Sequences and Series
Is the sequence 2, 4, 8, 10, ... arithmetic, geometric, or neither?
Neither
Which of the following is a solution to the system of equations?
2x - 3y = 5
x + 2y = -1
(a) (1, 1)
(b) (1, -1)
(c) (3, 2)
(b)
Find the roots (with multiplicity) of
x4 - 3x3 - 10x2
0 (multiplicity 2)
-2 (multiplicity 1)
5 (multiplicity 1)
Compute log3(1/27)
-3
A $2500 bond grows to $3729.56 in 10 years under continuous compounding. Find the interest rate. (round to the nearest whole percent)
4%
Give a formula for the nth term of the sequence
2, 5, 8, 11, 14, ...
an = 2 + 3(n - 1)
Which of the following is a solution to the system of inequalities?
2x - 3y < 5
x + 2y > -1
(a) (1, 1)
(b) (-5, -2)
(c) (3, 2)
(a) and (c)
Fully simplify the expression
1/(x - 1) + x/(2x + 3)
(x2 + x + 3)/((x - 1)(2x + 3))
Fully simplify the expression
log(2x - 3) + 4log(x + 1) - (1/2)log(x)
log((2x - 3)(x+1)4/(x1/2))
A long jumper leaves the ground at an angle of 20° at a speed of 11 m/s. The height of the jumper can be modeled by h(x) = -0.046x2 + 0.346x, where h(x) is the jumper's height in meters, and x is the horizontal distance from the start point.
What is the jumper's maximum height? (round to 2 decimal places)
0.72 m
Give a formula for the nth term of the sequence
4, 12, 36, 108, 324, ...
an = 4 * 3n-1
Solve the system
3x + 4y = -11
-x + y = 6
(-5, 1)
Solve the equation
(w + 3)/(4w) + 1 = (w - 5)/w
w = -23
Solve the equation
log2(x - 31) = 5 - log2(x)
x = 32
A pharmacist wants to mix a 30% saline solution with a 10% saline solution to get 200 mL of a 12% saline solution. How much of each solution should be used?
20 mL of the 30% solution and 180 mL of the 10% solution
Give a formula for the nth term of the sequence
4/2, 9/4, 16/6, 25/8, 36/10, ...
an = (n+1)2/2n
Solve the system
5x - 2y = 4
3x + 3y = 15
(2, 3)
Divide x5 + 32 by x + 2
x4 - 2x3 +4x2 - 8x + 16
Find the inverse function f-1(x) of the function
f(x) = log3(2x - 1)
f-1(x) = (1/2)*3x + 1/2
The perimeter of a rectangle is 30 ft, and the area is 50 ft2. What are the dimensions of the rectangle?
5 ft by 10 ft
Compute 1 + 2 + 3 + ... + 99 + 100
5050
Solve the system
2x2 + y2 = 17
x2 + 2y2 = 22
(2, 3), (-2, 3), (-2, -3), (2, -3)
Solve the inequality (x + 3)(2x - 4)(x - 5) > 0
(-3, 2) U (5, ∞)
Solve the equation
36x + 5 = 52x
x = (5*ln(3))/(2*ln(5) - 6*ln(3))
The sum of the squares of two positive numbers is 145 and the difference of the squares of the numbers is 17. Find the numbers
8 and 9