<u>3/4</u> = 1/2 + 1/4
<u>5/8</u> = 1/2 + 1/8
<u>7/12</u> = 1/2 + 1/12
Answer:
0.128rad/sec
Step-by-step explanation:
Let x represent the between the man and the point on the path
θ = the angle
dx/dt = 4 ft/s
dθ/dt = rate is the searchlight rotating when the man is 15 ft from the point on the path closest to the searchlight
tan θ = x/20 ft
Cross Multiply
20tan θ = x
dx/dt = 20sec² θ dθ/dt
dθ/dt = 1/20 × cos² θ dx/dt
dθ/dt= 1/20 × cos² θ × 4
dθ/dt = 1/5 × cos² θ
Note : cos θ = 4/5
dθ/dt = 1/5 × (4/5)²
dθ/dt = 16/125
dθ/dt = 0.128rad/sec
Answer:
-4
Step-by-step explanation:
Pick any two points, let's go with (-7, 21) and (-6, 17) to find slope:
slope m = (y₂ - y₁) / (x₂ - x₁)
= (17- 21) / (-6 - (-7))
= -4 / 1
m = -4
---Extra info---
y-intercept using anyone point, let's use (-5, 13) and slope above:
y = mx + b
13 = -4(-5) + b
13 = 20 + b
b = -7
Equation of line:
y = mx + b
y = -4x - 7
Check:
(-7, 21)
y = -4x - 7
21 = -4(-7) - 7
21 = 21
(-4, 9)
y = -4x - 7
9 = -4(-4) - 7
9 = 9
other points should check out as well...
While it was true that the cotton gin reduced the labor of removing seeds, it did not reduce the need for slaves to grow and pick the cotton. In fact, the opposite occurred. Cotton growing became so profitable for the planters that it greatly increased their demand for both land and slave labor
