Math Answers

If f(x) =10^x and Φ(x) =log10 x, show that f[Φ(x)] = Φ [f(x)] = x.

If f(x)= x^2 -1 and g (x) =2x +1, show that f[g(x)]=4x(x+1).

If f(x) = sin x, show that f (2x)= 2f(x) f(1/2 π-x).

If P(x) =√x, show that P(x+h) - P(x) = h(√x+h + √x).

If Φ (r)= 2^r, show that Φ (r+1) =2 Φ(r).

If F(z)= log z, show that F(xy) = F(x) +F(y).

Using the methods suggested in the preceding problem, find the area of the trapezoid bounded by the line y= x+3, the ordinates x=1, x=3, and the x axis.

the mathematics teacher claims that the mean iq of statistics students is 110 with standard deviation of 12. The mean IQ of 28 randomly selected statistics students is 112 . Test the difference of the population and sample means at 5%level of significance.

A ball thrown straight up is located s feet above the ground at t seconds after it is thrown in accordance with the formula s= 112t-16 t^2. Find a formula for the velocity of the ball and find (a) the time required to reach its highest point, (b) the distance of the highest point above the ground, and (c) the acceleration of the ball at this point.

A ball rolling down an incline travels s feet in t seconds, where s= 5t^2. Derive a formula for the velocity of the ball at time t= t0. How fast is it going (a) after 2 seconds (b) after it has rolled 80 feet?