That would be a right-angled triangle.
Answer:
D
Step-by-step explanation:
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:
11484m
Step-by-step explanation:
if 1914 = 1hour
Then 6hours= ?
6/1 ×1914
= 11484m
Answer:
y=7/3x²-13/3x+2
Step-by-step explanation:
<u>Determine the value of c:</u>
y=ax²+bx+c
2=a(0)²+b(0)+c
2=c
<u>Substitute (1,0) into the quadratic and create an equation with a and b:</u>
y=ax²+bx+2
0=a(1)²+b(1)+2
0=a+b+2
-2=a+b
<u>Do the same with (3,10) to get a second equation:</u>
y=ax²+bx+2
10=a(3)²+b(3)+2
10=9a+3b+2
8=9a+3b
<u>Set the two equations equal to each other and solve for a and b:</u>
-2=a+b
8=9a+3b
<u>Multiply first equation by 3 and eliminate b to find a:</u>
-6=3a+3b
- (8=9a+3b)
_______
-14=-6a
14/6=a
7/3=a
<u>Substitute 7/3=a into the first equation:</u>
-2=7/3+b
-2-(7/3)=b
-13/3=b
<u>Final equation:</u>
y=7/3x²-13/3x+2
See the graph for a visual representation
