Separate the vectors into their <em>x</em>- and <em>y</em>-components. Let <em>u</em> be the vector on the right and <em>v</em> the vector on the left, so that
<em>u</em> = 4 cos(45°) <em>x</em> + 4 sin(45°) <em>y</em>
<em>v</em> = 2 cos(135°) <em>x</em> + 2 sin(135°) <em>y</em>
where <em>x</em> and <em>y</em> denote the unit vectors in the <em>x</em> and <em>y</em> directions.
Then the sum is
<em>u</em> + <em>v</em> = (4 cos(45°) + 2 cos(135°)) <em>x</em> + (4 sin(45°) + 2 sin(135°)) <em>y</em>
and its magnitude is
||<em>u</em> + <em>v</em>|| = √((4 cos(45°) + 2 cos(135°))² + (4 sin(45°) + 2 sin(135°))²)
… = √(16 cos²(45°) + 16 cos(45°) cos(135°) + 4 cos²(135°) + 16 sin²(45°) + 16 sin(45°) sin(135°) + 4 sin²(135°))
… = √(16 (cos²(45°) + sin²(45°)) + 16 (cos(45°) cos(135°) + sin(45°) sin(135°)) + 4 (cos²(135°) + sin²(135°)))
… = √(16 + 16 cos(135° - 45°) + 4)
… = √(20 + 16 cos(90°))
… = √20 = 2√5
Answer:
a. 8/24
divide denominator and numenator by three
1:3
b. 16/24
2:3
Answer:
angle 1: 72.5°
angle 2: 107.5°
Step-by-step explanation:
x + y = 180
x - y = 35 ===> x = 35 + y
Substitution to find angle y:
x + y = 180
(35 + y) + y = 180
35 + 2y = 180
2y = 145
y = 72.5
Substitution to find angle x:
x = 35 + y
x = 35 + (72.5)
x = 107.5
Answer:
A.
mean=82.286
Rounded to the tenths place would be= 82.3
Step-by-step explanation:
The Mean is found by adding all of the values together
Then dividing it by how many values there are.
In this instance, all the values added up equal 576
576 now will be divided by how many temperatures are recorded.
576/7=82.286
82.286 Rounded to nearest tenth=82.3
