of a tray is used to make a small box of cookies. If a baker has made8 trays of cookies, how many boxes can be filled?

Use the function f(x)=2^x/x to answer the question.

Which combination could result in the function f(x)?

• adding a quadratic function and a rational function
• dividing an exponential function by a linear function
• adding an exponential function and a linear function

(select the correct option)

find the equation of the line that has a gradient of 3 and goes through (1,1)

An economy is forecasted to grow continuously so that the gross national product (GNP), measured in billions of dollars, after ‘t’ years is given as

GNP = 80.e^0.02t

(a)   Calculate the current GNP and the GNP in the three years’ time.

(b)In how many years is GNP forecasted to be $88 billion

Give a practical example of the studied mathematics topics in your particular fields (Biotechnology/Genetics/Microbiology). Example: Geometric sequence It is possible to predict the number of cells in a population when they split by binary fission (The most common mechanism of cell replication in bacteria) at a constant rate. As an example, consider what happens if a single cell divides every 30 minutes for 24 hours. Starting from two cells, the following table shows the increase in cell numbers for the first three generations.

No. of generations No. of Cells

1 2

2 4

3 8

Hence, the number of cells forms a geometric sequence 2, 4, 8, . . . and with a1 = 2 and r = 2, we can find its general term as follows: an = a1r n−1 an = 2(2)n−1 an = 2n Using this general term, we can find number of cells given any number of generation.

The second term of a geometric series is 3 and the common ratio is 4/ 5 . Find the sum of first 23 consecutive terms of this series. 

. Find the term independent of x in the expansion of (x^ 3+2/x)^ 20

2. A publishing house hed 40% of its total sales in Math books, 10% in pupil diary, 20%

in Filipino books, 20% in Science books and 10% in English books. If the sales

amounted to P1,250,000.00 find the total sales in each kind of book. What book had

the least sales

Solution: