Vectors and Polar Equations
Let u = <2, -1>, v= <4, 2>, w = <1, -3>
Find |u + v|
371/2
Find A + B
A = -1 3
4 0
B= 2 -1
4 3
1 2
8 3
Find the vertex, focus, directrix, and focal width of the
parabola y2=12x
Vertex: (0, 0); Focus: (3, 0);
Directrix: x =-3; Focal width: 12
Calculate 18C12
18,564
The sample space for a random variable X is {1, 2, 5, 10} is P(1) =0.45, P(2) =0.25, P(5) =0.15, and P(10) =0.05 a valid probability function?
No; sum≠1
Let u = <2, -1>, v= <4, 2>, w = <1, -3>
Find the dot product of u and v
6
Find AB
A = -1 4
B= 5 -3
2 1
3 7
Identify the conic section and find the center, vertices, and foci
(x - 2)2/16 + (y + 1)2/7 = 1
Ellipse
Centre: (2,-1)
Vertices: (6, -1), (-2, -1)
Foci: (5, -1), (-1, -1)
How many license plates begin with two letters followed by four digits or begin with three digits followed by three letters? Assume that no letters or digits are repeated.
14,508,000
In a state lottery, players must pick 5 winning numbers from 1 to 40. What’s the probability of winning for a player who buys a dozen different tickets?
0.00001824
Find the indicated power (write answers in polar form)
[3(cos pi/4 + i sin pi/4)]5
[243(cos 5pi/4 + i sin 5pi/4)]
Evaluate the determinant of the matrix
A = 1 -3 2
2 4 -1
-2 0 1
20
Identify the conic section, then complete the square to write the conic in standard form
2x2-3y2-12x -24y +60=0
Hyperbola
(y + 4)2/30 - (x - 3)2/45 = 1
Find the sum of the terms of the arithmetic sequence
-11, -8, -5, -2, 1, 4, 7, 10
-4
A box of candies contains 6 caramels and 4 butter-creams, all appearing identical. What’s the probability that a person who starts eating them one at a time won’t get a caramel until the third candy?
1/10
Convert to polar form
(x-3)2+(y+1)2=10
r = 6 cos(theta) - 2 sin(theta)
Find the reduced echelon form of
1 0 2
A = 3 1 5
1 -1 3
1 0 2
0 1 -1
0 0 0
Find the equation for the conic in standard form
x =-2+cos t, y =4+sin t, 2pi<=t <=4pi
(x + 2)2 + (y - 4)2 = 1
Find the sum of the terms of the geometric sequence
2, 6, 18,..., 39366
59,048
Find the expected value of the random variable defined by this probability model:
X 100 150 200 500
P(X) 0.4 0.3 0.2 0.1
175
Find the 4th root of 3 + 3i
181/8(cos pi/16 + i sin pi/16),
181/8(cos 9pi/16 + i sin 9pi/16),
181/8(cos 17pi/16 + i sin 17pi/16),
181/8(cos 25pi/16 + i sin 25pi/16)
Solve the system
x + z + w = 2
x + y + z = 3
3x + 2y + 3z + w = 8
Identify and graph the conic, and rewrite the
equation in Cartesian coordinates
r =2/(1+ cos(theta))
Parabola;
y2=-4(x -1)
Find the sum of the first 10 terms of the series
2187, 729, 243,...
3280.4444
Automobile brakes work when a part called a caliper squeezes brake pads against a spinning disk to slow the rotation of the wheels. The brakes won’t work correctly if the caliper is not moving freely. At the brake shop, the simplest fix is to clean and lubricate the caliper. This costs $50 and will work in 35% of cases. In 90% of the cars with a more serious problem, the caliper must be replaced at a cost of $85 for the part and $75 for the labor to install it. The remaining cars need a complete brake overhaul that costs $350. What’s the expected cost for car owners who come in for repair of this problem?
$133.85