F(x) = 2(2)2 – 3(2) + 7 = 2(4) – 3(2) + 7
1 answer:
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Answer:
B
Step-by-step explanation:
A graph is only a function when there is only one y value for each x value.
A trick is to draw a line through some points on the x-axis, and if the line goes through more than one point. Then it is not a function. (See picture)
Sorry, not all the lines are straight, but you get the point. B is the only one that doesn't have more than one point on the lines I drew.
Answer:
-0.133 radians/s is the angle between the ladder and the ground changing when the bottom of the ladder is 8 ft from the wall.
Step-by-step explanation:
Let
x= distance between the wall and ladder
Ф = angle between the ladder and ground
The rate of change is: dx/dt = 0.8 ft/s
We need to find dФ/dt when x = 8 ft/s
From the triangle in the figure we see that:
cos Ф = x/10
=> x = 10 cosФ
Now, the rate of change will be
d(x)/dt = d/dt (10cosФ)
dx/dt = -10 sin Ф dФ/dt
dx/dt = 0.8 (given)
to find dФ/dt
we need to find sin Ф when x = 8
By Pythagoras theorem
(hypotenuse)^2 = (Perpendicular)^2+(base)^2
(10)^2 = (8)^2+ (Perpendicular)^2
100 = 64 + (Perpendicular)^2
=> (Perpendicular)^2 = 100-64
(Perpendicular)^2 = 36
Perpendicular = 6
sin Ф = Perpendicular/hypotenuse
sin Ф = 6/10 = 3/5
Putting values in:
dx/dt = -10 sin Ф dФ/dt
0.8 = -10(3/5) dФ/dt
0.8 = -6 dФ/dt
=> dФ/dt = 0.8 / -6
dФ/dt = - 0.133 radians/s
So, -0.133 radians/s is the angle between the ladder and the ground changing when the bottom of the ladder is 8 ft from the wall.
