Will85237

By observation, we can see that x = 1 is a root because (1)^3 - 2(1) + 1 = 1 - 2 + 1 = 0

If x = 1, then (x - 1) = 0

Assuming x^3 - 2x + 1 = 0 can be written as (x+a)(x+b)(x+c) = 0, where -a, -b, and -c are the roots, then we can divide the equation by the root we already know to simplify it.

(x^3 - 2x + 1) / (x - 1) = x^2 + x - 1

Use the quadratic equation to find the roots of x^2 + x - 1

x = (-b +/- (b^2 - 4ac)^(0.5)) / (2a) = (-(1) +/- ((1)^2 - 4(1)(-1))^(0.5)) / (2(1)) = -0.5 +/- (5^0.5) / 2

The other 2 roots are x = -0.5 + (5^0.5) / 2 ~= 0.6 and x = -0.5 - (5^0.5) / 2 ~= -1.6

The largest root is x = 1, so let r = 1, s = 0.6, t = -1.6

r^3 - s - t = (1)^3 - (0.6) - (-1.6) = 2

2 is the maximal value!

A loose definition of a normal distribution is when the data follows a bell curve.

The number of minutes to complete a maraton and the pareticipants age varies from person to person and could plausibly follow a bell curve.

However, the number of miles in a marathon is a fixed value, and is not normally distributed.

To reflect a function over the x-axis, we put a negative sign in front of it.

\(-cos(x)\)

To shift it 2 units down, we subtract 2.

\(-cos(x)-2\)

\(\frac{f}{r^2}+a=n+k\)

Subtract a from each side.

\(\frac{f}{r^2}=n+k-a\)

Multiply each side by r^2.

\(f=(n+k-a)\times r^2\)

Divide each side by (n+k-a).

\(\frac{f}{n+k-a}=r^2\)

And then take the square root of each side, and you get an equation equal to r.

I'll leave this last step for you to do.

Yes, you're almost right, it's because 4 + 5 is less than 10. No matter which direction the forces are acting in, the 10 N force will be greater than any opposing force, so the system cannot be in equilibrium.

400 / 250 * 20,000 = 32,000 feet.

\(3^{-\frac{1}{4}}=\frac{1}{3}^{\frac{1}{4}}=\sqrt[4]{\frac{1}{3}}=0.759...\)

I, II, and III

The c term basically decides how much the parabola is shifted vertically. Moving the parabola would change all three of those things.

y = +/-(sqrt(3^2 - (x+5)^2)) - 5

y = +/-(sqrt(x^2 + 10x - 16)) - 5

A is true. The probability of winning with the first card does not affect the probability of losing with the second card.

B is true. The probability of A winning and B losing is equal to the product of their probabilities because they are independant.