Hello,
Please, see the attached file.
Thanks.
The graph of g is one-fifth as steep as the graph of f.
The function g basically takes the inputs for f and multiplies them by one-fifth, which means the outputs are one-fifth times those of f. Multiplying by one-fifth makes something smaller (it's the same as dividing by five). It helps to visualize this relationship, so I've attache the graphs below.
<span>Length of outer track = sum of length of 10 pieces = circumference of the outer circle
if R is the Radius of outer circle then...
Circumference of the outer track = 2pi*R
Similarly the circumference of the inner track (with radius r) = 2pi*r
length of each outer piece is 3.4 inch more than length of inner piece
So total outer length is 10*3.4 =34 inches more than the inner length.
=> Outer Circumference - Inner Circumference = 34 inches
=> 2pi*R - 2pi*r = 34
=> 2pi(R -r) = 34
=> R-r = 34/2pi = 5.41 inches
=> R-r = Width of the track = 5.41 inches</span>