Same curves as in problem 4 rotated about x 1 y sin2x 1

Same curves as in problem 4 rotated about x = - 1 y = sin^2(x) + 1 and y = 1 on [0, pi]. Rotate about x = 5 A spring requires 6 N of force to keep it stretched from its 4.5 m. Find the work required to stretch the spring from its A stack of books is moved 25 m along a line with a done?

Solution

x04234f(x)01010

The trig function can be graphed using the amplitude, period, phase shift, vertical shift, and the points.

Amplitude: 1

Period:

Phase Shift: 0 (0 to the right)

Vertical Shift: 0

x04234f(x)01010

The data below is taken from Table 1.1, 1.2, Fig 1.5 and Fig 6.4 in the 2002 edition of the book^{[verification needed]}.

This table presents some of the main findings presented in Chapter 1 and some related text. Stocks on the long term have returned 6.8% per year after inflation, whereas gold has returned -0.4% (i.e. failed to keep up with inflation) and bonds have returned 1.7%^{[clarification needed]}. The equity risk premium (excess return of stocks over bonds) has ranged between 0 to 11%, it was 3% in 2001. Also see [1] where equity risk premium is computed slightly differently. The Fed model of stock valuation was not applicable before 1966. Before 1982, the treasury yields were generally less than stock earnings yield.

Why the long-term return is relatively constant^{[further explanation needed]}, remains a mystery.

The dividend yield is correlated with real GDP growth, as shown in Table 6.1.

Explanation of abnormal behavior:

In Chapter 2, he argues (Figure 2.1) that given a sufficiently long period of time, stocks are less risky than bonds, where risk is defined as the standard deviation of annual return. During 1802–2001, the worst 1-year returns for stocks and bonds were -38.6% and -21.9% respectively. However, for a holding period of 10-years, the worst performance for stocks and bonds were -4.1% and -5.4%; and for a holding period of 20 years, stocks have always been profitable. Figure 2.6 shows that the optimally lowest risk portfolio even for a one-year holding, will include some stocks.

In Chapter 5, he shows that after-tax returns for bonds can be negative for a significant period of time.

Key Data Findings: annual real returns

Duration	Stocks	Gold	Bonds	Dividend Yld	Inflation rt	Eqity Prem	Fed Model
1871–2001	6.8	-0.1	2.8	4.6	2.0	0–11	NA
1946–1965	10.0	-2.7	-1.2	4.6	2.8	3–11	NA
1966–1981	-0.4	8.8	-4.2	3.9	7.0	11–6	TY<EY
1982–2001	10.5	-4.8	8.5	2.9	3.2	6–3	YT>=EY.