Answer: 40
Step-by-step explanation:
Answer: see proof below
<u>Step-by-step explanation:</u>
Use the Double Angle Identity: sin 2Ф = 2sinФ · cosФ
Use the Sum/Difference Identities:
sin(α + β) = sinα · cosβ + cosα · sinβ
cos(α - β) = cosα · cosβ + sinα · sinβ
Use the Unit circle to evaluate: sin45 = cos45 = √2/2
Use the Double Angle Identities: sin2Ф = 2sinФ · cosФ
Use the Pythagorean Identity: cos²Ф + sin²Ф = 1
<u />
<u>Proof LHS → RHS</u>
LHS: 2sin(45 + 2A) · cos(45 - 2A)
Sum/Difference: 2 (sin45·cos2A + cos45·sin2A) (cos45·cos2A + sin45·sin2A)
Unit Circle: 2[(√2/2)cos2A + (√2/2)sin2A][(√2/2)cos2A +(√2/2)·sin2A)]
Expand: 2[(1/2)cos²2A + cos2A·sin2A + (1/2)sin²2A]
Distribute: cos²2A + 2cos2A·sin2A + sin²2A
Pythagorean Identity: 1 + 2cos2A·sin2A
Double Angle: 1 + sin4A
LHS = RHS: 1 + sin4A = 1 + sin4A 
Answer:
Step-by-step explanation:
ii) Perimeter = 8 + 7 + 17 + 16 + (17-8) + (16-7)
=8+ 7 + 17 +16 + 9 + 9
= 66 m
Area = area of upper rectangle + area of lower rectangle
= 8*7 + 16*9
= 56 + 144
= 200 m²
Answer:
C = 25 + 3n
Step-by-step explanation:
Andre has a summer job selling magazine subscriptions.
We are told that:
Andy earns $25 per week plus $3 for every subscription he sells.
Let us represent
C = Total amount of money he makes this week
n = the number of magazine subscriptions Andre sells this week.
Hence, Our Algebraic expression =
C = $25 + $3 × n
C = 25 + 3n
Answer:
596.34m approx
Step-by-step explanation:
Given data
Let the Starting point be x
A helicopter flew north 325 meters from x
Then flew east 500 meters
Let us apply the Pythagoras theorem to solve for the resultant which is the distance from the starting position
x^2= 325^2+500^2
x^2=105625+250000
x^2= 355625
x= √355625
x=596.34m
Hence the distance from the starting point is 596.34m approx