I would but I’m stuck on this problem too
Answer:
Work done in stretching the spring = 7.56 lb-ft.
Step-by-step explanation:
Normal length of the spring = 8 in or ft
= ft
If the spring has been stretched to 11 inch then the stretched length of the spring is = 11 in
= ft
Force applied to stretch the spring = 12 lb
By Hook's law,
F = kx [where k is the spring constant and x = length by which the spring is stretched]
12 = k()
k = 18
Work done (W) to stretch the spring by ft will be
W =
=
=
= 9()²
= 7.56 lb-ft
The vertex will be when the velocity is equal to zero:
df/dx=-12x+24 (using the power rule for differentiation)
df/dx=0 only when:
-12x+24=0 add 12x to both sides
12x=24 divide both sides by 12
x=2, we find the y value to be:
y(2)=-6(2^2)+24*2-20
y(2)=-24+48-20=4
So the vertex is the point (2,4)
And the axis of symmetry is the line x=2
Now if you do not yet do calculus...
The vertex will occur midway between the two zeros.
6x^2-24x+20=0 (using the Quadratic Formula for simplicity)
x=(24±√96)/12
x≈(1.1835, 2.8165)
Now the vertex occurs at the average of the zeros...
x=(1.1835+2.8165)/2=2 (as we saw earlier)
y(2)=4
Vertex is at (2,4) and axis of symmetry is the vertical line x=2
Answer:
1. x is greater than or equal to 1
2. x is less than or equal to 5
3. x is less than or equal to 11
Step-by-step explanation: