ANSWER
The dot product is 10.
EXPLANATION
The given vectors are (2,4) and (1,2).
If we have the vectors
u=(a,b) and v=(c,d)
Then the dot product of the two vectors is given by

This implies that,

This simplifies to;

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:
Steve scored 59 points
Step-by-step explanation:
79 - 20 = x
79 - 20 = 59
x = 59
Answer:
9 more shots
Step-by-step explanation:
If the first golfer had a score of +6 and the second golfer had a score of -3, in order to know how many more shots the first golfer take, we will take the difference between both goals as shown;
= 6-(-3)
= 6+3
= 9
Hence the first golfer took 9 more shots than the second.
Answer:
Do you have a picture?
Step-by-step explanation: