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:
4/(√7 + √3)
Step-by-step explanation:
=> Multiply and divide by (√7-√3)
=> 4(√7 - √3)/((√7 + √3)(√7 - √3)
=> 4(√7 - √3)/((√7)² - (√3)²)
=> 4(√7 - √3)/((7) - (3))
=> 4(√7 - √3)/4
=> √7 - √3
A tenth is the number that occurs after the decimal
If the number after the tenth is five or higher, then you round up
If the number after the tenth if four or lower, then the tenth stays the same value as it is
In this case, the Ume after the tenth is exactly four, so the value of the tenth stays the same
So your answer is 478.5
