Answer:
34.43
Step-by-step explanation:
A differential of length in terms of t will be ...
dL(t) = √(x'(t)^2 +y'(t)^2)
where ...
x'(t) = 4cos(4t)
y'(t) = 7cos(7t)
The length of c(t) will be the integral of this differential on the interval [0, 2π].
Dividing that interval into 10 equal pieces means each one has a width of (2π)/10 = π/5. The midpoint of pieces numbered 1 to 10 will be ...
(π/5)(n -1/2), so the area of the piece will be ...
sub-interval area ≈ (π/5)·dL((π/5)(n -1/2))
It is convenient to let a spreadsheet or graphing calculator do the function evaluation and summing of areas.
__
The attachment shows the curve c(t) whose length we are estimating (red), and the differential length function (blue) we are integrating. We use the function p(n) to compute the midpoint of the sub-interval. The sum of sub-interval areas is shown as 34.43.
The length of the curve is estimated to be 34.43.
Answer:
The correct option is C). When it was purchased, the coin was worth $6
Step-by-step explanation:
Given function is f(t)=
Where t is number of years and f(t) is function showing the value of a rare coin.
A figure of f(t) shows that the graph has time t on the x-axis and f(t) on the y-axis.
Also y-intercept at (0,6)
hence, when time t was zero, the value of a rare coin is 6$
f(t)=
f(0)=
<em>f(0)=6</em>
Thus,
The correct option is C). When it was purchased, the coin was worth $6