Recall that parallel lines have the same slope.
A line parallel to y= (-3/5)x + 8 would have the same equation EXCEPT for a different constant, C, replacing that '8.'
This new line passes thru (-5,-3). In y= (-3/5)x + C, replace x with -5 and replace y with -3. Then:
-3 = (-3/5)(-5) + C. Find C:
-3 = 3 + C. Thus, C = 6
Thus, the equation of the new line is y= -(3/5)x - 6
Check: Let x = -5 and y = -3. Is the above equation true?
-3 = (-3/5)(-5) - 6
-3 = 3 - 6, or -3 = -3.
It’s 4,366,813 km that’s the suns length
Answer:
a) clockwise sense
b) x² + y² = 1
c) y ∈ [0,1]
Step-by-step explanation:
a) x = cos (t) y = -sin (t)
for t ∈ [ 0 , 2π ]
for t = 0 point P is x = cos (0) = 1 y = -sin (0) y = 0
The point is on the x axis
Now let´s see what happens for t = π/4
x = cos (π/4) x = √2/2 and y = - sin (π/4) y = - √2/2
Note π/4 is 45°
The coordinates of the new point P ´(t = π/4) are in the fourth quadrant
that means the point is moving clockwise sense.
b) x = cos(t)
y = -sin(t)
Squaring on both sides of each equation we get:
x² = cos²t
y² = sin²(t)
Adding side by side
x² + y² = cos²t + sin²t
x² + y² = 1
Values for y are y ( 0 , 1)
1,400 - 1,250 = 150
150/1250 = 0.12
0.12 x 100 = 12%
Population increased by D. 12%
