# college algebra: volumes, polynomials, points, etc.

#### arodss3

##### New member
Im having problems with these questions. Would appreciate any help given.

1. 1. The volume of a cylindrical tank is given by formula V=PIE(SYMBOL)h r^2 where h is the height of the cylinder and r is its radius. Find the volume to the nearest tenth of a cubic foot of a cylinder tank that has a radius of 3 feet and a height of 5 feet.
a. 47.1 cu.ft
b. 49.2 cu.ft
c.135.0 cu.ft
d.141.4 cu.ft
2. Express as a polynomial (x+a)[x^2-ax/x]
a.x^2
b.x^2-2ax-a^2
c.x^2-2ax+a^2
d.x^2+ax+a^2
3.If points A,B,and C lie on a cordinate line and points A and B have coordinates 15 and 7 respectively, then which of the possible coordinates for point C satisfy(ies) d(A,C)<d(B,C)?
A.12
B.17
C.Both (a) and (b)
d.neither (a) nor (b)
4. Solve the inequality 21/15-3X<0, AND EXPRESS THE SOLUTION AS AN INTERVAL.
A.(5,o0)
B.(7,o0)
C.(-o0,5)
D.(-o0,7)
5.Find the distance between the points A(4,-3) and B(-4,3).
A.5
B.7
C.10
D.14
6.Find the domain of f(x)=7+squarerootsymbol 3x+21, and express it using interval notation
A. [-7,o0)
B. [0,o0]
c. [7,o0]
d. [21,o0]
7. If f(x)=x(x+1)(x- 4),use interval notation to give all values of x where f(x)>0.
a. (-1,4)
b. (-1,0) u(symbol looks like a horseshoe) (4,o0)
c. (-1,4)
d. (0,1) u (4,o0)
8. The degree three polynomial f(x) with real coefficents and leading coefficent 1, had -3 and +4i among its roots. Express f(x) as a product of linear and quadratic polynomials with real coefficients.
a. f(x)=(x+3)(x^2+16)
b. f(x)=(x+3)(x^2+8x +16)
c. f(x)=(x+3)(X^2-8X+16)
d. f(x)=(x-3)(x^2+16)
9. Find the inverse of the function f(x)=x^1/3+2.
a.(x-2)^3
b.x^1/3+2
c.(y-2)^3
d.doesnt exist
10. a bacteria culture with a count of 720 at 8:00 AM, and after t hours is expected to grow to f(t)=720(3/2)^t. ESTIMATE THE NUMBER OF BACTERIA IN THE CULTURE AT 11:00 A.M. THE SAME DAY.
A.1620
B.2160
C.2430
D.2880

#### stapel

##### Super Moderator
Staff member
arodss3 said:
Im having problems with these questions. Would appreciate any help given.
Um... Do you have no idea how even to start any of these...? :shock:

arodss3 said:
I1. 1. The volume of a cylindrical tank is given by formula V=PIE(SYMBOL)h r^2 where h is the height of the cylinder and r is its radius. Find the volume to the nearest tenth of a cubic foot of a cylinder tank that has a radius of 3 feet and a height of 5 feet.
I don't know what a "PIE" symbol would be (in mathematics). Do you perhaps mean the Greek letter "pi", being approximately equal to 3.14159...?

You're given a formula with three variables, and you are given the values of two of the variables. You've plugged the values in, and simplified. Where are you stuck?

arodss3 said:
I2. Express as a polynomial (x+a)[x^2-ax/x]
What you have posted means the following:

. . . . .(x + a)[x^2 - (ax/x)]

I suspect, however, that you mean:

. . . . .(x + a)[(x^2 - ax) / x]

If so, then simplify the expression in the square brackets, multiply the two binomials, and simplify the result. Where are you stuck?

arodss3 said:
I3.If points A,B,and C lie on a cordinate line and points A and B have coordinates 15 and 7 respectively, then which of the possible coordinates for point C satisfy(ies) d(A,C)<d(B,C)?
Draw the number line. Label the points A and B. If C is the midpoint, what can you say about the distances d(A,C) and d(B,C)? What adjustment could you make to alter these distances in the required direction?

arodss3 said:
I4. Solve the inequality 21/15-3X<0, AND EXPRESS THE SOLUTION AS AN INTERVAL.
You might mean (21/15) - 3x < 0, or you might mean 21/(15 - 3x) < 0. The answer (and solution method) will depend upon the meaning you intended.

Note: There is no such number as "oh-zero". Did you perhaps actually mean "infinity"...?

arodss3 said:
I5.Find the distance between the points A(4,-3) and B(-4,3).
What did you get when you plugged the coordinates into the Distance Formula that you've memorized?

arodss3 said:
I6.Find the domain of f(x)=7+squarerootsymbol 3x+21, and express it using interval notation
You might mean "7 + sqrt[3x + 21]", "7 + sqrt[3x] + 21", "7 + sqrt[3]x + 21", "7 + cbrt[x + 21]", or something else. The domain will depend upon your intended meaning.

Meanwhile, you've looked at the graph. What have you concluded? And how far have you gotten in the algebra?

arodss3 said:
I7. If f(x)=x(x+1)(x- 4),use interval notation to give all values of x where f(x)>0.
You've set the function equal to zero, and used test points on each interval. What did you conclude? Where are you stuck?

arodss3 said:
I8. The degree three polynomial f(x) with real coefficents and leading coefficent 1, had -3 and +4i among its roots. Express f(x) as a product of linear and quadratic polynomials with real coefficients.
You know that factors of the form "x - a" solve for the roots by setting the factors equal to zero, "x - a = 0", and solving for "x = a". In this case, of course, you're working backwards. How far did you get? Where are you stuck?

arodss3 said:
I9. Find the inverse of the function f(x)=x^1/3+2.
Your class and/or book should have provided a list of steps to take; something along the lines of:

. . . . .i) Rename "f(x)" as "y".

. . . . .ii) Solve for "x=" in terms of y.

. . . . .iii) Switch "x" and "y".

. . . . .iv) Rename the new y as "f[sup:2tgr4j6r]-1[/sup:2tgr4j6r](x)".

Note: Steps (ii) and (iii) might be reversed, with you solving for "y=" in terms of x. The results at the end of step (iv) will be the same, however.

So how far have you gotten?

arodss3 said:
l10. a bacteria culture with a count of 720 at 8:00 AM, and after t hours is expected to grow to f(t)=720(3/2)^t. ESTIMATE THE NUMBER OF BACTERIA IN THE CULTURE AT 11:00 A.M. THE SAME DAY.
You are given a formula for the number "f" of bacteria at time "t", and are given a time. You've plugged the time-value into the formula, and... then what? Where are you stuck?

Please be complete. Thank you!

Eliz.

#### arodss3

##### New member
I really dont remember where to start on any of these but your hints have helped. I took this class online over a year ago and missed this last 50 question test i needed to complete, i dont even have the books anymore these 10 i was completly lost on.

Question 1 i came up with 141.37155 so to the nearest tenth the answer would be D. 141.4 cu.ft.
Question 2 i came up with x^2 -a^2 which was A.
Question 3 im totally lost on.
Question 4 yes they are infinity and the question is 21/(15 - 3x) < 0

#### Subhotosh Khan

##### Super Moderator
Staff member
So this is a part of a test.

Are you supposed to seek external-help for test?

If you are planning to take any further mathematical course, you really need to understand the topics adressed in those questions.