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Math 121, Final Test, 23 March 2006
Name.
Instructions. Do 20 of the following 22 questions. Each question is worth 5pts. Please show all appropriate work in order to obtain maximal credit. Good Luck.
- Solve the formula F =
Gm 1 m 2 d^2
for m 1.
- A total of $7500 is deposited into two accounts. One account earned 5% interest while the other earned 7% interest. The total amount of interest earned was $405. How much was invested in each account?
- Find all solutions of the equation x^3 + 27 = 0.
- Solve the inequality
3 x + 4 x + 1
โฅ 2. Write the solution in interval notation.
- (a) Find the distance between the points (2, 3) and (โ 4 , 11).
(b) Find the equation of a circle that has a diameter with endpoints (2, 3) and (โ 4 , 11). Write your answer in standard form.
- Find the equation of the line that passes through the points (3, 1) and (โ 1 , 4). Write the equation of the line in slope intercept form.
- Find and simplify the difference quotient
f (x + h) โ f (x) h
for f (x) = โx^2 + 3x โ 3.
- Find all asymptotes (horizontal, vertical or slant) for the rational function F (x) =
x x + 4
For each vertical asymptote determine the behavior of F near the asymptote from the right and left (Do not graph F ).
- Find the sixth term of (3x โ y^2 )^13. Do not write the full binomial expansion.
- Write 1 โ 8 + 27 โ 64 + 125 in summation notation.
- (a) Write the equation
log 8 (x + 5) โ 3 log 8 y as a single logarithm with a coefficient of 1.
(b) Write the equation log 3 271 = x + 2 in exponential form, and then solve it.
- Find the inverse of A =
๏ฃป (^) if it exists. Show all steps.
- Solve the system of equations
2 x โ y โ z = โ 1 โx + 3 y โ z = โ 3 โ 5 x + 5 y + z = โ 1
