Write an equation for a fourth-degree polynomial that has a double root at x = -3, a complex root of x = 1 - 2i, and passes through the point (2, -25).

We have differential equation

$$my''+\mu y'+ky=F(t)$$

and initial conditions a mass 50g which stretches a spring 10cm, with magnitude 0.01v and force F(t)=5 cos 4.4t N. Find the position of the mass as function of time if is y(0)=0 and y'(0)=0.

Anthony leaves Kingstown at 2:00 P.M. and drives to Queensville, 160 mi distant, at 45 mi/h. At 2:15 P.M. Helen leaves Queensville and drives to Kingstown at 40 mi/h. At what time do they pass each other on the road?

Anthony leaves Kingstown at 2:00 P.M. and drives to Queensville, 160 miles distant, at 45 mi/hr. At 2:15 P.M. Helen leaves Queensville and drives to Kingstown at 40 mi/hr. At what time do they pass each other on the road?

A 1.50-kg, horizontal, uniform tray is attached to a vertical ideal spring of force constant 185 N/m and a 275-g metal ball is in the tray. The spring is below the tray, so it can oscillate up and down. The tray is then pushed down to point A, which is 15.0 cm below the equilibrium point, and released from rest. (a) How high above point A will the tray be when the metal ball leaves the tray? (This does not occur when the ball and tray reach their maximum speeds.) (b) How much time elapses between releasing the system at point A and the ball leaving the tray? (c) How fast is the ball moving just as it leaves the tray?

A 2.00-kg bucket containing 10.0 kg of water is hanging from a vertical ideal spring of force constant 450 N/m and oscillating up and down with an amplitude of 3.00 cm. Suddenly the bucket springs a leak in the bottom such that water drops out at a steady rate of 2.00 g/s. When the bucket is half full, find (a) the period of oscillation and (b) the rate at which the period is changing with respect to time. Is the period getting longer or shorter? (c) What is the shortest period this system can have?

Which questions about Della and Jim came to your mind as you read?

Find the LCM of the numbers $3, 17$ using prime factorizations.

Name all angles

$$\theta , 0 ^ { \circ } \leq \theta < 360 ^ { \circ }$$

, that make the statement true.

$$\sin \theta = 1$$

A certain simple pendulum has a period on the earth of 1.60 s. What is its period on the surface of Mars, where $g = 3.71 \mathrm { m } / \mathrm { s } ^ { 2 }$?

Consider the function $f(x)=x^3-3 x^2 + 3$.

Use Newton's Method with $x_1=1$ as an initial guess.

Consider the function

$f(x) = x^3 - 3x^2 - 144x - 140$.

Using the graph of part (c), find the roots (zeros) of f.

You want to find the moment of inertia of a complicated machine part about an axis through its center of mass. You suspend it from a wire along this axis. The wire has a torsion constant of $0.450 \mathrm{N} \cdot \mathrm{m} / \mathrm{rad}$. You twist the part a small amount about this axis and let it go, timing 165 oscillations in 265 s. What is its moment of inertia?

You learned how to solve "power equations" of the form $x^{a}=b$, where a and b are real numbers, by raising each side to a well-chosen power. Review this, method by completing the parts below. a. Equation: $x^{1.05}=2$ Start by estimating the solution so that you know what to expect when you use a calculator. b. Algebraically solve the equation. Write your answer in exact form. c. Use a calculator to obtain a value for x accurate to three decimal places. d. Explain why logarithms are not needed to solve the equation.