Answer:
6.667 ft/s
Step-by-step explanation:
Given
Height of street light = 15ft
Height of man = 6ft
Speed away from pole = 4ft/s
Let x represents the distance between the man and the pole, and Let y represents the distance between the tip of the man's shadow to the pole.
This forms a similar triangle (see attachment below).
From similar triangles, we have
(y - x)/6 = y/15 ----- Solve equation
15(y - x) = 6 * y
15y - 15x = 6y ---- Collect Like Terms
15y - 6y = 15x
9y = 15x --- divide through by 9
y = 15x/9
y = 5x/3 ---- differentiate with respect to time, t
dy/dt = 5/3 dx/dt
dx/dt represents rate of change of distance per time = 4ft/s
while dy/dt represents rate of movement of his shadow tips
dy/dt = 5/3 * 4
dy/dt = 20/3 = 6.667 ft/s
Answer: 6.67ft/s
Step-by-step explanation: PLEASE SEE PICTURE ATTACHED, IT IS A DIAGRAM THAT HELPS YOU TO ANALYSE THE QUESTION.
STEP 1: DEFINE ALL VARIABLES
The man's shadow distance from the pole (Y)
The man's height=6ft
The height of the pole= 15ft
The man's shadow length (X-Y)
The man's speed = 4ft/s
STEP 2: FIND THE MAN'S SHADOW DISTANCE FROM THE POLE (Y)
((X-Y)÷Y) = 6ft÷15ft
Open up bracket and cross multiply
15(X-Y)=6Y
15X-15Y=6Y
collecting like terms together
15X=9Y
Y= 15X/9
Y= 5X/3
STEP 3: FIND THE SPEED OF THE MAN'S SHADOW
Dy/dt = 4ft/s
Therefore
Dy/dx= (4ft/s) × (5X/3)
20ft/3s = 6.67ft/s
The speed of the shadow a cross the pole is 6.67ft/s
The system of equations is consistent and dependent.
The system of equations is given as:
Start by plotting the graph of both equations (see attachment)
From the attached graph, we can see that both equations are represented on a single line.
This means that, the system of equations is consistent and dependent.
This is so because, the system of equations have infinite many solutions.
Read more about system of equations at:
Answer:
Step-by-step explanation:
substitute n = 5 into the equation: