Answer:
100
Step-by-step explanation:
Based on the histogram given :
The vertical axis gives the number of student in the school :
For the range :
0 - 5 = 40
5 - 10 = 30
10 - 15 = 20
15 - 20 = 5
20 - 25 = 3
25 - 30 = 2
Taking the sum :
(40 + 30 + 20 + 5 + 3 + 2) = 100
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
Subtract 20n from both sides of the equation.
n^2+100-20n=0
factor using the perfect square rule.
(n-10)^2=0
set the n-10 equal to 0.
n-10=0
add 10 to both sides of the equation.
n=0
Answer:
Harrison earns: $208.14
Sherrie earns: $216.57
Step-by-step explanation:
Sherrie earns more money than Harrison in 2 years.
Answer:
Step-by-step explanation:
x+10=0
x=-10
so vertex is (-10,-105)
