Which of the following would triple the volume of the egyptian square-based pyramid below? a. multiply only the height by 3. b. add 3 to each dimension of the pyramid. c. multiply every dimension of the pyramid by 3. d. add 3 to the slant height.

The volume of a pyramid with a square base is given by: . This is the way the volume is usually given but we can also multiply the two terms and write it this way: .

We are looking to triple the Volume which means we want to multiply it by 3. With respect to our volume equation, we multiply both sides by 3 to obtain:


So, we are looking to see which of the choices given produces a volume equal to .

The first choice is the right answer. Notice what happens when we take the volume formula and multiply the h by 3. We get: and since there is a 3 in both the numerator (top) and the denominator (bottom) we can cross these out. That leaves us with a volume equal to which is what we were looking for!

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0

answer: the function g(x) has the greatest slope.