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
Given:
DE contains the points D(1, -2) and E(3, 4).
FG contains the points F(-1, 2) and G(4, 0).
To find:
Is DE perpendicular to FG.
Solution:
Slope of DE:
Here 
m = 3
Slope of FG:
Here 
<em>Two lines are perpendicular if product their slopes are -1.</em>
Slope of DE × Slope of FG
≠ -1
The solution is no, because the product of the slopes is not -1.
Answer: y = 15
Step-by-Step Explanation:
=> y^2 = 225
Therefore,
y = √225
=> y = 15
Hence, y = 15
Ac and BE are the diameters of a circle F
diameter passes through the centre
Answer:
<h2>( 2 , 1 )</h2>
Step-by-step explanation:
2x - 2y = 2
<u>5</u><u>x</u><u> </u><u>+</u><u> </u><u>2</u><u>y</u><u> </u><u>=</u><u> </u><u>1</u><u>2</u>
7x = 14
<h3>
x = 2</h3>
(2x - 2y = 2)-5
<u>(5x + 2y = 12)</u><u>2</u>
-10x + 10y = -10
<u> 10x + 4y = 24</u>
14y = 14
<h3>
y = 1</h3>
x = 2
y = 1
(2,1)
