Define i as a unit vector in the eastern direction.
Define j as a unit vector in the northern direction.
Part I
Because the wind is blowing west, its velocity vector is
-23i mph or as (-23, 0) mph
Because the plane is traveling north, its velocity vector is
200j mph or as (0, 200) mph
Part II
The actual velocity of the plane is the vector sum of the plane and wind velocities.
That is,
200j - 23i or (-23, 200) mph
Part III
The ground speed of the plane is the magnitude of its vector.
The ground speed is
√[200² + (-23)²] = 201.32 mph
The ground speed of the plane is 201.3 mph (nearest tenth)
Not:
The direction of the plane is
tan⁻¹ 23/200 = 6.56° west of north.
Answer:
1) gradient (00) (-2 4) = y2-y1 / 2-1 = 4/-2 = -2 m = -2/1 means = m = -2 (negative slope) 2) gradient y2-y1 / x2-x1 = 3-0 / 2-0 = 3/2 = (1 1/2)/1 m = 1 1/2 (positive slope) we use the formula y-values divided by the change in the x-values. The equation of the gradient each goes like this 1) y = -2x as y is at origin nothing else to add The equation of the gradient each goes like this 2) y = 1 1/2x The equation of the point formula 1) we take the y -y1 = m (x +x 1) = y-0 = -2x (x +0) (as m = -2) y = -2(x +0) and The equation of the point formula 2) y - 0 = m ( x +x1) y - 0 = 1 1/2( x +0) = y = 1 1/2( x +0)
Answer:
Boys - 36$ 33 cents
Girls - 72$ 67 cents
Step-by-step explanation:
Boys x
Girls 2x
Total 109
2x+x=109
3x=109/:3
X=36,3333
Boys x =36$ 33c
Girls 2x= 72,666= 72$ 67c
E^x^2 - 9 = 1
e^x^2 = 1 + 9 = 10
Ln e^x^2 = Ln 10
x^2 = Ln 10
x = sqrt (Ln 10) = 1.517
x = 1.517
