Verifying Inequalities In Exercises 5 3 - 6 4 , verify (a) the Cauchy-Schwarz Inequality and (b) the triangle inequality for given vectors and inner products. A = [ 0 1 2 − 1 ] , B = [ 1 1 2 − 2 ] , 〈 A , B 〉 = a 11 b 11 + a 12 b 12 + a 21 b 21 + a 22 b 22
Verifying Inequalities In Exercises 5 3 - 6 4 , verify (a) the Cauchy-Schwarz Inequality and (b) the triangle inequality for given vectors and inner products. A = [ 0 1 2 − 1 ] , B = [ 1 1 2 − 2 ] , 〈 A , B 〉 = a 11 b 11 + a 12 b 12 + a 21 b 21 + a 22 b 22
Solution Summary: The author explains the Cauchy-Schwarz inequality. The inner product of the given matrices is langle A,Brangle & =
Verifying Inequalities In Exercises
5
3
-
6
4
, verify (a) the Cauchy-Schwarz Inequality and (b) the triangle inequality for given vectors and inner products.
A
=
[
0
1
2
−
1
]
,
B
=
[
1
1
2
−
2
]
,
〈
A
,
B
〉
=
a
11
b
11
+
a
12
b
12
+
a
21
b
21
+
a
22
b
22
Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).
Directions: Use the equation A = Pet to answer each question and be sure to show all your work.
1. If $5,000 is deposited in an account that receives 6.1% interest compounded continuously, how much money is in the
account after 6 years?
2. After how many years will an account have $12,000 if $6,000 is deposited, and the account receives 3.8% interest
compounded continuously?
3. Abigail wants to save $15,000 to buy a car in 7 years. If she deposits $10,000 into an account that receives 5.7% interest
compounded continuously, will she have enough money in 7 years?
4. Daniel deposits $8,000 into a continuously compounding interest account. After 18 years, there is $13,006.40 in the account.
What was the interest rate?
5. An account has $26,000 after 15 years. The account received 2.3% interest compounded continuously. How much was
deposited initially?
TRIANGLES
INDEPENDENT PRACTICE
ription Criangle write and cow
Using each picture or description of triangle write and solve an equation in ordering the
number of degrees in each angle
TRIANGLE
EQUATION & WORK
ANGLE MEASURES
A
B
-(7x-2)°
(4x)
(3x)°
(5x − 10)
C
(5x – 2)
(18x)
E
3.
G
4.
H
(16x)°
LL
2A=
2B=
ZE=
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