Algebra Answers

A water pail in your backyard has a small hole in it. You notice that it has drained a total of 2.5 liters in 4 days. What is the average change in water volume each day?

The average change in water volume is   liter(s) per day.

Construct a table of valued of the function using the interval of -5 to 5.

a. g(x)= x³+3x-5/x²

A formula for calculating the magnitude of an earthquake is M=2/3log(EE0)

 that uses the common (base 10) logarithm. This is called the Moment Magnitude Scale (MMS), an alternative to the more well known Richter Scale. One earthquake has magnitude 3.9

 on the MMS. If a second earthquake has 800

 times as much energy as the first, find the magnitude of the second quake.

An environmental study of a certain community suggests that the average daily level of pollution in the air will be Q(p) = √ 0.6p + 20 units when the population is p thousand. It is estimated that after t years the population will be p(t) = 9 + 0.5t 2 thousand.

(a) Express the level of pollution in the air as a function of time.

(b) compute the level of pollution after 5 years from now.

(c) When will the pollution level reach 10 units? 

A certain bacterium grows in culture in a circular region. The radius of the circle, measured in centimeters, is given by r(t) = 6 − 5 (t 2+1) , where t is time measured in hours since a circle of a 1 cm radius of the bacterium was put into the culture.

(a) Express the area of the bacteria as a function of time.

(b) Find the exact and approximate area of the bacterial culture in 2 hours.

(c) Express the circumference of the bacteria as a function of time.

(d) After how long the circumference of the bacteria will be 10π cm.

1. Let f(x) = √ x + 1 − 1/4−x² Compute the following

i. f(0)

ii. f(-3)

iii. f(2)

iv. f(-1)

v. f(3)

vi. Domain(f(x)) 

2. (a) Let f( x/x−2 ) = 3x + 4 find f(x).

(b) Compute difference quotient of the function g(x) = √ x 2 − 9, and simplify your answer.

3. Let f(x) = 1 − x, g(x) = x 2 + bx + c. find b and c such that fog(x) = −X²+ 5x + 4.

2x+4y=8

If P+1/p=8, then find the value of (p-8)^11+(1/p^11) =?

Determine the solution set of the inequality x^(2)-3x-10>0

Give a numerical example to show that "a<b and c<d => a-c<b-d" is false.

Compare the graphs of y = 2x² + 8x + 8 and y=x² without graphing the functions. How can factoring help in comparing the parabolas? Explain in detail.